Cyclotron RF Design: 492 Sourced Rules

Size: 10-inch pole diameter ... Dee voltage: 10,000 to 14,000 volts dee-to-dee; R.F. power: 2,000 watts; R.F. frequency: 25.68 megacycles ... Magnetic field strength: 17,000 gauss

McGuire, The Iowa State University 1.5 MeV Undergraduate Cyclotron (1961) — p. 9

Editorial note, tabletop extrapolation: The closest historical analogue to a next machine's target: same pole diameter as the reference machine, and the ~3x field buys the ~10x energy (E ~ B^2*r^2 at fixed radius). The ~10x dee voltage buys turn count, phase margin and beam survival at that field - not the energy ceiling itself.

Cyclotron magnet design should always consider interaction with subsystems: RF system, vacuum pumping, ion source or injection system, extraction system or internal target, diagnostic probes.

Zaremba, Magnets for Cyclotrons (2005) — p. 3, 45

Editorial note, tabletop extrapolation: A magnet that works but leaves no port for the probe or the pump is a classic amateur trap - exactly what this five-item checklist exists to prevent; run it on every layout iteration for a next machine.

For best RF efficiency, k=0.5 BUT to decrease machine dimensions k >0.5 (more hill, thus more field) CHOICE : k=0.67 (60 deg hills)... CHOICE : nu_z = 0.2

Zaremba, Magnets for Cyclotrons (2005) — p. 32-33

Editorial note, tabletop extrapolation: If a next machine goes AVF to escape the weak-focusing energy ceiling, IBA's documented choices are a starting point, not proven tabletop values: k between 0.5 (best RF room) and 0.67 (compactness), and a modest vertical-tune target like their nu_z = 0.2 - each re-derived for the actual geometry, since a 60-degree hill only gives k = 0.67 in their sector periodicity, and sector count and valley usage carry their own trades.

The cyclotron circuit was originally tuned to a frequency of 13.56 MHz due to the requirements of the commercial RF generator in use ... a magnetic field of 0.889 Tesla is required.

Chun, The Cyclotron Magnet and RF Oscillator (2003) — p. 10-11

Editorial note, tabletop extrapolation: Directly actionable option for a next machine: targeting ~0.89 T instead of 0.59 T puts the machine on the 13.56 MHz ISM band, where used generators, amplifiers and matchboxes are plentiful. Legality rides on emissions containment rather than the band label (dg-1373's verification), and the match must still be designed for the dee's actual impedance (dg-287).

B (Tesla) 1 ... 1.6 ... f (MHz) 15.23 ... 24.36

Baumgartner & Heuer, The Cyclotron Kids 14-Inch Accelerator (2010) — p. 12

Editorial note, tabletop extrapolation: The reference machine's 0.59 T resonates at ~9.0 MHz; a next machine's field choice fixes the synchronous frequency via this 15.23 MHz/T constant (fundamental-harmonic protons). The tank tuning range then follows from the chosen inductance - the source's capacitance column is specific to theirs.

Polepieces of meehanite steel facemilled to a profile that gave appropriate field index... 1.6kVpp on Ds, 400Wpk. Base pressure 0.01mTorr

Niell, Effective Scientific Equipment Procurement Strategies: Building on a Budget (2010) — p. 11-17

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: the engineering menu at the reference machine's energy class — modest dee voltage (1-2 kVpp), 1e-5 torr, a machined pole profile, not heroic RF or UHV — is what the deck describes pursuing below ~300 keV. It documents the approach, not a completed machine: the existence-proof framing is withdrawn, and the census carries the documented Niell beam record separately.

12 inch diameter poles pieces forming a 4-inch gap to which upper and lower pole tips up to 1-inch thick can be easily attached and removed. ... all capable of producing a maximum central axial field, Bz(r=0), of 1.2 Tesla ... a single 5-inch radius DEE with a 0.9 inch vertical aperture and a matching dummy DEE. The Radio Frequency (RF) supply is tunable from 2 to 30 MHz with adjustable power up to 1.5 kW ... capable of achieving a peak DEE voltages on the order of 10 kV ... the 2-inch tall, 13-inch diameter cyclotron vacuum chamber's operating pressure of 1E-5 Torr.

Koeth, Undergraduate Education with the Rutgers 12-Inch Cyclotron (2015) — p. 2

Editorial note, tabletop extrapolation: A complete cross-check machine for a next machine's sizing; note the removable-pole-tip trick that lets one magnet host many field profiles.

For best RF efficiency, k=0.5 BUT to decrease machine dimensions k >0.5 (more hill, thus more field) CHOICE : k=0.67 (60 deg hills)

Beeckman, Cyclotron Magnets — ECPM37 lecture, Groningen (2009) — p. 69

Editorial note, tabletop extrapolation: The arithmetic to go from a required <B> to hill/valley fields and sector angle - first-order and reusable at any scale, with fringe and gradient effects refining it in the field code.

A position of suitably low field intensity, < 60 oersteds, was located by mapping the stray field about the magnet.

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 59

Editorial note, tabletop extrapolation: Map the reference machine's H-frame fringe field with a Hall probe and site the LDMOS amplifier, its magnetics and instrumentation by each component's OWN field tolerance - 60 G is the historical machine's siting outcome, not an immunity standard. Copper lining screens RF and electric fields, not the DC fringe; DC-sensitive items need distance or a high-permeability shield.

Increasing the dee voltage, however, requires increasing the required voltage breakdown gap and thus the magnet hill gap, so that some compromise must be reached.

Livingston & Howard (eds.), The Oak Ridge Relativistic Isochronous Cyclotron — ORNL-2648, OSTI 4275955 (1958) — p. 65

Editorial note, tabletop extrapolation: The coupled optimization transfers: pick a next machine's dee voltage and magnet gap together, since dee clearance ultimately costs ampere-turns and field.

The conductivity is maintained at 10 micromhos or less, with a pH of about seven. Dee system water temperature stability of 1 F or better is required for steady operation.

Ramler & Parker, The Argonne 60-Inch Cyclotron — ANL-5907 (1959) — p. 6

Editorial note, tabletop extrapolation: Two portable METHODS, not specs: monitor conductivity and pH on any hollow-conductor DI loop, and stabilize dee-water temperature if a next machine water-cools the dee (the RF tune walks with dee temperature). Set the actual limits from conductor material, voltage to ground, and measured RF drift, not from ANL's numbers.

It is necessary for the secondary coil to be cooled with oil or deionized water... because even minute thermal expansion of the copper can change the inductor's value.

Heuer & Baumgartner, Design of a 2 MeV Cyclotron (2009) — p. 23

Editorial note, tabletop extrapolation: Explains RF drift during long runs at the reference machine's power levels; cooling the tank coil stabilizes tune.

the Dee may be oscillated with voltage amplitudes of up to approximately 3000V relative to the grounded Dummy Dee. The Dee capacitance is approximately 76 pF. The secondary coil inductance of 0.87 uH or more in parallel with the Dee capacitance yields a resonance as high at 19.5 MHz, which is the maximum cyclotron frequency corresponding to 411 keV protons in the maximum magnetic field of 1.28 T. ... These inductors are 1/4 inch copper tubing, wound coaxially, with the 6 cm diameter primary coil outside the 4 cm diameter secondary coil. The inductance of the primary coil can be changed by replacing the coil with one having a different number of turns, several of which have been constructed

Yuly, The Houghton College Cyclotron: a Tool for Educating Undergraduates — Cyclotrons 2013, WE1PB01 (2013) — p. 3

Editorial note, tabletop extrapolation: Concrete worked values at the same scale, but measure your own machine's total capacitance (dee + stray + coil) and size the coil from L = 1/((2*pi*f)^2 * C_total); the swappable-primary approach lets you retune coupling without rebuilding the tank. The 411 keV is that machine's figure at its own field and extraction radius.

It is important for the coils should be in the air stream of one of the cooling fans (they will run hot if not).

Buckler, Solid-State, 2-Decade, 1.25 kW Linear Amplifier — Development Notebook (2015) — p. 28

Editorial note, tabletop extrapolation: Applies to the homemade dee-tank coil: assess its RF loss and temperature under the intended loaded-Q and coupling conditions (resonator circulating current depends on Q and coupling, not on the DC feed), and give it forced air if it runs hot.

This operated normally at 65 C but when an identical coil, which had been nickel plated, was substituted, the operating temperature rose to 350 C.

Fowler, Radio Frequency Performance of Electroplated Finishes — Proc. IREE Australia (1970) — p. 4

Editorial note, tabletop extrapolation: Reject nickel-plated hardware anywhere RF current flows in the resonator, coil, or ground-return path unless the overplate is verified thick and continuous - or validate by measuring loss and temperature.

Most commercially available copper tube contains 0.015% to 0.08% phosphorus as a de-oxidising agent, so that its conductivity may range from 60% to 90% I.A.C.S.

Fowler, Radio Frequency Performance of Electroplated Finishes — Proc. IREE Australia (1970) — p. 6

Editorial note, tabletop extrapolation: Buy the tank-coil tubing as electrolytic/electrical-grade (C10100/C11000) copper with certified conductivity, not generic plumbing tube - worth roughly 6-23% lower RF surface resistance depending on where the plumbing tube fell in its range.

typically have true Q values of up to about 800. Very few practical circuits require a Q above 900. Attempting to design a coil with a True Q much over 1,000 usually results in a coil with abnormal physical dimensions

Murphy, The Elusive Q of Single-Layer Air-Core Coils — CQ Magazine, May 1999 (1999) — p. 1

Editorial note, tabletop extrapolation: Do not budget the resonant step-up on textbook thousands: measure or model the loaded Q of the actual resonator under representative coupling (loaded Q sits well below the coil's unloaded Q), then size the amplifier for 5-13 kV dees from that measurement.

the presence of the coil's distributed capacity causes the Q observed by the Q meter to be lower than the true Q of the coil

Murphy, The Elusive Q of Single-Layer Air-Core Coils — CQ Magazine, May 1999 (1999) — p. 1

Editorial note, tabletop extrapolation: For the cited Q-meter method, treat the reading as a lower bound and keep leads and fixture capacitance minimal. A VNA measurement is a different animal: state whether loaded or unloaded Q is being extracted, calibrate and de-embed the fixture, and include the distributed capacitance in the fit - VNA errors can bias either direction.

Q increases with coil diameter (see figs. 1-4). Q increases with coil length, rapidly when the L/d ratio is small ... Q increases with frequency

Murphy, The Elusive Q of Single-Layer Air-Core Coils — CQ Magazine, May 1999 (1999) — p. 1-2

Editorial note, tabletop extrapolation: At 9 MHz a 3-4 inch diameter tank coil in the charted geometries reads Q over 1000. At fixed frequency and capacitance the dee voltage scales as sqrt(P*Q) - doubling Q at the same drive buys about 40% more voltage, not double - so treat Q gains as helpful, and verify with the loaded Q actually measured.

The conductor diameter must be within the range of 0.45 and 0.70 times the center-to-center distance between adjacent turns (not all commercial stock coils meet this condition).

Murphy, The Elusive Q of Single-Layer Air-Core Coils — CQ Magazine, May 1999 (1999) — p. 2

Editorial note, tabletop extrapolation: For a 9 MHz matching/tank inductor, space the turns so the wire fills 45-70% of the pitch - close-winding bare tubing costs Q (proximity effect is the standard explanation, beyond this source's scope) - and check any stock coil against the ratio before trusting its rated Q.

Maximum Q occurs at a coil L/d ratio of between (depending on other coil design parameters) 0.35 and 0.45, decreasing rapidly below that ratio and more slowly above

Murphy, The Elusive Q of Single-Layer Air-Core Coils — CQ Magazine, May 1999 (1999) — p. 2-3

Editorial note, tabletop extrapolation: Make the resonator coil short and fat (length a bit under half its diameter), not the long skinny solenoid that fits most easily in a corner - and not a pancake either: below the optimum Q collapses quickly.

The equations do not hold for coils with a length-to-diameter ratio of less than 0.35:1, coils with less than about 4 turns, or coils with conductor diameter-to-turn spacing ratios of less than 0.45:1 or greater than 0.70:1.

Murphy, The Elusive Q of Single-Layer Air-Core Coils — CQ Magazine, May 1999 (1999) — p. 3

Editorial note, tabletop extrapolation: A 2-3 turn link or coupling loop at 9 MHz is outside the formulas; measure it rather than calculate it.

C_top+bottom = 2C = 70.5 pF ... C_edge = 7.04 pF ... For a total C of: 77.5pF. Measurement of the capacitance with an L-C meter yields a value of 78.1pF. Nice agreement seen!

Koeth, Theoretical Calculations and Measurements of the DEE Voltage in the Rutgers 12 Inch Cyclotron (2005) — p. PDF 1 (page 1 of the September 2005 Koeth memo) as cited

Editorial note, tabletop extrapolation: Directly usable on the reference machine's 8-inch dee: sum simple parallel-plate terms for top/bottom/edge and verify with a cheap L-C meter before winding the tank coil.

the trend of DEE voltage to follow the square root law of the input RF power is accurate over all measured power ranges

Koeth, Theoretical Calculations and Measurements of the DEE Voltage in the Rutgers 12 Inch Cyclotron (2005) — p. 2-3

Editorial note, tabletop extrapolation: The sizing equation for the reference machine's LDMOS upgrade - with P as the power actually DELIVERED to the tank: at a good match forward power approximates it; otherwise net out the reflected fraction first. Doubling dee voltage costs 4x power, so 1.3 kV to 5-13 kV needs a 15-100x power increase unless L/C or Rs improves (dg-239's knobs).

as if Rs had the value of 800mOhm - sixteen times that of the expected coil Rs ... take into account the stainless steel vacuum chamber return, the stainless steel Conflat DEE stem support and RF feed throughs.

Koeth, Theoretical Calculations and Measurements of the DEE Voltage in the Rutgers 12 Inch Cyclotron (2005) — p. 2-3

Editorial note, tabletop extrapolation: When predicting a next machine's dee voltage, include every RF current path - chamber return, stem, feedthroughs, contacts - and prefer copper returns where possible; then measure the assembled tank's Q and infer Rs from it rather than assume a multiplier. [Note revised 2026-08-23: earlier note told the builder to 'expect ~1 ohm scale Rs', a number that belongs to Rutgers' geometry.]

after a power level of 200 watts, the measured voltage of the P6015 probe departed from the trend and dropped below the expected value. It is as if an additional resistance is introduced. The behavior was similar to that of a high-resistance break-down ... while the P6015 probe's value deviated from the trend, the induced voltage on the chamber's capacitively coupled pickup continued to followed the trend which was consistent with the theoretical model ... the induced voltage on the capacitive pickup facing the DEE was calibrated against forward power at lower levels. Extrapolation allowed us to measure forward power levels up to 1300 watts

Koeth, Theoretical Calculations and Measurements of the DEE Voltage in the Rutgers 12 Inch Cyclotron (2005) — p. 3-4

Editorial note, tabletop extrapolation: The measurement chain for the LDMOS upgrade, rebuilt on the reference machine's own hardware: calibrate its pickup against an independently validated dee-voltage measurement over an overlapping safe range, confirm linearity and unchanged tuning, and never transfer the 3710 ratio or the power breakpoints between machines.

the P6015 probe introduced 3.0pF of capacitance; the tank circuit was indeed reduced in frequency corresponding to 3 pF

Koeth, Theoretical Calculations and Measurements of the DEE Voltage in the Rutgers 12 Inch Cyclotron (2005) — p. 4

Editorial note, tabletop extrapolation: With the reference machine's ~78 pF-class dee, 3 pF is a ~2% frequency pull - enough to detune a high-Q tank, so calibrate with the probe on, then remove it and retune.

The connections to one of the coils are then interchanged and the equivalent inductance is measured again. The difference between the two measured inductances is then 4M.

Koeth, Theoretical Calculations and Measurements of the DEE Voltage in the Rutgers 12 Inch Cyclotron (2005) — p. 5-6

Editorial note, tabletop extrapolation: A bench L-C meter trick for characterizing the coupling loop: measure series-aiding and series-opposing, difference is 4M. The M a matched loop NEEDS follows from M = sqrt(R_tank*Z_source)/omega with the tank's measured series resistance and the source impedance at the operating frequency - compute it for the actual tank rather than expecting a stock tens-of-nH answer.

is exactly 1/2 of Qo when the primary is critically coupled corresponding to the value giving maximum response ... a simple reflected RF power meter will suffice to show a perfect match - indicating critical coupling.

Koeth, Theoretical Calculations and Measurements of the DEE Voltage in the Rutgers 12 Inch Cyclotron (2005) — p. 6-7

Editorial note, tabletop extrapolation: The builder can tune their coupling loop with just an SWR bridge: adjust loop position/taps until reflected power nulls, and check Qloaded = Q0/2 with a NanoVNA S21 sweep.

From Fig.12 we determine Qmeasured at a distance of 11mm to be 460. This implies a Qo of 920.

Koeth, Theoretical Calculations and Measurements of the DEE Voltage in the Rutgers 12 Inch Cyclotron (2005) — p. 6-8

Editorial note, tabletop extrapolation: A benchmark to scale, not a floor: for the reference machine's ~9 MHz tank, skin-effect scaling of the same coil suggests Q0 ~ sqrt(9/15)*920 ~ 700-class; a measured Q0 far below the scaled expectation is the excess-loss flag (bad joints, steel in the return path) worth hunting.

Empirically it was found for a given forward power into each of the (50+j0) Ohm points, the peak capacitor voltage was always the same.

Koeth, Theoretical Calculations and Measurements of the DEE Voltage in the Rutgers 12 Inch Cyclotron (2005) — p. 7

Editorial note, tabletop extrapolation: Good news for coupler design: don't agonize over loop position vs tap point - but on a new tank, after nulling reflected power, verify dee voltage and coupler temperature once per geometry before treating settings as equivalent; a nominal match can hide coupler or cable loss.

minimizing Rs, or increasing L2 while simultaneously decreasing C2 (to maintain the resonant frequency) are the only parameters that can be adjusted to increase the DEE voltage for a given amount of RF power.

Koeth, Theoretical Calculations and Measurements of the DEE Voltage in the Rutgers 12 Inch Cyclotron (2005) — p. 8

Editorial note, tabletop extrapolation: For a next machine, shrinking dee-to-liner capacitance (larger dee-to-lid spacing) and a bigger low-loss coil raise dee voltage before amplifier watts do - bought, not free: more L usually brings more conductor and more Rs, and dee-to-lid spacing spends the magnet-gap budget (dg-163). Optimize the L/C-versus-Rs package together, then buy watts.

inductance of 1.1uHy, capacitance of 78.1pF, and the estimated AC resistance of 50mOhm ... Preliminary tests with the new generator show that the cyclotron chamber is capable of withstanding 2000 watts of input power. The tank, tank housing, cyclotron chamber and DEE stem become very warm. It is not necessary to operate at 2000 watts, as shown above 1000 watts produces a peak-to-peak DEE voltage of approximately 15kV.

Koeth, Theoretical Calculations and Measurements of the DEE Voltage in the Rutgers 12 Inch Cyclotron (2005) — p. 2, 8

Editorial note, tabletop extrapolation: Scales the reference machine's plan only under ideal sqrt-power scaling at unchanged loaded shunt impedance: 500 W -> ~10.6 kVp-p, comfortably in the 5-13 kV target - but measure the actual dee voltage with a calibrated pickup; thermal management of stem and coil becomes the real issue.

the original purpose of the shield was to prevent RF from coupling to the pickup ... We agreed a large series inductance (an RF Choke) should mitigate this concern.

Koeth, Rutgers 12 Inch Cyclotron Ion Source Studies: Part I (2006) — p. 1

Editorial note, tabletop extrapolation: For nA-level collection near a ~9 MHz dee, treat the choke as one element of a verified filter: choose it from measured impedance and self-resonant-frequency data at the RF frequency, keep whatever shielding the noise floor turns out to demand, and validate by running RF with no beam - displacement currents into an unshielded tip can dwarf the beam signal.

an input RF power level of 50 watts is too low, and 500 watts should be sufficient. The first ions are expected to clear the chimney at approximately 200 watts.

Koeth, Rutgers 12 Inch Cyclotron Ion Source Studies: Part I (2006) — p. 5

Editorial note, tabletop extrapolation: A geometry trap for a next machine: any chimney or source structure must be smaller than the first half-turn diameter set by the dee voltage, or beam dies before the first gap crossing.

Protons: f (megacycles) = 1.52B (kilogauss) ... The actual technique used to control resonance in a cyclotron is to vary the magnetic field, with the applied frequency held constant.

Livingston & Blewett, Particle Accelerators (1962) — p. 156

Editorial note, tabletop extrapolation: The reference machine's 0.59 T (5.9 kG) gives 8.97 MHz, confirming their ~9 MHz choice; for a next machine pick B first, then f = 1.52*B.

there will be a somewhat lower potential at the ends of the D faces nearest the lines ... measured in some cyclotrons to be as great as 5 per cent ... a displacement of the ion source of over 2 in. has been necessary.

Livingston & Blewett, Particle Accelerators (1962) — p. 164

Editorial note, tabletop extrapolation: Make the source mount adjustable in both directions and tune position for beam, not for geometric center. Size the travel from RF-field and orbit modelling for the actual dee geometry - the large machines needed over 2 inches; what a tabletop machine needs is its own calculation, and generous commissioning range is cheap.

Cited in: Beam Dynamics: An Interactive Laboratory

the practical maximum migration in phase will be from zero to -pi/2 and back to zero, a total phase migration of pi radians or one half-cycle.

Livingston & Blewett, Particle Accelerators (1962) — p. 166-171

Editorial note, tabletop extrapolation: With a 3-4% field droop and 160 turns-scale acceleration, the reference machine's dee voltage sets how much phase slip they can afford: higher V = fewer turns = more field-shape tolerance.

Increasing the D voltage requires fewer turns for acceleration to maximum energy and will compensate for a larger phase shift. However, D voltage is usually limited by ... power and spark breakdown.

Livingston & Blewett, Particle Accelerators (1962) — p. 172

Editorial note, tabletop extrapolation: At ~1.3 kV and ~150 keV the reference machine's ions make ~60 turns; doubling dee voltage halves turns and dramatically relaxes both field-uniformity and vacuum (scattering) requirements.

The gap between chamber lids was chosen to be 5 in., leaving 1 1/4-in. clearance between D's and lids ... resulting in a D-voltage limit of about 70 kv due to breakdown. ... The limit can be raised by designing for greater clearance between D's and chamber lids and by providing round, smooth contours and clean, polished surfaces.

Livingston & Blewett, Particle Accelerators (1962) — p. 175, 189

Editorial note, tabletop extrapolation: At 1.3 kV the reference machine has large margin against this failure mode. For a next machine at several kV, treat MIT's ~56 kV/in at breakdown as one calibration point, not an allowable: analyze peak surface fields, round and polish, assemble clean, and expect to condition (see dg-253) - no universal safe kV/in exists for vacuum gaps.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

these tubes spaced as closely as 2 to 3 in. to prevent local heating and warping of the D's under power. Approximately 10 kw of heat is dissipated in each D and D line during operation.

Livingston & Blewett, Particle Accelerators (1962) — p. PDF p.175 (printed p.159)

Editorial note, tabletop extrapolation: At tens of RF watts the builder likely needs no water, but check rather than assume: what matters is local RF current density and the thermal path, not total power. Dee thermal drift detunes the resonator - keep dee structures stiff and thermally anchored, and watch tuning drift as power rises.

At MIT, with an internal D aperture of 1.6 in. the optimum length of ionization column was 5/8 in. For 4-in.-wide D's in the Carnegie Institution 60-in. machine it was 1 3/8-in.

Livingston & Blewett, Particle Accelerators (1962) — p. 178

Editorial note, tabletop extrapolation: Hood or collimate the reference machine's source with the exposed column ADJUSTABLE, starting near a third of the aperture height, and optimize against extracted beam and dee voltage together - the historical ratios locate the starting point; the machine's own optimum may sit elsewhere.

The resonant circuit is electrically equivalent to a pair of quarter-wave coaxial transmission lines with the D's supported on the ends of the inner conductors. ... two power tubes in push-pull and two coupling loops is the more common arrangement.

Livingston & Blewett, Particle Accelerators (1962) — p. PDF pp.185-187 (printed pp.169-171)

Editorial note, tabletop extrapolation: If a next machine goes two-dee push-pull, watch for the push-push mode (no dee-to-dee voltage, oscillator happily locked); a single-dee-plus-dummy design sidesteps that mode entirely - one reason small machines favor it.

This loading of the D circuit by discharge currents holds the D potentials down to a few hundred volts ... Unless the loading is removed, the chamber will continue to operate in the low-voltage, blue-glow discharge condition indefinitely.

Livingston & Blewett, Particle Accelerators (1962) — p. 188

Editorial note, tabletop extrapolation: The reference machine's dee operates in the range where these discharge phenomena live: the ~100 V-class multipactor band is crossed at every start, and blue-glow gas discharge appears when pressure and surfaces allow. Surface conditioning, low pressure, and drive that can snap up fast are the standard escapes - and whether a given stall is multipactor or gas discharge is diagnosed, not assumed (dg-1273).

Cited in: The Vacuum Budget of a Cyclotron

A technique frequently used to adjust or trim the relative resonant frequencies of the two D-line circuits is to use one or more trimmer capacitors which can be adjusted by remote control under full power operation. Such a variable capacitance can be provided by a movable plate on the side wall of the chamber facing one edge of the D. It must have excellent electrical contact to the walls for the radiofrequency currents and a range of motion sufficient to tune over about 1 per cent in frequency. The availability of such a tuning device makes it possible to adjust relative D voltage as desired for optimum operation.

Livingston & Blewett, Particle Accelerators (1962) — p. 188

Editorial note, tabletop extrapolation: A bellows-actuated plate near the dee gives the builder live resonance trim without opening the chamber - invaluable when thermal drift walks the dee frequency.

It is common experience, however, that no amount of smoothing or polishing will eliminate the necessity of some high-voltage conditioning under vacuum. Clean laboratory techniques in preparing a chamber for reassembly after opening are essential; dust should be controlled and all grease removed (even fingerprints), and under no circumstances should steel wool or coarse abrasives be used in cleaning. The oscillator circuit must be capable of driving the cyclotron through these varied conditions of sparking and discharge, without the necessity of tuning or of manual resetting of overload relays.

Livingston & Blewett, Particle Accelerators (1962) — p. 189

Editorial note, tabletop extrapolation: After every chamber opening, ramp dee voltage gradually with vacuum and arc-rate monitoring until sparking subsides before expecting stable beam; how long that takes is the machine's answer, not a fixed budget.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

The most significant advantage of this circuit is its simplicity and compactness along with the freedom from delicate tuning requirements or precise construction.

Livingston & Blewett, Particle Accelerators (1962) — p. 190-193

Editorial note, tabletop extrapolation: The same logic favors a drive that follows the dee on the reference machine: self-excited, or a PLL tracking the resonator - similar in spirit though not identical in dynamics, since a PLL adds its own loop behavior. Either way, mechanical drift retunes the drive instead of killing the beam.

about 50 per cent thicker than the depth of the groove to allow for compression ... 1/4-in. gaskets have proved adequate for even the largest seals ... Conductivity for rf currents through such a seal can be assured by half-covering the gasket with a thin copper-foil strip. ... Most natural or artificial rubbers have unacceptable vapor pressures and also deteriorate when used with lubricating greases. Neoprene is free of these faults and is widely used in cyclotrons.

Livingston & Blewett, Particle Accelerators (1962) — p. 199-201

Editorial note, tabletop extrapolation: The copper-foil RF bridge over elastomer joints prevents mysterious Q loss and local heating and transfers directly. For the gasket itself, a modern machine should size grooves from the O-ring manufacturer's vacuum-service squeeze and gland-fill tables - the historical 1.5x ratio is the era's flat-gasket practice, not an O-ring spec.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

apply a radio frequency oscillating voltage to the electrode that is slightly less than the cyclotron frequency given at the center of the field, but greater than [that] near the edges.

King, A Preliminary Design for a Small Permanent Magnet Cyclotron — Houghton College thesis (2002) — p. 20

Editorial note, tabletop extrapolation: A concrete tuning rule for the builder: do not tune RF to the central field alone - place it inside the quoted window and find the best point empirically by beam current; the phase-history reasoning is the theory behind the knob, not a substitute for turning it.

It would only take a few cycles, on the order of 12, for most cyclotrons to have reached this velocity.

King, A Preliminary Design for a Small Permanent Magnet Cyclotron — Houghton College thesis (2002) — p. 20

Editorial note, tabletop extrapolation: Explains failed runs where beam dies at small radius, and quantifies how little phase budget a mistuned machine has - for the actual machine, integrate the slip turn by turn from the measured B(r) and dee voltage rather than using 12 turns as a threshold.

it has one dee-shaped copper electrode, and the grounded vacuum chamber functions as the other electrode

Dewan, Design and Construction of a Cyclotron Capable of Accelerating Protons to 2 MeV — MIT thesis (2007) — p. 13

Editorial note, tabletop extrapolation: The reference machine already does this, and it stays attractive for a next machine - one HV feedthrough fewer, the chamber as return electrode - unless push-pull two-dee RF is wanted for higher energy gain per turn. A common choice among documented small machines, not a rule.

The dees, made of thin sheet copper, arc 22.5 cm in diameter, 2.4 cm high, and they are separated by a gap of 1.5 cm.

McGuire, The Iowa State University 1.5 MeV Undergraduate Cyclotron (1961) — p. 7

Editorial note, tabletop extrapolation: A documented dee geometry near the reference machine's scale - note it exceeds an 8-inch pole, so it fits 10-inch-class machines as-is: scale the proportions, not the dimensions. Dee cooling need tracks the dissipated RF power and construction, not a fixed kilowatt line: compute it from the RF budget (dg-313) and watch dee temperature during commissioning.

This value is about 10% for 120 uamp of deflected deuterons, increasing to 15% for a 200 uamp beam. About 30% of the internal beam at the exit radius is extracted.

Ramler & Parker, The Argonne 60-Inch Cyclotron — ANL-5907 (1959) — p. 19

Editorial note, tabletop extrapolation: Sets expectations if a next machine attempts a deflector: capturing a third of the circulating beam was a mature machine's result, so plan around numbers of that order - and account for where the rest goes (septum heating, sputtering, and at higher energies activation), rather than booking the loss as free.

The voltage breakdown limit determines the necessary gap width. The empirically determined limit (valid for clean, flat surfaces) is d[mm] >= 1.41 x 10^-2 * phi[kV]^(3/2).

Wolf (ed.), Handbook of Ion Sources (1995) — p. 379

Editorial note, tabletop extrapolation: Direct rule for source-to-puller spacing - clean DC gaps are the law's home turf: a few-kV gap needs sub-mm minimum, with real margin because sputtered metal films spoil the 'clean surface' assumption fast. For dee-to-ground RF clearances use it only as a lower-bound sanity check: edges, insulators, RF conditioning and enhancement move the practical limit (dg-353, dg-662).

Dielectric strength / Thickness: 240 kV/mm at 0.025 mm; 70 kV/mm at 5 mm.

Wolf (ed.), Handbook of Ion Sources (1995) — p. 523

Editorial note, tabletop extrapolation: When insulating the reference machine's extraction or dee leads, design from certified data for the actual material, thickness, frequency and environment - a bulk breakdown number is a test-condition figure, not a working rating. Grade the field at edges, design creepage and surface flashover paths separately, and qualify the finished assembly under vacuum with a conservative withstand test.

Compared to T or Pi networks, the L network uses only one combination of inductance and capacitance. This simplifies the microcontroller tuning algorithm. The disadvantage is that one L network cannot match all possible load impedances. Figure 3 shows two L network types with complimentary matching ranges on the Smith Chart. The IMS uses an RF switch to select one of the two L networks, allowing a wider matching range.

Blodgett, 3.5 to 30 MHz Automatic Antenna Impedance Matching System (2012) — p. 11

Editorial note, tabletop extrapolation: If the builder automates their dee match at 9 MHz, a stepper-driven L-network is the simplest topology for the search algorithm; verify the two configurations' combined range covers the tank's actual impedance excursions (a Smith-chart sweep or simulation) before committing.

The coupling factor is high, ~1000 or 30 dB, to minimize main line power loss ... enables 200 W power measurements using the AD8307 logarithmic detector IC

Blodgett, 3.5 to 30 MHz Automatic Antenna Impedance Matching System (2012) — p. 18

Editorial note, tabletop extrapolation: For the reference machine's 100-500 W upgrade: a homebrew 30 dB coupler plus AD8307 board works with a calibrated pad (10 dB or more) between them; include coupler tolerance and mismatch peaks in the level budget, and calibrate the chain end to end.

Ferrite toroids wound with AWG 26 wire and surrounding two 2 inch sections of RG-8 50 Ohm coaxial cable form the coupling transformers.

Blodgett, 3.5 to 30 MHz Automatic Antenna Impedance Matching System (2012) — p. 18-19

Editorial note, tabletop extrapolation: A cheap coupler build bracketing the reference machine's 9 MHz band - built from the source's full schematic, not the one-line summary: the shield treatment and grounding are what make the directivity, so replicate them exactly, then bench-test directivity, insertion loss and core heating at 9 MHz through the intended power and mismatch range before trusting it.

the SWR measured using this directional coupler is 1.08 and 1.03 for 28 dB and 35 dB of directivity, respectively

Blodgett, 3.5 to 30 MHz Automatic Antenna Impedance Matching System (2012) — p. 19-20

Editorial note, tabletop extrapolation: Do not chase - or trust - SWR readings within the bridge's directivity band: near-1.0 does not prove a good match any more than 1.08 proves a bad one. Characterize the actual homebrew bridge's directivity first; then readings inside its band are 'unresolved', not data.

Figure 42 - 30 W to 100 W Power Calibration Setup using Bird 43 Wattmeter

Blodgett, 3.5 to 30 MHz Automatic Antenna Impedance Matching System (2012) — p. 57-58

Editorial note, tabletop extrapolation: A Bird 43 (owned or borrowed) transfers power calibration to permanently installed cheap sensors - within the installed element's frequency range, power range and its own accuracy spec, so record which element was used. Take the AD8307's slope and intercept from its datasheet and the actual unit's measured response, not nominal folklore.

actuates stepper motors to alternately adjust a variable capacitor and a variable inductor to reduce VSWR to less than 1.5:1 ... The antenna tuner system can match loads of up to 26:1 initial VSWR within a frequency range of 3.5 MHz to 30 MHz.

Blodgett, 3.5 to 30 MHz Automatic Antenna Impedance Matching System (2012) — p. 6-8, 40

Editorial note, tabletop extrapolation: Coordinate-descent on C then L is not guaranteed to converge on an interacting high-Q load - test it against the dee resonator before trusting it - and set the LDMOS amplifier's reflected-power shutdown from that device's own specification, not from the 1.5:1 convention.

fo = qBo/2pi mi = (1.52x10^7) Bo(tesla)/A

Humphries, Principles of Charged Particle Acceleration (1986) — p. 524

Editorial note, tabletop extrapolation: One-line check of the reference machine's operating point: 0.59 T -> ~9.0 MHz for protons; sets the next machine's RF band for any target field.

the final kinetic energy is maximized by taking Vo large... a high gap voltage accelerates particles in fewer revolutions so that there is less opportunity... to get out of synchronization.

Humphries, Principles of Charged Particle Acceleration (1986) — p. 530-531

Editorial note, tabletop extrapolation: At sub-MeV this limit is distant - by this formula a 10 kV dee puts the proton ceiling near 7 MeV - but the same physics governs field-flatness tolerance: fewer turns forgives more field error.

Low energy proton in 1 T field: 15.23 MHz

Antaya, Cyclotron Basics — MIT 8.277, Unit 10, Lecture 14 (2010) — p. 29

Editorial note, tabletop extrapolation: The single most-used number in the reference machine's notebook: 0.59 T -> 9.0 MHz; a 1.2 T higher-field successor -> 18.3 MHz, still comfortable amateur-radio-technique territory.

250 MeV protons; 17 KeV/turn: N~15,000... 250 MeV protons r=0.3m: dr/dN ~ 20 microns!

Antaya, Cyclotron Basics — MIT 8.277, Unit 10, Lecture 14 (2010) — p. 43

Editorial note, tabletop extrapolation: For the builder: 1 MeV at 2 kV per gap (2 gaps) is ~250 turns with final-orbit spacing ~0.25 mm at r = 12 cm - which is why higher dee voltage directly eases both extraction and vacuum requirements.

dphi/dn=360 [gamma-1] -> 8 deg. An ion on peak phase is lost in 11 revolutions. Only solution- very high energy gain per turn - 360kV

Antaya, Cyclotron Basics — MIT 8.277, Unit 10, Lecture 14 (2010) — p. 51

Editorial note, tabletop extrapolation: At 1 MeV the instantaneous slip is only ~0.4 deg/turn, but slip accumulates over every turn, so what that buys depends on volts per turn: a machine gaining a few kV per turn spends thousands of turns getting to 1 MeV and can run out of phase well below the textbook ceiling. The design check is the summed slip across all turns against the +/-90 deg window, not the per-turn number.

The second DEE has been faked using the image of the real DEE on a grounded conductor ... By twisting the inductor, we can change the inductance to match our inductance requirements.

Chun, The Cyclotron Magnet and RF Oscillator (2003) — p. 11

Editorial note, tabletop extrapolation: This is the reference machine's exact topology, in use on a comparable documented machine; the deformable-inductor trim is a simple tuning mechanism worth copying on a next machine.

high precision is necessary for a coil or circuit with a high Q value ... The Q of this cyclotron was measured at 1600, under no loading.

Chun, The Cyclotron Magnet and RF Oscillator (2003) — p. 11-12

Editorial note, tabletop extrapolation: A benchmark, not an expectation: measure the reference machine's own unloaded AND loaded Q, compare against a loss model to decide whether joints are costing Q, and judge retuning needs from measured thermal drift against the loaded bandwidth - Q alone predicts neither the drift rate nor the need for active tuning.

For typical cases of interest, 'vacuum' pressure is lower than 10-5 torr, and 'gas' pressure higher than 10-4 torr.

Werner, Probing and Modeling Voltage Breakdown in Vacuum — Cornell dissertation (2004) — p. 23

Editorial note, tabletop extrapolation: A gas-fed cyclotron chamber often sits in exactly this transition decade, so the spark limit can move with operating pressure: measure holdoff with the actual gas flowing at operating pressure as well as at base vacuum, and interlock conservatively - which direction the limit moves depends on where the geometry sits relative to the Paschen minimum.

Cited in: The Vacuum Budget of a Cyclotron

The power and length of application should be gradually increased until the vacuum remains less than 10^-4 mm with r.f. on steadily at, perhaps 2 kv. ... it may mean the presence of organic matter in the tank

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. PDF p.10 (printed -11-)

Editorial note, tabletop extrapolation: Directly applicable startup ritual at the reference machine's 1.3 kV dee level - ramp in short bursts with current-limited RF, arc detection and pressure monitoring. The report reads failure to reach its endpoint as organic contamination (grease, oil, rubber) in the tank; leaks and ordinary outgassing can mimic it, so inspect or run an RGA before blaming contamination.

Cited in: The Vacuum Budget of a Cyclotron

the 'single-dee' construction; this has many advantages ... Better ion focussing can be obtained by installing a 'dummy' grounded dee edge symmetric to the insulated dee, but this is a refinement

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 8

Editorial note, tabletop extrapolation: Exactly the reference machine's architecture. The dummy-dee edge is the source's named refinement for better ion focusing - a natural next-machine upgrade once the basic machine works, which is the sequencing the source itself implies ('but this is a refinement').

The dee-to-ground capacity appears as the major portion of the capacitance in the tank circuit, which must be calculated taking this into account

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 8

Editorial note, tabletop extrapolation: Even with a modern solid-state chain, the builder must treat dee capacitance as the resonator's dominant C when designing the matching network; the confine-the-RF-current lesson is timeless.

it is important to provide short, broad paths for current flow, especially in the ground circuits ... While the tube should be placed as close to the tank as possible, it must yet be kept away from the magnetic field

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 8-9

Editorial note, tabletop extrapolation: Directly applicable to the reference machine's amplifier: wide copper sheet or strap grounds and a short feed run, with magnetically SENSITIVE parts kept out of the fringe field - the tube in the quote; in modern gear whatever actually cares (fans, ferrites, meters - dg-670's shield-or-relocate).

All circuits connected to tank elements should have adequate choking and bypassing to prevent r.f. from reaching the meters and supply lines.

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 9

Editorial note, tabletop extrapolation: Directly applicable: the reference machine's beam-current, bias and gauge lines all deserve feedthrough RC/choke filtering at 9 MHz - with 'adequate' proven by measurement: an RF sniff at the meter terminals with the transmitter running.

The voltages employed on the various cyclotron components are deadly; proper precautions must be taken, even during preliminary testing ... Interlock switches on the power supply covers and grounding hooks

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 9

Editorial note, tabletop extrapolation: Directly applicable home-lab safety baseline for the HV systems of a next machine - covers interlocked, hooks in reach, and the full discharge discipline around them (dg-522).

the top and bottom of the chamber to bow in, which affected the capacitance of the dee and reduced the maximum voltage that the dee could withstand before flashing over.

Baumgartner, The Cyclotron Kids' 2 MeV Proton Cyclotron — Cyclotrons 2013, WE1PB05 (2013) — p. 2

Editorial note, tabletop extrapolation: Directly relevant to any thin-lid chamber on a next machine squeezed into a small magnet gap: design the lids to a calculated stiffness (the lid-deflection calculator) from the start. Internal posts clear of the beam spiral and the RF high-field region are one remedy; thicker or dished lids and external ribs are others, and each needs its own deflection, buckling, venting and weld checks. [Note revised 2026-08-23: earlier note planned posts as the remedy.]

Cited in: Cyclotron Vacuum Chamber Design and Sealing

Having only one dee rather than two doubles the voltage requirement, but reduces the cost and complexity of having two RF feedthroughs in the vacuum chamber.

Baumgartner, The Cyclotron Kids' 2 MeV Proton Cyclotron — Cyclotrons 2013, WE1PB05 (2013) — p. 2

Editorial note, tabletop extrapolation: Supports the single-dee choice for a next machine unless attainable dee voltage, insulation or the coupling scheme becomes the binding constraint.

Mammoflex M-1 HV cable has C of 56 pF per foot ... ~20 feet total ~0.4 Joules at 30 kV ... Removed excess cable. Run is now ~ 5 feet total

Ponter, Beam Energy Measurements with a New HV Deflection System and Ion Source Upgrades on the Rutgers 12-Inch Cyclotron (2010) — p. 43-49

Editorial note, tabletop extrapolation: For any HV feed on a next machine (deflector, source bias): keep cable runs short. Stored cable energy is delivered into an arc in the first instant, faster than any supply limiter acts - it adds to what the supply and other capacitances feed the fault, it does not replace them. Series resistance at the load (dg-286) limits the follow-on current.

We've encased the resistor in a grounded shield, and the coax shields go through 68 Ohm, 2 watt resistors ... 150 Meg HV resistor ... 5 Meg HV resistor ... inside an acrylic tube covered with copper mesh.

Ponter, Beam Energy Measurements with a New HV Deflection System and Ion Source Upgrades on the Rutgers 12-Inch Cyclotron (2010) — p. 49 (also 43, 45, 47, 48)

Editorial note, tabletop extrapolation: A staged-resistance pattern for electrostatic HV feeds (deflector, PIG source bias) whose load draws no standing current: series megohms limit arc current at the price of regulation under load, so it does not transfer to circuits that must deliver current. Even with this shielding the arcs stopped only after the cable-energy fix (dg-285) - resistors limit damage, they don't prevent flashover.

HP 33120A Function Generator - ENI 155LCRH Power Amp - LDG AT-200PC Tuner - Bird 43A RF Power Meter - Dee

Yuly et al., Modifications on the Houghton College Cyclotron (2010) — p. 12-14

Editorial note, tabletop extrapolation: Essentially the reference machine's current architecture. A ham antenna tuner can match a dee-shaped load in this frequency range - but its voltage ceiling is construction- and tuning-dependent: expect the ~kV class rather than the 5-13 kV a dedicated resonator supports (the LDMOS upgrade path), and MEASURE the dee voltage (dg-quoted methods in the dee-coupling deep dive) instead of inferring it from the tuner's rating.

3.55 MHz 1700 Vpp (26 W) ... 3.48 MHz 800 V (10 W)

Yuly et al., Modifications on the Houghton College Cyclotron (2010) — p. 17-19

Editorial note, tabletop extrapolation: A benchmark for the order of magnitude the reference machine's autotuner path reaches (its ~1.3 kV from a 5 W amplifier is in the same band), not a curve to read values off: state the voltage convention, tuning and loading before comparing, and do not infer a plateau from two points.

No peaks for magnetic fields larger than H2+ at 0.5 T -> 35 keV; 44 orbits at 800 Vpp

Yuly et al., Modifications on the Houghton College Cyclotron (2010) — p. 21

Editorial note, tabletop extrapolation: Quantifies why the reference machine's dee-voltage upgrade matters: at 1.3 kV their protons need ~hundreds of turns to reach interesting energies, and ~44 turns was already the survival ceiling at Houghton's pressures.

To develop high voltages with modest RF power. The highest voltage for given power occurs when: Qloaded = 1/2 Qo

Koeth et al., The Rutgers 12-Inch Cyclotron for Students (2010) — p. 18

Editorial note, tabletop extrapolation: The one-slide justification for the builder to move from an antenna-tuner match to a true high-Q tank circuit in a next machine.

Record Input Power 2kW: 8.4 kVpeak

Koeth et al., The Rutgers 12-Inch Cyclotron for Students (2010) — p. 19

Editorial note, tabletop extrapolation: Anchors the power budget with one measured point: 2 kW bought 8.4 kV peak on that 12-inch tank. Scaling to the reference machine's planned LDMOS runs through ITS shunt impedance (dg-313's formula with measured Q and C): at comparable impedance, 500 W supports roughly 1/2 the voltage (P ~ V^2), a ~4 kV class - measure, then budget.

Calculation showing first ions squeak by at 165 Watts ... Beam current abruptly dropped to zero at 170 watts !

Koeth et al., The Rutgers 12-Inch Cyclotron for Students (2010) — p. 20

Editorial note, tabletop extrapolation: A free end-to-end CONSISTENCY check for the builder: the power at which beam vanishes ties the trajectory model, the dee-voltage estimate and the RF chain together at one point. It is a cross-check, not a probe-independent voltage measurement - source emission, phase, pressure and detector sensitivity all sit inside the observed threshold - so use it alongside a calibrated pickup, not instead of one.

the DEE, chamber, tank coil, etc. heat up and slightly change the resonant frequency ... A DC 'error signal' is derived from comparing the phase of the driving RF to the Phase of the DEE pickup.

Koeth et al., The Rutgers 12-Inch Cyclotron for Students (2010) — p. 21

Editorial note, tabletop extrapolation: At 100-500 W expect real warm-up drift and MEASURE it: the measured drift against the loaded bandwidth decides whether hand-touchup, a slow motor loop, or nothing is needed. The cyclotron constraint is the point - the RF must stay synchronous with qB/(2 pi m), so the resonator follows the beam frequency, not the other way round.

Beam Inferred DEE Voltage ... In the 1st half revolution E(r) = (qB^2/2m) r^2 = 1/2 Vp-p

Koeth et al., The Rutgers 12-Inch Cyclotron for Students (2010) — p. 33

Editorial note, tabletop extrapolation: The builder can cross-check a dee-voltage estimate by measuring where the first half-turn lands - the beam is the most honest voltmeter - provided the landing radius is converted to orbit radius using the actual source-to-probe geometry, and the ion is assumed to cross near peak phase (real phases read low).

A large increase in current occurs only as the local field approaches 10^10 V per meter... After several minutes of current flow at the constant voltage, a remeasurement of the threshold voltage shows that it has increased. This phenomenon is called conditioning.

Miley & Murali, Inertial Electrostatic Confinement (IEC) Fusion: Fundamentals and Applications (2014) — p. 111-113

Editorial note, tabletop extrapolation: Bring the reference machine's dee and extraction voltages up gradually on first pump-down, watching for micro-discharge pulses. Conditioning raised the measured threshold in the source's account; the gain is not permanent capital - re-condition after venting rather than assuming the old ceiling still holds.

They found that at a critical angle of 31.5 deg, the surface charge was zero; this angle was independent of the applied voltage. The surface charges were positive at smaller angles, but negative at larger ones. ... Fryszman and colleagues found that by screening the section of the insulation surface near the cathode or covering this section with a semiconducting layer, the breakdown voltage was raised by a factor of approximately 2.5. ... Roughening the surface of the insulator in a region adjacent to the cathode increased the breakdown voltage by about 40 %. Roughening the surface adjacent to the anode had little effect.

Miley & Murali, Inertial Electrostatic Confinement (IEC) Fusion: Fundamentals and Applications (2014) — p. 113-114

Editorial note, tabletop extrapolation: For the next machine's source stalk - a DC cathode-junction context like the studies' - cone the insulator toward the negative electrode and consider recessing the triple junction behind a screen. The factors come from separate experiments and are not multiplicative, and a dee-stem RF feedthrough alternates polarity every half cycle: there, treat all of this as qualitative guidance to be tested, not booked margin.

Gleichauf also found that the breakdown voltage was strongly dependent on the material of the insulator but independent of the material of the electrodes.

Miley & Murali, Inertial Electrostatic Confinement (IEC) Fusion: Fundamentals and Applications (2014) — p. 113-114

Editorial note, tabletop extrapolation: The source's fixture works out to 2-4.5 kV/mm of creepage - a first sanity check for an extraction stalk, not a design allowable: flashover depends on triple-junction geometry, finish, contamination and conditioning, and does not scale linearly with length (the source's own longer insulators held less per mm). Size real hardware by test, with margin.

Air spaces exist in solid and liquid dielectrics... the air will have the higher stress, possibly causing sparkover through the air space... The stress in the air gap can thus be k times that in the solid.

Miley & Murali, Inertial Electrostatic Confinement (IEC) Fusion: Fundamentals and Applications (2014) — p. 116, 119

Editorial note, tabletop extrapolation: The classic failure of home-built HV feedthroughs: a loose PTFE sleeve over a rod arcs in the annular air film. Fill the gap - potting or liquid dielectric - so no gas layer sits in series with the solid. Evacuating the annulus removes the Paschen path but leaves field-emission breakdown and surface flashover, so vacuum is not a substitute for filling.

The optimum ratio as r_i/r_o = 1/e. This optimum ratio minimizes the stresses within the coaxial electrode arrangement, independent of the material of the dielectric used. ... In order to keep stress at Z below that at X in Fig. 4.15, the radius of curvature at Z should not be less than the radius of the inner cylinder.

Miley & Murali, Inertial Electrostatic Confinement (IEC) Fusion: Fundamentals and Applications (2014) — p. 117, 122-124

Editorial note, tabletop extrapolation: Preliminary ideal-coax sizing for the reference machine's HV stalk: a grounded 25-mm-bore port gives a ~9.2-mm center conductor at the 1/e optimum - then check the complete feedthrough (ends, dielectric interfaces, triple junctions) electrostatically, and never leave a sharp-edged washer or nut on the HV end.

This phenomenon causes the cathode grid material from the IEC device to be deposited on the high-voltage (HV) stalk. That can in time cause premature breakdown at the stalk. ... The electrode is surrounded by a coaxial aluminum tube, which in turn is shadowed by a coaxial large diameter, aluminum tube. ... The stalk is a conical-shaped insulator facing toward the cathode grid that is expected to block the ions passing through the cathode grid. ... The corrugated surface is intended to lengthen surface current path lengths, preventing premature surface breakdown.

Miley & Murali, Inertial Electrostatic Confinement (IEC) Fusion: Fundamentals and Applications (2014) — p. 87, 105, 109

Editorial note, tabletop extrapolation: In the reference machine's small chamber everything sees the source; a washer-stack or skirt shielding the feedthrough ceramic from the chimney slit is the same shadow-shield idea and should lengthen time between cleanings - validate on the actual geometry, since much of the sputtered flux travels as neutral atoms and simple line-of-sight shielding is the right first-order defense.

The axial component of the magnetic field can be decreased at larger radii in order to increase the radial (focusing) component, provided the ions only have a few revolutions left once they reach this portion of the field.

Morrow, Focusing in the Houghton College Cyclotron — Houghton College thesis (2015) — p. 27-28

Editorial note, tabletop extrapolation: One candidate for the reference machine's next big win: at ~150 keV on a low Dee voltage the turn count is large, and cutting it relaxes both the phase budget and gas-scattering exposure. Whether Dee voltage or field shaping pays more on a given machine is a diagnosis - measure what actually limits the beam first; the quote's own condition is narrower: late-radius focusing tricks need few turns remaining.

the location of current spikes at a given field strength always occur at or very near the theoretical resonances... at B/3, B/5, and so on.

Fuller, Exploring the Capabilities of the Houghton College Cyclotron — Houghton College thesis (2013) — p. 46-47

Editorial note, tabletop extrapolation: Essential for interpreting the reference machine's magnet scans: a peak at one-third field is likely a subharmonic, not a mystery species. H2+ vs H+ assignments need more than one matching peak - or an independent species diagnostic - since different q/m patterns can overlap.

It can be seen that in general, an increase in dee voltage results in a higher beam current.

Fuller, Exploring the Capabilities of the Houghton College Cyclotron — Houghton College thesis (2013) — p. 49-50

Editorial note, tabletop extrapolation: For a fill-gas machine, dee volts are a strong current knob - the measured trend here: fewer turns, less path, fewer collisions. Whether they are THE binding knob depends on what limits the machine that day: source output, pressure, phase acceptance and detuning all compete (dg-359, dg-525). Measure before spending.

the RF generator was adjusted in steps of 0.5 MHz ... adjusted in steps of 0.1 MHz near the maximum voltage ... a third sweep was performed using steps of 0.01 MHz ... The data points represent the voltage gain between the RF amplifier and the dee. The voltage gain will be a maximum at the resonant frequency. For this plot, f0=3.55MHz.

Haas, Characterizing the Performance of the Houghton College Cyclotron — Houghton College thesis (2009) — p. 63-64

Editorial note, tabletop extrapolation: A simple, scope-only resonance-finding recipe after any mechanical change to a next machine's dee or stem: coarse-to-fine, with the fine step sized to the resonance linewidth rather than copied - and use a rated or noncontact voltage pickup on the dee side.

the quality factor of the Houghton College cyclotron was determined to be Q=16.1. The previous chamber and dee constructed in 2006 had a quality factor of 22.

Haas, Characterizing the Performance of the Houghton College Cyclotron — Houghton College thesis (2009) — p. 64

Editorial note, tabletop extrapolation: Quantifies the architecture choice: the reference machine's antenna-tuner match delivers kV-class dee voltage at low measured Q, and multi-kV wants a high-Q tank coil. The caveat travels: a low measured LOADED Q reflects the whole coupled system, matching-network losses included - so measure Q on the actual assembly and compare loaded with loaded when weighing the upgrade.

the resonant frequency occurred at f0=3.55 MHz ... Its results were f0=3.63 MHz at a SWR of 1.4:1 ... when the CT2591 HV probe was placed near the dee, the overall capacitance changed slightly. This would, of course, change the value of the resonant frequency.

Haas, Characterizing the Performance of the Houghton College Cyclotron — Houghton College thesis (2009) — p. 64-65

Editorial note, tabletop extrapolation: When cross-checking NanoVNA SWR sweeps against powered probe measurements, probe loading is the first hypothesis for a small frequency disagreement - confirm it (adding the probe should lower the frequency, repeatably) before ruling out coupling, calibration-plane or mechanical causes; Houghton's 2 percent is their number, not a generic tolerance.

By comparing the CT2591 HV probe with the pickup probe, a scaling factor can be determined ... It was determined that the real voltage was roughly 11,300 times the pickup voltage. The frequency of the RF system will affect the values recorded by the pickup probe. For this reason, the probe had to be recalibrated every time the frequency was adjusted. The results given here were for a frequency of 3.55 MHz. ... A linear fit was performed and indicated that the real voltage was roughly 11,300 times the pickup voltage at an RF frequency of 3.55 MHz.

Haas, Characterizing the Performance of the Houghton College Cyclotron — Houghton College thesis (2009) — p. 65-66

Editorial note, tabletop extrapolation: The pickup scale factor is frequency-dependent - the builder must recalibrate their pickup whenever they retune, not assume one constant.

First, the RF system was tuned to a resonant frequency of 3.55 MHz while the filament was set to 2.0 A and floated at -100 V relative to the chamber. At these settings, a SWR of 1:1 and forward power of 15.43 W were measured. ... there is a resonance peak with a magnitude of 1.5 pA at around 0.23 T. ... Collection took place at a radius of roughly 5.95 cm corresponding to proton energies of 9.2 keV.

Haas, Characterizing the Performance of the Houghton College Cyclotron — Houghton College thesis (2009) — p. 69

Editorial note, tabletop extrapolation: Reassurance for commissioning a next machine: hunt for first beam at tens of watts with a clean match before scaling power - on the cited machine, detection sensitivity rather than RF power was the limiting factor at first beam.

higher potential on the dees results in fewer orbits and a shorter time of acceleration, allowing for a higher maximum kinetic energy... gives a maximum of 15 MeV for protons with 50 kV peak-to-peak

Loucks, Initial Results from the Houghton College Cyclotron — Houghton College thesis (2007) — p. 24-26

Editorial note, tabletop extrapolation: At the reference machine's ~150 keV the relativistic shift is small (gamma-1 ~ 0.02%), but phase slip accumulates over the whole turn count, so low volts-per-turn can still spend the +/-90 deg budget well below the textbook ceiling (dg-273's summed-slip check). This rule sets the fixed-frequency ceiling for any future MeV-class ambition.

A standard AEI hairpin electron microscope filament floating at approximately -90 V is heated by 2 A of current ... RF pickup on each filament lead is shorted through a 0.001 uF capacitor to ground.

Yuly, The Houghton College Cyclotron: a Tool for Educating Undergraduates — Cyclotrons 2013, WE1PB01 (2013) — p. 3

Editorial note, tabletop extrapolation: A replaceable-filament pattern worth copying next to a live dee: bias the filament, and RF-bypass every lead at the feedthrough - but size the bypass for the actual RF impedance and current, and use capacitors rated for the DC bias plus transients rather than copying 1 nF.

the Dee may be oscillated with voltage amplitudes of up to approximately 3000V relative to the grounded Dummy Dee ... For normal operation, 10-40 W of RF power are required

Yuly, The Houghton College Cyclotron: a Tool for Educating Undergraduates — Cyclotrons 2013, WE1PB01 (2013) — p. 3-4

Editorial note, tabletop extrapolation: Tells the builder that Dee voltage is a tank-Q problem, not a brute-force power problem: a modest amplifier into a good resonator beats a big amplifier into a lossy one - and dg-313's formula computes the actual watts-per-kV pairing for any target.

It was believed desirable to operate at as low a frequency as possible because of the larger amount of engineering information available for oscillators in the region below 15 megacycles/sec.

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 15

Editorial note, tabletop extrapolation: The reference machine's 9 MHz benefits from the modern form of the same effect: HF amateur-radio technique and parts are abundant below ~30 MHz. Today's sweet spots follow ham bands and ISM frequencies rather than a 15 MHz line; the transferable point is choosing field and frequency where the RF art is cheap.

This curve indicates that 96 kW of rf power is required for exciting the dees to 400 kv. ... The oscillator input was 162 kw.

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 16, 25

Editorial note, tabletop extrapolation: Formula transfers once the conventions are fixed: at 9 MHz, ~50 pF and unloaded Q ~ 1000, 5 kV peak dee-to-ground dissipates ~35 W in the resonator - tens of watts, the FLOOR an amplifier must clear with margin for coupling loss, detuning and arcs. Double the voltage, four times the power.

It is possible to calculate the various effects quantitatively and to predict the minimum dee voltage required to obtain a given energy in a particular cyclotron.

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 17-19

Editorial note, tabletop extrapolation: Directly applicable design step for a next machine: compute threshold voltage for the target energy and field taper before freezing the RF chain power budget.

momentary beam meter readings exceeded two milliamperes but operation at this level was very unsteady due to sparking; further increases were not attempted

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 24

Editorial note, tabletop extrapolation: Test discipline for a next machine's dee-voltage conditioning: rate the machine at the level it holds quietly under a defined acceptance protocol (duty cycle, thermal soak, vacuum stability, RF interlocks), not at the level it touches momentarily.

As measured, efficiency tends to increase with dee-to-dee potential and with beam power.

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 24-26

Editorial note, tabletop extrapolation: The order of magnitude transfers as expectation-setting: most RF power goes to resonator and ion-loading losses, so size a next machine's RF from resonator dissipation (dg-313), not from beam power.

two 12 in. split silver-plated, water-cooled copper rings which can be clamped securely around the stems; the dee stems are also silver plated over the adjustment range

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 53

Editorial note, tabletop extrapolation: Scaled down: any sliding or bolted joint in the reference machine's dee-stem/coil path should be a broad, clean, firmly clamped contact - poor joints are a common and avoidable Q killer in small resonators; whether plating or water cooling is warranted follows from contact loss and temperature, not from the 86-inch's spec.

Since the dees are insulated to operate at a dc bias, ... two-inch rubber hose about seven feet long are used to insulate the dees and to connect to the inlet and outlet headers at the extension wall. ... The ceramic 'Lapp' coils originally used for introducing cooling water to the tube and the plate line failed whenever the oscillator voltage was increased to give 200 kv. They have since been replaced with choke coils wound from copper tubing.

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 55, 59

Editorial note, tabletop extrapolation: The principle - a conductive-liquid line into an RF-hot electrode must itself be an insulator or a choke - applies whenever a next machine adds cooling or bias plumbing to the dee. A hose is not automatically insulation: the water column conducts, so check coolant conductivity and path length for leakage current, the choke's impedance and self-resonance at the RF frequency, and creepage and pressure rating.

a fused disconnect switch in the output of each supply permits the operator to remove a faulty unit from service without disturbing the remainder

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 61

Editorial note, tabletop extrapolation: Modular paralleled supplies (or PA pallets) with individual protection can give a home machine graceful degradation - but that takes design, not just fuses: current sharing or ORing, backfeed isolation, DC-rated load-break disconnects, fault coordination, and a written de-energization procedure before anyone touches a unit. Never hot-swap hardware that wasn't designed and tested for it.

Oscillator starting difficulties due to 'ion loading' are avoided by the use of insulated negatively-biased dees.

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 7, 47

Editorial note, tabletop extrapolation: Directly applicable if a next machine's RF start-up stutters or the dee glows at low voltage: insulate the dee for DC and feed a negative bias through an RF choke. The same lever also bears on multipactor (dg-324), which lives in the same low-voltage start regime. The source records the method; the bias magnitude is found on the machine.

The selected value of 100 kv peak voltage requires about 1.5-in. clearance from dee-to-liner ... Since the magnetic gap is so precious ... this minimum value is taken for design.

Livingston & Howard (eds.), The Oak Ridge Relativistic Isochronous Cyclotron — ORNL-2648, OSTI 4275955 (1958) — p. 100

Editorial note, tabletop extrapolation: The reference machine's 1.3 kV is electrically trivial by this calibration - its clearances are set by beam aperture and mechanical tolerance. For a 20-50 kV dee on a next machine, set clearance from electrostatic analysis of the actual geometry (edges, finish, conditioning, pressure regime), not by scaling kV/cm linearly.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

the maximum voltage gain/dee is Vd = 2*V0 sin(theta/2); for particles rotating on subharmonics of the dee frequency the angular width of the dee is n*theta to the particle

Livingston & Howard (eds.), The Oak Ridge Relativistic Isochronous Cyclotron — ORNL-2648, OSTI 4275955 (1958) — p. 100

Editorial note, tabletop extrapolation: Directly applicable when trimming a next machine's dee for probe or source clearance: keep the dee close to 180 degrees or compute the sin(N*theta/2) penalty for the harmonic in use. Fundamental-mode trims are gentle - 15 degrees off costs about 1% at N = 1 - but the same trim costs more at higher harmonics.

The high dee voltage required in cyclotrons can be achieved for practical driving power only by using a high-Q resonant circuit.

Livingston & Howard (eds.), The Oak Ridge Relativistic Isochronous Cyclotron — ORNL-2648, OSTI 4275955 (1958) — p. 17

Editorial note, tabletop extrapolation: Directly applicable framing for the reference machine's matching network: every dB of resonator Q lost to bad joints or lossy insulators is paid in amplifier watts.

it is possible to bias the dees to prevent multipactoring, and a more complex booster oscillator circuit is required

Livingston & Howard (eds.), The Oak Ridge Relativistic Isochronous Cyclotron — ORNL-2648, OSTI 4275955 (1958) — p. 99

Editorial note, tabletop extrapolation: Directly applicable: multipactor lives in the low-voltage, MHz regime every starting tabletop dee passes through, so anticipate it - designing the dee stem so DC-bias insulation CAN be added is cheap at design time and expensive after. Whether the bias is actually needed is learned at first RF turn-on.

No solder to hold the board to the spreader, the screws are enough. Heat sink compound between copper spreader and aluminum heat sink.

Buckler, Solid-State, 2-Decade, 1.25 kW Linear Amplifier — Development Notebook (2015) — p. 10

Editorial note, tabletop extrapolation: A workable pattern for a kW-class dee driver assembled from LDMOS boards - but the transistor/module manufacturer's mounting spec wins: check flange flatness, clamping force, and which interfaces want grease, pads, solder, or dry metal contact for the specific device.

the part description says '15 nH, connecting wires to R14 and R15, 1.5 cm each #20 AWG,' implying that they are just wires, not even coiled.

Buckler, Solid-State, 2-Decade, 1.25 kW Linear Amplifier — Development Notebook (2015) — p. 15

Editorial note, tabletop extrapolation: Relevant if building a broadband solid-state dee driver: these devices carry enormous low-frequency gain, so low-end stability needs deliberate design - feedback networks of this kind are one tool, verified by stability analysis or measurement on the actual amplifier; neither the 15 nH value nor certain oscillation without it transfers between layouts.

many amplifiers use a push-pull topology that tends to attenuate the second harmonic. For those amplifiers, it is often the third harmonic that has the highest amplitude ... The classic way is with a spectrum analyzer ... you would want to have about 40 dB of attenuation between the amplifier and the measuring device. ... The real issue was the third harmonic, though; in general, it was only down 10 dB down and on some bands only 8 dB down.

Buckler, Solid-State, 2-Decade, 1.25 kW Linear Amplifier — Development Notebook (2015) — p. 19

Editorial note, tabletop extrapolation: A cyclotron dee tank is narrowband, but the rule holds: measure what the PA actually emits before designing filtering or worrying about interference from a garage machine. Take the sample through a power-rated coupler or sampler and compute the pad from actual PA power against the analyzer's rated input - at 1.4 kW (61.5 dBm) a bare 40 dB still leaves +21.5 dBm, too hot for most analyzers.

reflecting all that energy back into the output of the FETs risked driving the oscillations I had worried about in the detailed design of the power deck... I chose the diplexer

Buckler, Solid-State, 2-Decade, 1.25 kW Linear Amplifier — Development Notebook (2015) — p. 19-20

Editorial note, tabletop extrapolation: Relevant if the builder drives the dee with a broadband solid-state PA instead of a tube - but a harmonic diplexer does not protect the FETs from the dee's reactive load at the fundamental. That protection is matching, reflected-power shutdown and, where needed, an isolator; the diplexer only tames the harmonic terminations.

a fundamental flaw in my design settings had been that all the crossover and cutoff frequencies were too low, causing too much insertion loss and high VSWR in the passband.

Buckler, Solid-State, 2-Decade, 1.25 kW Linear Amplifier — Development Notebook (2015) — p. 20

Editorial note, tabletop extrapolation: Schedule measurement-and-adjustment time for any homemade filter bank, dee tank or matching network as a first-class line item; which DIRECTION values move is what the measurements tell you - this author's all-upward shift was his design's particular error, not a law.

I also added a limiting power resistor (20 ohms at 50w) in series with 50v to the TIP102 as a precaution...with this resistor in place, a short on the 12v line will limit the current and prevent a catastrophic failure. ... I used 500v micas but slowly but surely I am changing them to 1000v specs because they are more robust.

Buckler, Solid-State, 2-Decade, 1.25 kW Linear Amplifier — Development Notebook (2015) — p. 31-32

Editorial note, tabletop extrapolation: Cheap fault-tolerance for a homebuilt RF deck, as the source built it. Check the fault arithmetic before copying: 50 V across 20 ohm is 2.5 A and 125 W, above the resistor's continuous rating, so the part rides through brief faults only - pair it with a fuse or fast shutdown rather than treating it as continuous-duty protection. Voltage-derating the filter caps matters more with the reactive load a dee presents.

the maximum output power I've measured ... is about 1.4 kW. After going through T/R switches, filters and couplers, you can expect about 1.3 kW at saturation

Buckler, Solid-State, 2-Decade, 1.25 kW Linear Amplifier — Development Notebook (2015) — p. 4

Editorial note, tabletop extrapolation: Size the RF chain from a component-by-component loss budget (relays, filters, couplers, feedline, matching, resonator) measured or taken from datasheets - the cited 7% is one chain's number; a cyclotron drive's tax depends on what sits in its line, so derive the PA headroom rather than assigning a stock percentage.

a plating having about half the conductivity of the copper base will cause the greatest increase in overall resistance ... the conductivity of much of the commercial silver plating is about half of that of pure copper

Fowler, Radio Frequency Performance of Electroplated Finishes — Proc. IREE Australia (1970) — p. 1

Editorial note, tabletop extrapolation: Before specifying silver on the dee or coil, get the plating process's conductivity data and compare thickness to skin depth at 9 MHz; an uncharacterized jobbing-shop bright-silver finish risks raising resonator loss, while a verified high-conductivity deposit can lower it.

a layer of high conductivity copper plating at least two skin depths in thickness, at the operating frequency, then protecting this against corrosion by a very thin layer of low conductivity plating or a layer of low-loss lacquer

Fowler, Radio Frequency Performance of Electroplated Finishes — Proc. IREE Australia (1970) — p. 10

Editorial note, tabletop extrapolation: For dees, stems, and tank coils at 9 MHz: copper at least ~45 um thick plus a thin low-loss protective finish beats unspecified decorative plating; properly specified high-conductivity silver can do better still, and nickel remains excluded on permeability grounds (dg-222).

The resistance of the composite conductor reaches a maximum value when the thickness of the plating is approximately one and one half times the skin depth for the plated metal.

Fowler, Radio Frequency Performance of Electroplated Finishes — Proc. IREE Australia (1970) — p. 3

Editorial note, tabletop extrapolation: Assess a proposed coating by computing the multilayer surface impedance with the coating's own conductivity AND permeability against its own skin depth - the trap case is a mid-thickness medium-conductivity layer, and magnetic coatings (nickel!) cannot be cleared by nonmagnetic skin-depth arithmetic; very thin protective flashes are usually small in effect at 9 MHz, verified by that same calculation rather than assumed harmless.

A gold flash (10 micro-inches) is often used although many workers have shown that the deposits are not pore-free and that at least 200 micro-inches of gold are necessary to provide adequate protection.

Fowler, Radio Frequency Performance of Electroplated Finishes — Proc. IREE Australia (1970) — p. 7

Editorial note, tabletop extrapolation: For RF contact fingers and connectors on the resonator, distrust thin gold flash: specify a qualified contact-plating system at proven thickness. Lacquer belongs only on non-contact surfaces, and only after RF-loss and vacuum-outgassing checks - never on a current-carrying contact interface.

the contact resistance of two silver-plated wires rose from 6 milliohms to 200 milliohms after two hours' exposure to hydrogen sulphide.

Fowler, Radio Frequency Performance of Electroplated Finishes — Proc. IREE Australia (1970) — p. 7

Editorial note, tabletop extrapolation: Where sulfur contamination is credible (some shop atmospheres, rubber outgassing, industrial air), protect silver-plated RF joints or periodically inspect and measure their resistance - raised contact resistance heats under the resonator's high circulating RF current.

Several reasons have been given for the decrease in conductivity below the bulk values, including: (a) the Beilby layer ... (c) the hill and dale effect ... This last problem has been investigated fully by Benson who recommends chemical or electrolytic polishing to produce a smooth surface and lower losses.

Fowler, Radio Frequency Performance of Electroplated Finishes — Proc. IREE Australia (1970) — p. 8

Editorial note, tabletop extrapolation: Polishing dee edges and stems lowers RF resistance. Smooth, clean, well-conditioned electrodes may also reduce field emission, but the breakdown voltage must be established by field analysis and testing - do not book the second benefit in advance.

safety monitoring of temperature, load failure, and diplexer HPF outputs, and ALC feedback for driver

Buckler, A Solid State 1.25 kW Linear Amplifier — QST, January 2015 (2015) — p. 1

Editorial note, tabletop extrapolation: A directional coupler with fast drive-cut on high reflected power is a strong defense when the cyclotron dee arcs or drifts off resonance mid-run - one protection among the source's set (thermal, load-failure), not a complete answer on its own.

regulated and temperature compensated bias, separate VDD feeds to the output transistor drains to keep high dc currents out of the RF transformers

Buckler, A Solid State 1.25 kW Linear Amplifier — QST, January 2015 (2015) — p. 2

Editorial note, tabletop extrapolation: Directly applicable to a homebrew 9 MHz LDMOS deck: thermal-tracking bias holds the operating point against drift, and DC-free transformers remove one saturation mechanism - still verify RF flux density and transformer temperature at full drive.

the design underwent several changes along the way, including the addition of degenerative feedback after a 'smoke in the cockpit' incident after about 350 contacts had been made.

Buckler, A Solid State 1.25 kW Linear Amplifier — QST, January 2015 (2015) — p. 2-3

Editorial note, tabletop extrapolation: A dee resonator is a narrowband, sometimes-detuned load: design feedback in from day one with a stability analysis over the expected load range, and pair it with real mismatch protection - drain-current limiting and reflected-power foldback - since feedback alone is not a detuned-load defense.

Rather than mounting the output transistors directly to a heat sink, they are first flow soldered to a thick copper heat spreader, which is then mounted to the heat sink.

Buckler, A Solid State 1.25 kW Linear Amplifier — QST, January 2015 (2015) — p. 3

Editorial note, tabletop extrapolation: At 100-500 W a copper spreader under the LDMOS pallet is cheap thermal margin; the reference machine's earlier MOSFET amplifiers died in service without a firm post-mortem, and die-temperature margin is the inexpensive insurance either way.

But the real issue was the third harmonic, which was only 10 dB down generally and on some bands only 8 dB down!

Buckler, A Solid State 1.25 kW Linear Amplifier — QST, January 2015 (2015) — p. 3

Editorial note, tabletop extrapolation: At 9 MHz the 27 MHz third harmonic can couple into a spurious dee-resonator mode if one lies nearby; filter between amp and matching network, sized from the measured spectrum.

favored the diplexer design for solid state amps in the HF range, because reflecting all that energy back into the output of the field effect transistors (FETs) risked driving the oscillations

Buckler, A Solid State 1.25 kW Linear Amplifier — QST, January 2015 (2015) — p. 3

Editorial note, tabletop extrapolation: The dee's off-resonance reflection is a fundamental-frequency problem the diplexer does not solve: give the LDMOS reflected-power foldback or shutdown and, if needed, an isolator, and characterize the dee's impedance across its detuning range. The diplexer buys clean harmonic terminations - that is all.

The position of the connection point at the drain trace is critical as it affects the match.

Buckler, A Solid State 1.25 kW Linear Amplifier — QST, January 2015 (2015) — p. 4

Editorial note, tabletop extrapolation: When copying an LDMOS pallet layout, preserve the cited design's output-transformer tap geometry, and if anything about it changes, remeasure the output match - the source says position is critical; how sensitive, at what power, is a measurement on the actual build.

the maximum energy gain corresponds to a system in which the RF size of the dee is close to 180 degrees or is a multiple of 180 degrees with a factor of 3, 5, 7

Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 11

Editorial note, tabletop extrapolation: The reference machine's single ~180-degree dee on h=1 is already the optimum; the formula lets the builder tool compute turns-to-energy for any future dee angle or harmonic choice.

With a practically realizable energy set today, the final energy is limited to 10-15 MeV for protons when one or two [dees are used] ... By selecting the value of the generator frequency, it is possible to achieve that the point of changing the direction of the phase motion is near -90 degrees.

Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 22

Editorial note, tabletop extrapolation: At 100 keV-1 MeV the reference machine is far from the ceiling. Setting the oscillator slightly below the central-field frequency is the source's strategy for spending the phase budget symmetrically - the same lever helps a machine whose field profile is imperfect, but the check remains the summed slip (dg-273), not the detuning itself.

in the presence of one accelerating dee and a voltage of 60-70 kV, protons can be accelerated in a decreasing magnetic field to an energy of 9-10 MeV

Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 51

Editorial note, tabletop extrapolation: Sets the scale, not a law: the quoted machine class pairs 60-70 kV with 9-10 MeV, and the reference machine's ~1.3 kV dee at ~150 keV sits consistently below that line. Final energy in a classical machine is phase-budget-limited (the summed slip, dg-273), which dee voltage relieves nonlinearly - compute the budget rather than scaling proportionally.

the common boundary of the maximum voltage in the accelerating gaps in the central region of the accelerator is traced, which is 1.3-1.4 times higher than the Kilpatrick criterion

Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 57-58

Editorial note, tabletop extrapolation: The right sizing framework if a next machine pushes dee voltage to tens of kV across small central-region gaps: compute the LOCAL peak surface field from the electrode geometry (not the average gap field), compare against Kilpatrick as a benchmark, and plan on conditioning and breakdown testing - margin is demonstrated, not assumed.

the relative radial increase is only half the relative energy increase. However, for a given cyclotron, the turn separation dr0 will double when the dee voltage is doubled.

Kleeven & Zaremba, Cyclotrons: Magnetic Design and Beam Dynamics — CAS 2015, arXiv:1804.08961 (2018) — p. 44

Editorial note, tabletop extrapolation: The reference machine (~150 keV, 2.6 keV/turn, r ~ 9.6 cm) gets ~0.8 mm/turn. A 10 kV dee at the same radius scales it by the ratio of per-turn energy gains - computed from the actual voltage convention and gap count: 10 kV peak with two crossings at good phase is ~20 keV/turn, ~6 mm; one effective crossing or poor phase halves it or worse.

This results in a phase acceptance of only a few degrees for the typical case of a few hundred turns.

Baartman, Cyclotrons: Why/How Are Their Dynamics Different? — JINST 18 T03005 (2023) — p. 10

Editorial note, tabletop extrapolation: Do not chase single-turn extraction on a small machine: accept multi-turn with spread of order the turn energy gain (~20 keV at a 10 kV dee - the simple-picture floor; turn overlap and precession can widen it), which PIXE tolerates. (Spread and dB/B detail: botman pp.11-14.)

it is mostly the squared ratio of extraction radius and pole gap at extraction which determines the maximal number of turns or the minimal energy gain

Baumgarten, Cyclotron Beam Extraction by Acceleration — arXiv:2205.04124 (2022) — p. 5-6

Editorial note, tabletop extrapolation: A next machine with R ~ 10 cm and half-gap 1.27 cm allows at most ~9 turns by the bound (needing ~18 keV per turn); shrinking the edge half-gap to 6-7 mm allows ~32-44 turns - a few keV per turn, reachable for a 5-10 kV LDMOS dee.

Source extraction voltage is 10-30 kV dc for external sources, with the anode being biased positive. For internal sources, the anode is usually grounded and 30-100 kV of rf voltage is used for extraction

Clark, Ion Sources for Cyclotrons — Cyclotrons '81, Caen (1981) — p. PDF p.3 (printed p.233 of the 9th Int. Conf. on Cyclotrons proceedings)

Editorial note, tabletop extrapolation: The reference machine extracts with its few-kV dee - far below the surveyed machines. Compensating with a small source-puller gap follows Child-Langmuir-like scaling (I ~ V^1.5/d^2 in the planar model - a guide in this geometry, not a law): documented small gaps run 2.3-2.9 mm (Siemens, K100 - dg-624), and expect proportionally lower current than published microamp figures until measured.

It is supported on insulating columns, making it possible to provide a DC bias.

Creutz, Design and Construction of Synchro-Cyclotron — NYO-780 (1950) — p. 15

Editorial note, tabletop extrapolation: A DC-isolated dee mount costs little at design time and provides the discharge-control knob the era's reports repeatedly reach for (dg-320, dg-680, dg-805). A kilovolt-class bias means the mount and its feed are HV-insulated by design, not as an afterthought.

Numerous holes are drilled in them to facilitate vacuum pumping.

Creutz, Design and Construction of Synchro-Cyclotron — NYO-780 (1950) — p. 19

Editorial note, tabletop extrapolation: Virtual leaks behind liners and skins are a classic small-chamber trap: vent every otherwise-trapped volume on the next machine with holes or slots sized for pumping conductance - checked against RF current paths, structure and field quality - and deburr and clean the openings.

Cited in: Cyclotron Vacuum Chamber Design and Sealing · The Vacuum Budget of a Cyclotron

Parasitic modes at higher frequencies than desired for proton acceleration were successfully eliminated with light-bulb loads inductively coupled to the tube lines, and the lower mode ... was avoided by means of a series resonant circuit from dee to vacuum chamber.

Creutz, Design and Construction of Synchro-Cyclotron — NYO-780 (1950) — p. 30

Editorial note, tabletop extrapolation: The general methods transfer - coupled lossy loads to damp unwanted modes, and a tuned series trap for a specific mode - but not component values or topology: identify the actual unwanted modes of the LDMOS-driven resonator first, then design the damper/trap for the measured mode, checking its dissipation and its effect on the operating mode.

results now indicate that four 880's will suffice, while the data from the three-fourths scale model had indicated that six would be necessary.

Creutz, Design and Construction of Synchro-Cyclotron — NYO-780 (1950) — p. 29

Editorial note, tabletop extrapolation: Transferable caution - stray capacitance, proportions and device parameters do not scale cleanly; validate a next machine's dee voltage vs drive on the actual resonator, using models as guides.

good contact is established by the use of strips of thin soft copper sheet backed by foam rubber pads.

MacKenzie et al., Design of the Radio-Frequency System for the 184-inch Cyclotron — UCRL-64 (1948) — p. 10

Editorial note, tabletop extrapolation: The cheap 1948 equivalent of RF finger stock for external, low-temperature joints - removable housing panels and line covers. For vacuum-facing or high-current joints (dee-stem clamps), use vacuum-compatible spring contacts or engineered clamps with verified pressure and RF heating: ordinary foam rubber outgasses and relaxes.

Initially the model condenser blades were bare steel. As had been expected, the Q dropped by a factor of two at the lowest frequency, so all surfaces were copper-plated.

MacKenzie et al., Design of the Radio-Frequency System for the 184-inch Cyclotron — UCRL-64 (1948) — p. PDF 10 (printed -7-) for the quote; PDF 15 (printed -12-) for the halved-Q figure

Editorial note, tabletop extrapolation: On a next machine keep steel (chamber walls, bolts, pole faces) out of RF current paths or plate/line it with copper - Q and dee voltage per watt are at stake; how much a given steel surface costs is a measurement or model result for that geometry.

the vacuum gap be sufficient to withstand 50 kilovolts rf at the accelerating gap. Consequently, a minimum of 3" spacing was employed in the vicinity of the open front end of the dee; near the rear end (i.e. supported end) a minimum of 2" was allowed. ... [a] 0.080" gap between copper or copper-plated surfaces having a reasonable polish would hold a maximum of 50 kilovolts at 13 mc at a pressure of about 5 x 10-6 mm

MacKenzie et al., Design of the Radio-Frequency System for the 184-inch Cyclotron — UCRL-64 (1948) — p. 10

Editorial note, tabletop extrapolation: Do not scale these linearly: vacuum holdoff is nonlinear in gap and dominated by geometry, finish and conditioning (their own bench gap held the same 50 kV across 0.080 inch). Set a next machine's clearance by electrostatic analysis of the actual geometry with conservative peak-field limits, then prove it by conditioning at full voltage.

Over 50 kilovolts rf could be developed across the insulator at 13 mc by a 5 kilowatt oscillator. Under the most severe test conditions, air blast cooling of the insulators was found necessary.

MacKenzie et al., Design of the Radio-Frequency System for the 184-inch Cyclotron — UCRL-64 (1948) — p. 13

Editorial note, tabletop extrapolation: A bench resonator lets the builder soak-test dee-stem insulators at full 5-13 kV RF from modest drive - how modest depends on the fixture's measured loaded Q (constant-Q scaling of the cited point suggests tens of watts at 5 kV but hundreds at 13 kV), so measure Q and compute the drive rather than assuming it.

a .080" gap between copper or copper-plated surfaces having a reasonable polish would hold a maximum of 50 kilovolts at 13 mc at a pressure of about 5 x 10-6 mm.

MacKenzie et al., Design of the Radio-Frequency System for the 184-inch Cyclotron — UCRL-64 (1948) — p. 13

Editorial note, tabletop extrapolation: Directly applicable breakdown data for setting a next machine's dee-to-liner and puller gaps at 5-13 kV - with the derate compared in FIELD, not voltage (the two units had different gaps), and remembering vacuum RF hold-off does not scale as fixed kV-per-gap: bench-verify the actual geometry (dg-419).

The water circuit is completed to ground potential by means of sets of flexible polyethylene tubing, each several feet long. Treated water of low conductivity is used.

MacKenzie et al., Design of the Radio-Frequency System for the 184-inch Cyclotron — UCRL-64 (1948) — p. 13

Editorial note, tabletop extrapolation: Applicable if the next machine's dee or stem is water-cooled while biased - but hose length plus DI water is the historical arrangement, not a sufficiency proof: calculate the water-column resistance at worst-case conductivity (DI water degrades in service - monitor it), include RF capacitive current through the column, and ground/interlock accordingly.

For reasons of convenience, a quarter scale was chosen. The resonant frequency is then increased fourfold and all inductances and capacitances are reduced by a factor of four.

MacKenzie et al., Design of the Radio-Frequency System for the 184-inch Cyclotron — UCRL-64 (1948) — p. 14

Editorial note, tabletop extrapolation: Transferable method: prototype a next machine's resonator at reduced scale with a VNA - remembering effective dee capacitance is not the static value, which is exactly what the model run is for.

The evident discrepancy in transmission line length was eventually traced to a cumulative error of about two inches in various small errors in model dimensions.

MacKenzie et al., Design of the Radio-Frequency System for the 184-inch Cyclotron — UCRL-64 (1948) — p. 22

Editorial note, tabletop extrapolation: Directly applicable: give a next machine's resonant line or tank a deliberate tuning range - trombone section, tuning vane, trimmer capacitor - instead of trusting calculated dimensions to land the frequency.

disclosed a re-entrant cavity resonator mode between the two pole pieces of the magnet with the vacuum tank walls as the return circuit resonant near the lower frequency limit. This was easily suppressed by strapping the pole pieces together.

MacKenzie et al., Design of the Radio-Frequency System for the 184-inch Cyclotron — UCRL-64 (1948) — p. 22

Editorial note, tabletop extrapolation: The pole-chamber geometry of an 8-inch machine forms the same class of parasitic cavity - sweep or model the assembled structure, and add a verified pole-to-pole RF bond if a mode lands near the operating band; don't strap preemptively, since added straps can perturb the intended RF structure or form current loops.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

All discharges were eliminated by cutting down the available volume by means of perforated shields around the sides of the dee, by adding a grounded dummy dee and by applying a negative bias to the dee.

MacKenzie et al., Design of the Radio-Frequency System for the 184-inch Cyclotron — UCRL-64 (1948) — p. 23

Editorial note, tabletop extrapolation: Directly applicable - the 1948 combination that cleared THAT machine's discharges: reduced free volume (perforated shields preserve pumping speed), a grounded dummy dee, and negative dee bias. On a new machine, apply the elements as diagnosis suggests (dg-1273's discrimination between multipactor and gas discharge) rather than as one obligatory bundle - though all three are cheap to design in from the start.

There is sufficient magnetic field at the rotary condenser to allow a Philips gauge discharge when positive bias is applied; a negative bias is therefore imperative.

MacKenzie et al., Design of the Radio-Frequency System for the 184-inch Cyclotron — UCRL-64 (1948) — p. 23

Editorial note, tabletop extrapolation: The next machine's dee sits in 0.59 T, so if a DC bias is used to kill discharges, start negative on the strength of this precedent - then verify empirically: whether a Penning discharge ignites depends on the E/B geometry and pressure, not the field alone.

the upper two insulators are under pure compression, the lower two under pure tension. ... The rf insulators have given no trouble whatever since installation one year ago, though at the time of assembly, their fragility was evidenced insofar as shear forces were concerned. The care taken in insuring that only pure tension and compression forces would be applied was thus well justified.

MacKenzie et al., Design of the Radio-Frequency System for the 184-inch Cyclotron — UCRL-64 (1948) — p. 24

Editorial note, tabletop extrapolation: Directly applicable to a next machine's dee-stem standoffs and feedthroughs: arrange the support geometry (threaded rods, spherical seats) so ceramics never see bending or shear - prefer compression where practicable, avoid point loading, and respect the manufacturer's tensile rating, which is far below the compressive one.

the inner face, or back, is made of 1/2 in steel ... this house serves as a magnetic shield for the oscillator tube. A crude replica (1/16 size) was tested by the magnetic measurements group ... using the 1/16-scale 184-inch model magnet, and this shielding was found sufficiently effective, the field being cut from 140 Gauss to less than 20 Gauss. This is further reduced at the 9C21 elements by means of a 1/2 in steel sleeve slipped over the cooling jacket. The magnetic force on the oscillator box amounts however to 450 lbs.

MacKenzie et al., Design of the Radio-Frequency System for the 184-inch Cyclotron — UCRL-64 (1948) — p. 20

Editorial note, tabletop extrapolation: LDMOS amplifiers, fans and ferrite-cored parts near a 0.59 T magnet want a steel housing - and the source's method is the transferable part: they verified the shielding on a scale model before committing, and budgeted the large attractive force on the box. Measure the fringe field at the amplifier location and check the housing's effect; do not assume a thickness.

It would produce 15 kv peak volts on the dee at 10 me and 9 kv at 20 me with 6 kw input. It averages around 70%.

MacKenzie & Waithman, R.F. System for Frequency Modulated Cyclotron — MDDC-1045 (1946) — p. 4

Editorial note, tabletop extrapolation: A benchmark near the reference machine's 9 MHz - and transferring it runs through the resonator parameters: scale by the actual dee capacitance and Q via dg-313's formula, not by watts-per-kV alone.

The upper and lower frequency limits can be varied together about 6% by a tuning vane which varies the impedance of the transmission line. It is a movable copper sheet with flexible end connections.

MacKenzie & Waithman, R.F. System for Frequency Modulated Cyclotron — MDDC-1045 (1946) — p. 5

Editorial note, tabletop extrapolation: Directly applicable to a fixed-frequency machine: a vane gives few-percent trim to land the dee resonance on the magnet's cyclotron frequency. The range you get depends on your line's geometry - size the vane by calculation and keep a fallback adjustment (dg-665's trombone/trimmer).

The horizontal joints are also rubber backed, but no particular care is necessary to insure contact as the current flow is parallel to the joint.

MacKenzie & Waithman, R.F. System for Frequency Modulated Cyclotron — MDDC-1045 (1946) — p. 6

Editorial note, tabletop extrapolation: Plan a next machine's panel seams along the RF current direction and spend the contact-strip effort on the seams that cross current - remembering fringing and return currents can cross nominally parallel seams, so verify with a current map or by checking seam temperatures at power.

It was tried this way at 20 megacycles, but it soon became necessary to copper plate most of the surfaces.

MacKenzie & Waithman, R.F. System for Frequency Modulated Cyclotron — MDDC-1045 (1946) — p. 6

Editorial note, tabletop extrapolation: At 9 MHz bare steel may survive, but plating (or copper construction) is cheap insurance for Q and hot spots - decide from an Rs estimate and verify temperatures at full power rather than reading 10-vs-20 Mc as a safe cutoff.

Polystyrene of this thickness used in this manner will stand over 15,000 volts DC and approximately 1500 volts r.f. provided the metal parts remain cool.

MacKenzie & Waithman, R.F. System for Frequency Modulated Cyclotron — MDDC-1045 (1946) — p. 8

Editorial note, tabletop extrapolation: A historical construction worth knowing, not a transferable rating: the implied DC stress is ~59 kV/mm, so the numbers belong to that geometry, cooling and test practice. For a next machine's RF chain, prefer certified RF/HV capacitors; if building, take the dielectric's own data (Kapton is often lossier than polystyrene or PTFE at RF), derate heavily, design creepage and corona control, and test thermally and at withstand voltage.

Such oscillations will usually not occur if the time constant of the resonant system is more than ten times the time constant of the grid leak grid condenser network.

MacKenzie & Waithman, R.F. System for Frequency Modulated Cyclotron — MDDC-1045 (1946) — p. 8

Editorial note, tabletop extrapolation: The bias-network-vs-resonator time-constant race is the transferable idea for any self-excited driver on a next machine's dee - for transistor circuits the mechanisms are topology-dependent, so do a small-signal/transient stability analysis rather than relying on this RC ratio.

The loops are therefore made of large diameter tubing and the length of tubing which is not serving as mutual inductance in the dee stem circuit is kept at a minimum. ... the total shift between plate and filament voltages is 21 [deg]. The correction is made in the filament circuit by inserting a capacitor of 140 uuf (c, in Figure 3) in series with the loop. ... The capacity (c, Figure 3) used in the actual installation is around 220 uuf, part of which serves to neutralize the inductance of the filament chokes. It was made adjustable over a small range and varied until minimum plate current was obtained.

MacKenzie & Waithman, R.F. System for Frequency Modulated Cyclotron — MDDC-1045 (1946) — p. 9

Editorial note, tabletop extrapolation: Minimum-DC-input trimming is a meterable, practical phasing procedure for a feedback-coupled driver - hold the required RF output/dee voltage while trimming, or the 'minimum' you find is just reduced drive; other topologies need their own phase-margin analysis.

the frequency of the plate loop could not be made higher than 38 megacycles. At one point this will coincide with the first harmonic. ... It has been predicted theoretically and demonstrated experimentally that most of the ions can be lost by such a variation if the ions reach their final radius at 19 megacycles. ... It was therefore necessary to add about 15 uuf to this circuit, which lowered its frequency to 34 megacycles.

MacKenzie & Waithman, R.F. System for Frequency Modulated Cyclotron — MDDC-1045 (1946) — p. 10

Editorial note, tabletop extrapolation: Even at fixed frequency, sweep the next machine's system for modes near 2x and 3x of 9 MHz; a found mode matters only if it is coupled and excited - measure its effect on dee voltage before detuning it, since an added capacitor perturbs the mode structure too.

Provision was made for arbitrary amplitude modulation by inserting an 893 triode in series with the power supply lead. As yet it has not been used for this purpose, but as it has a 20 kw plate dissipation, it has been used as an emission limiting device to protect the oscillator tubes when discharges occur in the tank and condenser.

MacKenzie & Waithman, R.F. System for Frequency Modulated Cyclotron — MDDC-1045 (1946) — p. 12

Editorial note, tabletop extrapolation: The principle transfers: fast current limiting or foldback in the LDMOS drain supply, plus a VSWR trip, is the modern form. It reduces fault energy; it is not immunity - reflected-power overvoltage and drain transients are separate failure paths needing their own protection (dg-338).

Above this voltage, which is in the neighborhood of 500 volts, the discharge is rapidly extinguished as electrons can no longer oscillate. However, the discharge is usually intense enough, even at 10-5 mm of Hg to prevent the voltage from building up to this extinction value. Such a discharge can be eliminated by a sweeping field obtained in any manner. The sweeping field was obtained on the 37-inch cyclotron by biasing the dee, transmission line, and condenser stator parts a few hundred volts positive.

MacKenzie & Waithman, R.F. System for Frequency Modulated Cyclotron — MDDC-1045 (1946) — p. 12

Editorial note, tabletop extrapolation: The single most relevant discharge fact for the reference machine: its ~1.3 kV dee lives just above this regime, and the 5-13 kV upgrade must punch through it during every start - plan for a bias supply on the dee from day one, and note the source's polarity (positive on the 37-inch; dg-320's machine used negative - both worked, because any sweeping field defeats the resonance).

At 20 megacycles the space between electrodes which will allow an electron to reach an energy around 30 volts in 5 cm. There are very few paths, along the magnetic field, in the neighborhood of the dee that are greater than this, so no trouble has occurred in this region. In the rotary condenser however, most of the paths are of the order of 20 cm. Electrons oscillating in this space can reach efficient ionizing energies long before their amplitude becomes equal to the distance between electrodes.

MacKenzie & Waithman, R.F. System for Frequency Modulated Cyclotron — MDDC-1045 (1946) — p. 12

Editorial note, tabletop extrapolation: Directly applicable geometry rule - at 9 MHz electron oscillation amplitudes are larger still, so keep open RF-exposed volumes and along-field gaps in the next machine's chamber small or shielded.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

Since the tickler oscillator does not derive its excitation from the load, it can drive the main oscillator over the critical voltage.

MacKenzie & Waithman, R.F. System for Frequency Modulated Cyclotron — MDDC-1045 (1946) — p. 12

Editorial note, tabletop extrapolation: With an externally driven LDMOS chain the analogue is a controlled fast RF ramp through the low-voltage (multipactor-prone) band - with vacuum, arc and reflected-power monitoring, since driving through a discharge can reflect hard; there is no self-excited handover in a driven architecture.

For reasons which are not clearly understood this bias usually increases the size of the beam by a factor of two or more.

MacKenzie & Waithman, R.F. System for Frequency Modulated Cyclotron — MDDC-1045 (1946) — p. 12

Editorial note, tabletop extrapolation: Conditionally applicable - and 'try both polarities' is a controlled test, not a knob: use an RF-rated bias network with proper isolation and discharge paths, current and arc monitoring, and vacuum interlocks, and assess Penning-discharge conditions (crossed E and B regions) before applying either polarity. The dee's RF stored energy does not care about the bias supply's current limit.

The measurements were made with G-R Impedance Bridge, Type 650-A Serial #1977, and are +/- 2 uuf. Lead capacity of 29 uuf has already been deducted.

Anderson, 184″ Cyclotron: Oscillator Capacitance Measurements — MDDC-964 (1947) — p. 3

Editorial note, tabletop extrapolation: A modern LCR meter with lead-nulling does the same job on the reference machine's dee stem. C-to-ground alone doesn't predict the ~9 MHz resonance - combine it with the stem inductance (or a distributed model), then confirm the assembled resonance with a low-power VNA; a kHz-range LCR reading can differ from the effective RF capacitance.

Dee-to-dee, kv 10 - 18 ... Internal Beam, Stable, ua 100

Howard, Cyclotrons and High-Energy Accelerators, 1958 — ORNL-2644 (1958) — p. 61

Editorial note, tabletop extrapolation: Proof that low dee voltage works at small radius: ISSP is the existence proof for a sub-MeV goal on a ~10 kV-class dee. Dee voltage buys turn count, phase budget and survival - the energy ceiling stays with B*r (dg-026) - and the field profile must keep the extra turns focused.

Oscillator tube one 8T11R ... Osc. input, max 10 kw ... Osc. output, max 6 kw ... Oscillator tube one, RCA 899A ... Osc. input, max 12 kw ... Oscillator tube 3Q 260E (S.T.C.) ... Osc. output, max 50 kw

Howard, Cyclotrons and High-Energy Accelerators, 1958 — ORNL-2644 (1958) — p. PDF 106 (printed -99-) as cited for BNL; ISSP on PDF 60 (printed -53-), Stanford on PDF 166 (printed -161-), ANU on PDF 26 (printed -19-)

Editorial note, tabletop extrapolation: Those kilowatts bought tens-of-kV dees at high Q, not beam power. A few-kV tabletop dee's budget comes from the resonator formula instead (dg-313: tens of watts dissipated, so a 100 W-1 kW amplifier class with margin) - and the census's plain self-excited oscillators show that sophisticated drive chains are not a prerequisite for running a cyclotron.

Beam defining slits used on 1, 2, and 3rd revolutions to define center of beam rotation; 3rd turn slit is 1/2 mm wide. 100% extraction efficiency with low beams, requires better than 1/2 % stabilization of dee volts.

Howard, Cyclotrons and High-Energy Accelerators, 1958 — ORNL-2644 (1958) — p. 27

Editorial note, tabletop extrapolation: A historically successful, mechanically simple extraction aid: slits in the center region plus tight dee-amplitude regulation. Evaluate it for a next machine by comparing its interception losses and centering benefit against the calculated turn separation and deflector tolerances - slits select phase space by throwing beam away, so they complement, not replace, deflector design.

Magnetic field variable, by only changing the coil current, from 14 to 18 kg with 1 to 2.5% field drop-off at the exit (r = 16 cm).

Howard, Cyclotrons and High-Energy Accelerators, 1958 — ORNL-2644 (1958) — p. 61

Editorial note, tabletop extrapolation: The builder can trim B to match a fixed RF (or vice versa) and expect the shim profile to survive over a modest range - PROVIDED the iron is not driven into locally different saturation, which reshapes the profile. Measure n(r) at both ends of the intended current range before trusting it.

As a result of these circuits improper tuning cannot damage the power tubes.

Osterlund & Smythe, A Cyclotron Power-Amplifier RF System Using a 4CW50,000C/8350 Tetrode — COO-535-543 (1963) — p. 5-6

Editorial note, tabletop extrapolation: For the LDMOS upgrade, take the architecture (limiters that seize the control loop) but not the sufficiency claim: LDMOS dies fail on single-cycle peak Vds, mismatch load-line excursions and oscillation faster than an averaged ALC responds - so add device-specific SOA protection, fast reflected-power shutdown, thermal sensing and a stability check, with polarities and response times defined and fault-tested.

to let the reference voltage vary with the rf plate voltage so that plate dissipation would be limited to a constant value

Osterlund & Smythe, A Cyclotron Power-Amplifier RF System Using a 4CW50,000C/8350 Tetrode — COO-535-543 (1963) — p. 6

Editorial note, tabletop extrapolation: The LDMOS analogue (editorial transfer, informed by modern device practice rather than this source): foldback on a calibrated dissipation estimate - DC input minus delivered RF between defined measurement planes (which lumps matching-network loss into the estimate), or cycle-averaged <vds(t)*id(t)> - tightened under mistuning. Dissipation limiting is one protection layer, not sufficient: add drain-voltage clamping, a reflected-power/VSWR trip, device-temperature sensing and fast fault shutdown, since LDMOS also dies of RF-cycle overvoltage, mismatch and fast thermal transients.

The dee voltage is depressed about 1% for each 10 uA of injected current, and because a balance is maintained at the input of the amplifier, the recovery time is limited only by the bandwidth

Osterlund & Smythe, A Cyclotron Power-Amplifier RF System Using a 4CW50,000C/8350 Tetrode — COO-535-543 (1963) — p. 6

Editorial note, tabletop extrapolation: A tabletop ALC loop gets dee-voltage modulation for free by injecting an offset into the amplitude setpoint - but that is voltage modulation, not proven beam gating: measure the transfer to extracted current, energy and extinction ratio (and where the un-extracted beam goes) before using it for activation or timing work; true beam-off needs a validated source-side chopper. The 1%/10 uA constant is their circuit's, not a scaling law.

below a dee voltage of 15 kV, the flip-flop will remain in one state and only if the dee circuit happens to be tuned to the low frequency side of resonance will the servo run in the proper direction

Osterlund & Smythe, A Cyclotron Power-Amplifier RF System Using a 4CW50,000C/8350 Tetrode — COO-535-543 (1963) — p. 7

Editorial note, tabletop extrapolation: Any auto-tune loop (phase comparison of PA drive vs dee pickup) needs a validity gate: characterize the detector's own signal-threshold, enable the servo only above it, bound the tuner's travel and rate so a confused loop cannot run away, and provide a manual jog mode to walk into range - the low-signal failure mode recurs across detector technologies even though its details differ.

adjusting Cn for coincidence of maximum dee voltage and minimum plate current as the dee was tuned through resonance

Osterlund & Smythe, A Cyclotron Power-Amplifier RF System Using a 4CW50,000C/8350 Tetrode — COO-535-543 (1963) — p. 4

Editorial note, tabletop extrapolation: Neutralization is a triode/tetrode matter, and the coincidence test belongs to a neutralized tuned-plate PA: on that class of amplifier the dee-voltage peak and plate-current dip should line up through resonance, and a skew flags feedback. On a solid-state or matched-line chain there need be no input-current dip at resonance at all - verify resonance and match there with dee voltage, reflected power and the device's rated currents instead. [Note revised 2026-08-23: the earlier note generalised the test to 'any amplifier-dee chain' and changed the observable to PA input current.]

a Phillips-Ion-Gauge-type discharge can start in the magnetic field inside the vacuum tank near the positive transmission line

Osterlund & Smythe, A Cyclotron Power-Amplifier RF System Using a 4CW50,000C/8350 Tetrode — COO-535-543 (1963) — p. 5

Editorial note, tabletop extrapolation: Very relevant at higher dee voltage on the reference machine or a next machine: crossed E and B in vacuum is exactly a PIG geometry - it is how the gauge and the source work - so route DC-carrying feedlines, bias leads and probe wires out of the field region or shield them. This failure mode is designed out at layout time.

It was decided to use Eimac grid collet (which is .020" thick in contrast to their regular line of finger stock which is .010" thick) mounted on water cooled copper blocks ... dee stem surface was silver-plated copper which was also water cooled. The shorting plane as originally installed has been in service for nearly three years and has performed flawlessly. There is no discoloration or other indication of heating of the contacts, despite routine operation to 110 A/in and occasional operation to higher current densities

Osterlund & Smythe, A Cyclotron Power-Amplifier RF System Using a 4CW50,000C/8350 Tetrode — COO-535-543 (1963) — p. 8

Editorial note, tabletop extrapolation: The recipe transfers - thick fingers, positive clamping, plated surfaces, cooling on both sides of the joint - the number does not: calculate the proposed tuner's actual contact current, then verify temperature rise and contact resistance under representative duty; a demonstrated operating point in one cooled geometry is not a ceiling for another.

vacuum capacitors have been used in various ways in its plate circuit. None has been found to stand up satisfactorily.

Osterlund & Smythe, A Cyclotron Power-Amplifier RF System Using a 4CW50,000C/8350 Tetrode — COO-535-543 (1963) — p. 8

Editorial note, tabletop extrapolation: Dated in absolute terms - but 'modern vacuum caps are fine at kW-class' is a ratings question, not a vintage question: they are suitable where the manufacturer's peak-voltage, RF-current, frequency and thermal ratings are met with margin, and fault energy is considered. The placement lesson stands either way: put lumped variable capacitors where RF current is low and do coarse tuning with distributed elements.

It minimizes electric defocusing, which is ordinarily a major cause of beam loss, and actually provides some focusing during the usually defocusing part of the phase excursion.

Goodman, A Square-Wave Cyclotron Oscillator — ORNL-2403 (1958) — p. 10-11

Editorial note, tabletop extrapolation: Electric defocusing on the first turns is a plausible and testable contributor to the reference machine's losses - not an established attribution; a flat-topped dee is likely too much RF plumbing for a next machine, but the mechanism explains why phase excursion and gap-crossing timing deserve modeling attention in any small machine.

the same bunching occurs even if a third harmonic is added to the r-f wave form to square the wave

Goodman, A Square-Wave Cyclotron Oscillator — ORNL-2403 (1958) — p. 10

Editorial note, tabletop extrapolation: Reassurance that waveform shaping and center-region bunching are separable problems in the source's treatment; any claimed voltage benefit depends on harmonic amplitude/phase and what is held fixed (peak voltage vs RF power), so quantify longitudinal acceptance by calculation before banking on it. The bunching mechanism itself (Cohen) is what sets which ions survive the center region. OCR note - theta prints as (c) in these appendix equations.

If this is done at the rate of 10 megacycles per second, the power requirement would be 20 megawatts!

Goodman, A Square-Wave Cyclotron Oscillator — ORNL-2403 (1958) — p. 13

Editorial note, tabletop extrapolation: The cleanest back-of-envelope argument in this collection for why dee voltage is bought with Q, not amplifier watts - scale it to a next machine (7-9.5 kV on tens of pF at 6.78 MHz) to show why a few hundred LDMOS watts suffice only through a good resonator.

The extra current element can, however, be a second transmission line

Goodman, A Square-Wave Cyclotron Oscillator — ORNL-2403 (1958) — p. 18

Editorial note, tabletop extrapolation: A lumped-plus-stub version is buildable at tabletop scale and the design tables (PDF 33-60) are precomputed; even unused, the method shows how to place a resonator's higher modes deliberately instead of discovering them by accident.

The following tuning procedure was found to be easy to follow: 1) Set the oscillator frequency at w0 and set the admittance meter to the correct reading for zero admittance at the junction to the system. 2) Tune the length of one of the lines for a null on the admittance meter. 3) Set the oscillator frequency to 3w and measure the admittance; note whether it is positive or negative. 4) Return to w0 and change a1, compensating with a change in a2 to keep the system tuned to w0. One can determine which way to tune by comparing the position of the resonances with numbers interpolated from Appendix III. 5) Remeasure admittance at 3w, and repeat the procedure until the admittance measures zero at 3w.

Goodman, A Square-Wave Cyclotron Oscillator — ORNL-2403 (1958) — p. 21

Editorial note, tabletop extrapolation: The written five-step procedure is a model for documenting any coupled-adjustment RF tune-up - a next machine's coupling loop and trimmer interact the same general way; precomputed knowing-which-way-to-tune tables are the transferable trick, though the dual-line tables themselves don't map onto a different topology.

if the coupling line is one-quarter of the fundamental wave length it is three-quarters of the third harmonic wave length, and the impedances are simply inverted by the line at both frequencies

Goodman, A Square-Wave Cyclotron Oscillator — ORNL-2403 (1958) — p. 22

Editorial note, tabletop extrapolation: A handy odd-harmonic identity - and a warning that a quarter-wave feeder presents TRANSFORMED impedances to your amplifier's harmonics even in a plain sine-wave system: evaluate the actual harmonic load with Z0(f) and measured S-parameters (connectors and loading shift the third-harmonic electrical length) before assuming either benefit or instability.

It was somewhat difficult to get both the phase and the amplitude of the third harmonic adjusted correctly; however no serious attempt was made to develop a good self-excited driving system.

Goodman, A Square-Wave Cyclotron Oscillator — ORNL-2403 (1958) — p. 25

Editorial note, tabletop extrapolation: Mirrors the next machine's decision already leaning MOPA: independent control of each degree of freedom is the argument, and a DDS + LDMOS chain is the modern form - while the self-excited literature (dg-1367, dg-254) holds the other seat. This source records a difficulty, not a verdict.

Cited in: Driving the Dee: RF Coupling

Tuning drifts are always experienced in cyclotron operation. Since a tuning drift would change the relative amplitudes and phases of the first and third harmonics, such a drift would alter the wave form. A visual means of monitoring the wave form and a remote tuning or an automatic servomechanism for tuning should be provided.

Goodman, A Square-Wave Cyclotron Oscillator — ORNL-2403 (1958) — p. 25

Editorial note, tabletop extrapolation: Even a plain sine system drifts (thermal detuning is logged on the reference machine); a calibrated capacitive pickup on a scope is the minimum instrument, and it is a prerequisite for any auto-tune servo on a next machine.

one degree of phase error will apply full power to the servo motor... the trimmer will shift the resonant frequency of the dee 1% in one minute... the dee trimmer should have sufficient range to shift the resonant frequency 2%.

Smith, A Three-Phase Radiofrequency System for Cloverleaf Cyclotrons — UCRL-3153 (1955) — p. PDF p.7 (printed -4-)

Editorial note, tabletop extrapolation: Good starting criteria for a stepper-driven trimmer on a next machine's resonator - then derive the actual range and slew from measured cavity drift (thermal and mechanical) and actuator dynamics, and verify loop stability margins; the field tolerance and the tuning range are separate constraints.

The phase detector is quite sensitive and produces an output signal of 0.76 volt for a phase error of 1

Smith, A Three-Phase Radiofrequency System for Cloverleaf Cyclotrons — UCRL-3153 (1955) — p. 13

Editorial note, tabletop extrapolation: Characterize K_d on the actual detector near the chosen null so loop gain is a number, not a knob - then size downstream amplification from the full loop model (actuator, mechanics, delays). Modern detector options span analog slopes to charge pumps to digital outputs; their gain is a datasheet-plus-measurement fact, not a folklore mV/deg figure.

the amplitude of the intermediate frequency is exactly equal to the magnitude of the local oscillator signal and entirely independent of the magnitude of the phase signals

Smith, A Three-Phase Radiofrequency System for Cloverleaf Cyclotrons — UCRL-3153 (1955) — p. 12-13

Editorial note, tabletop extrapolation: The principle transfers: servo dynamics should not change with dee-voltage level over the operating range, and the ion arc is a noise source the phase detector must tolerate. Modern equivalents are limiting amplifiers or digital phase detection - but every implementation has a floor: specify and test input dynamic range, limiter behavior, phase noise and loss-of-signal handling, because no detector stays accurate as the signal approaches its noise floor.

The most serious objection to the dee-to-dee capacitance is the coupling between servo systems which it provides. The problem of servo stability becomes insuperable.

Smith, A Three-Phase Radiofrequency System for Cloverleaf Cyclotrons — UCRL-3153 (1955) — p. 15

Editorial note, tabletop extrapolation: A single-dee next machine dodges the coupled-servo problem entirely - the design lesson. Any two-dee or dee-plus-tuned-dummy variant with separate tuners should measure the coupling matrix and analyze loop stability first: neutralizing lines are one narrowband remedy, and common tuning, coordinated (MIMO) control or reduced bandwidth are others.

It was necessary to do this while the machine was down to air, in order to avoid multipactoring. ... The coefficients for the 20-inch cyclotron were below 3%. In order to adjust the coupling loops of the neutralizing lines the dee stems were excited one at a time

Smith, A Three-Phase Radiofrequency System for Cloverleaf Cyclotrons — UCRL-3153 (1955) — p. 18

Editorial note, tabletop extrapolation: Two transferable habits: quantify RF isolation as a measured coefficient (set the pass number from your own loop-stability analysis), and remember low-level RF in vacuum can sit in a multipactor window - the reference machine has seen multipactor-like loading. Venting for the test sidesteps multipactor but is not blanket safety: corona, heating and hazardous RF voltage remain, so keep monitoring and interlocks in place.

if the line is excited from a constant current source the magnitude of the voltage appearing across the input of the line is constant but the phase of the voltage depends upon the load resistance

Smith, A Three-Phase Radiofrequency System for Cloverleaf Cyclotrons — UCRL-3153 (1955) — p. 11

Editorial note, tabletop extrapolation: A DDS sets phase digitally today, but the lambda/8 trick remains a zero-active-parts phase adjuster and a nice classroom transmission-line demonstration - measure the residual amplitude variation of the real cable, pot parasitics and finite source impedance before using it where amplitude flatness matters.

Once the three dees are isolated electrically by adjusting the neutralizing loops the machine behaves like three separate single-phase systems.

Smith, A Three-Phase Radiofrequency System for Cloverleaf Cyclotrons — UCRL-3153 (1955) — p. 18

Editorial note, tabletop extrapolation: The architectural moral - decouple where practical, then control each loop as SISO - applies to a next machine's interacting adjustments (tuner vs coupling vs amplitude); measure the residual interaction after decoupling, and where it stays significant use coordinated control rather than fighting coupled loops one at a time. The programme burned months servoing the coupled system first (ucrl-3187 p.5-6, 11).

The beam load would cause a two- to threefold increase in the amplifier plate currents compared to the source-off condition.

Heusinkveld et al., Studies with a Three-Dee Three-Phase Proton Cyclotron — UCRL-3187 (1955) — p. 14

Editorial note, tabletop extrapolation: The 2-3x signature does NOT transfer to nA beams (P_beam = I*E/q puts a nA beam far below amplifier-meter resolution - compute it for your parameters); what does transfer is the habit of plotting beam current against dee voltage empirically as a run-log staple, WITHOUT imposing linearity - capture and transmission bend that curve, and V_dee itself goes as sqrt(P) at fixed impedance.

protected by an interlocked air-cooling system, spark gaps at both ends of the half-wave transmission lines leading to the dee stems, and by an rf-dc fault circuit

Heusinkveld et al., Studies with a Three-Dee Three-Phase Proton Cyclotron — UCRL-3187 (1955) — p. 11

Editorial note, tabletop extrapolation: The rf-dc comparison is the tube-era ancestor of modern output-detect foldback and ports to the LDMOS upgrade: DC applied but no RF developing means something is wrong - an arc, a detune, or a failed stage - so kill drive and investigate. Spark gaps at the feedthroughs remain cheap insurance.

during this time the servos received spurious signals and tended to creep away

Heusinkveld et al., Studies with a Three-Dee Three-Phase Proton Cyclotron — UCRL-3187 (1955) — p. 12

Editorial note, tabletop extrapolation: A control-system rule that transfers verbatim to any next machine's auto-tune or ALC firmware - hold integrators and actuator positions during spark recovery/restart, and make both the recycle delay and the servo-hold adjustable; same lesson as coo-535-543's amplitude gate, learned independently.

thermal effects detuned the machine sufficiently so that ion lock prevented the rf from being restored ... It was then necessary to retune the machine by exciting each of the dee-stem tanks with a grid dip oscillator and adjusting the tuning capacitances for resonance.

Heusinkveld et al., Studies with a Three-Dee Three-Phase Proton Cyclotron — UCRL-3187 (1955) — p. 12

Editorial note, tabletop extrapolation: The transferable practice is a permanent low-level resonance-check capability - a VNA or dip meter on a pickup loop, with RF-rated isolation or interlocking so it can never see drive power - so resonance can be found cold, plus logging tune position vs temperature. The reference machine already shows warm-up drift.

peak efficiency did not correspond to 120 phase difference between the dees

Heusinkveld et al., Studies with a Three-Dee Three-Phase Proton Cyclotron — UCRL-3187 (1955) — p. 11

Editorial note, tabletop extrapolation: Measure the quantity you care about at the electrode (same moral in ucrl-3153 p.7): derive a next machine's tuning/phase feedback from the dee pickup, and before trusting LDMOS drain current or forward power as a tuning indicator, verify at the electrode that its optimum coincides with the dee-voltage optimum - the historical machine's did not.

the diode charges a capacitive load to the peak value, and the stored charge does not subtract (appreciably, at any rate) from the output voltage.

Smith, Deflector Power Supply for Sector-Focused Cyclotrons — UCRL-10655 (1963) — p. 10

Editorial note, tabletop extrapolation: Historical for parts choice - modern fast-recovery diodes moot the issue - and do NOT generalize the tolerance: reverse-recovery charge at 100 kHz can mean reverse current, heating, and poor sharing in other topologies. Select diodes on reverse voltage, recovery charge, leakage and sharing arithmetic; spend the savings on voltage rating and grading.

the switch must pass a peak current of 5000 amperes per transformer ... 8 in parallel on each transformer or 16 in all and introducing a very small inductance in each plate lead to make the tubes share the load

Kerns et al., High Voltage Pulser for 184-inch Cyclotron Electric Deflector — UCRL-95 (1948) — p. PDF p.13 (printed p.-10-)

Editorial note, tabletop extrapolation: The derating discipline - waveform-specific stress, not catalog rating - transfers to every switching element an amateur uses: MOSFET/IGBT avalanche and dV/dt limits in a Marx or inverter play exactly the role the 5C22's reversal limit played here.

These lines provide a 1000 volt trigger of 20 ohms impedance for approximately 0.20 microseconds. Applying this trigger to the grids results in positive ionization of all the tubes in 0.1 +/- 0.01 us.

Kerns et al., High Voltage Pulser for 184-inch Cyclotron Electric Deflector — UCRL-95 (1948) — p. 13

Editorial note, tabletop extrapolation: Relevant only if a next machine adds a pulsed element (fast chopper, time-of-flight kicker): pulse-forming-line triggering is the classic paralleling technique, one option beside modern isolated solid-state drivers - and note the quoted 0.1 +/- 0.01 us is turn-on delay with spread, from which inter-channel jitter is bounded, not measured.

Approximately ninety percent of the total power input to the system is eventually dissipated in the transformer cores as heat. At rated operating levels this loss is approximately 500 watts.

Kerns et al., High Voltage Pulser for 184-inch Cyclotron Electric Deflector — UCRL-95 (1948) — p. 12

Editorial note, tabletop extrapolation: Transferable craft here is the failure mode (interlaminar voltage at high volts-per-turn) and the de-aerated-oil practice - which reduces bubbles and partial discharge, not corona from bad geometry. The 300-kV survival was that transformer's result, not a portable 3x proof-test rule: overvoltage testing at these levels is itself hazardous and can leave latent damage, so test to an applicable HV standard's waveform, duration and partial-discharge limits, remotely, with discharge provisions - not to a generic multiple.

a plate voltage of 11,000 volts on the thyratrons can be maintained with a power supply voltage of 2,750 volts, a step up ratio of four to one ... Step up ratios as high as ten to one have been observed.

Kerns et al., High Voltage Pulser for 184-inch Cyclotron Electric Deflector — UCRL-95 (1948) — p. PDF p.15 (printed p.-12-)

Editorial note, tabletop extrapolation: Pulsed-modulator craft, not CW-deflector material; file under 'if a next machine ever needs a kicker'. The ratio is topology- and loss-dependent - simulate or measure the actual waveform before sizing a supply on it, and rate every capacitor, switch and insulator for the real reversal stresses.

It is an advantage to choose the smallest value of l, since the choice allows the least sensitivity in matching the perturbing frequency to the particle motion.

Stubbins, Radiofrequency System for Extracting Particles from a Cyclotron — UCRL-8578 (1958) — p. 7

Editorial note, tabletop extrapolation: A candidate extraction assist worth a TRACKER experiment before hardware: note that for l = 1 with nu_r near 1 the drive lands near TWICE the revolution frequency, and the required gradient, electrode voltage, bandwidth against tune spread, and isolation from the main RF are exactly what the tracking study must produce before 'an electrode pair and a small oscillator' can be promised.

where we use E = 4.3 kv/cm as the electrical gradient. ... This rf electrical-field gradient, less than 5 kv/cm, is believed to be easily obtainable by an oscillator which is independent of the cyclotron oscillator and which can be tuned to the optimum frequency and amplitude. ... Calculations on the IBM 650 have been done in the median plane only. The perturbation is introduced when the particle is beyond the synchronous radius in a region from 100 to 160 [deg].

Stubbins, Radiofrequency System for Extracting Particles from a Cyclotron — UCRL-8578 (1958) — p. 8

Editorial note, tabletop extrapolation: At a next machine's scale the voltages are small - 4.3 kV/cm across a 2 mm gap is ~860 V peak - but feasibility still means vacuum-RF behavior, feedthroughs, tuning and breakdown checks, and the scheme was never demonstrated on hardware in this report: a promising computed option, not proven practice.

f_z = f - f_0, where f_z equals (sqrt n) f_0 ... and n is the conventional cyclotron magnetic field parameter. The relation f = f_0 ((sqrt n) + 1) is one required condition for this process to occur

Stubbins, Radiofrequency System for Extracting Particles from a Cyclotron — UCRL-8578 (1958) — p. PDF p.5 = printed p.-3- (UCRL-8578, Sec. I Introduction)

Editorial note, tabletop extrapolation: A real design caution at any scale: an E_z gradient of the right symmetry near a nu_z resonance can dump the beam. Note dee misalignment gives mostly a dipole-like midplane E_z, not the z-proportional gradient this parametric resonance needs - but asymmetric liners and gap geometry can supply the gradient term, so keep the dee/dummy-dee vertically symmetric and check nu_z against strong rf harmonics at operating field.

A dee voltage of 75 kv dee-to-dee was reached after some routine difficulties were overcome. The cyclotron now maintains this voltage for long periods of time without showing any tendencies to failure.

Howard (ed.), Electromagnetic Research Division Quarterly, period ending 31 March 1952 — ORNL-1339 (1952) — p. 15

Editorial note, tabletop extrapolation: The transferable practice is endurance-above-operating-point as the acceptance test for the LDMOS upgrade - with the margin chosen from the new system's own component deratings (capacitors, feedthroughs, transistor SOA), stored energy and interlocks, and with arc and X-ray monitoring during the test. A margin that survives only seconds is not margin; a margin that exceeds a component rating is not a test, it is a failure in progress.

The location of the germanium crystals was such that neutron bombardment from the cyclotron affected the resistivity calibration. With the present system, the vacuum tube rectifiers are unchanged by neutron bombardment and, unless the probe-to-dee distance is changed, the calibration remains constant.

Howard (ed.), Electromagnetic Research Division Quarterly, period ending 31 March 1952 — ORNL-1339 (1952) — p. 10

Editorial note, tabletop extrapolation: Two transferable halves, properly scoped: (1) semiconductor sensors near the chamber are a calibration-drift RISK once neutrons appear - characterize candidate devices at the expected fluence rather than banning them; (2) a capacitive dee-voltage pickup is calibrated GEOMETRY - fix and document the complete pickup geometry and signal chain, or every calibration is void. Bears directly on retiring the reference machine's uncalibrated ~1.3 kV dee-voltage number.

the ion source arc slit was shortened from 2 1/2" to 1/2". Thereafter the ratio of accelerated beam power to ion loading power was increased, as predicted.

Howard (ed.), Electromagnetic Research Division Quarterly, period ending 31 March 1952 — ORNL-1339 (1952) — p. 16

Editorial note, tabletop extrapolation: On a tabletop machine where every watt of RF matters: try slit length as an EXPERIMENT, watching accepted beam per unit dee loading rather than raw source output. The over-emission mechanism is the natural reading of the ORNL result, but slit changes also move plasma and extraction optics, so let the measurement decide.

the net ion-loading efficiency was 40%, that is, 40% of the power expended in acceleration of ions was to the target. There was a two-fold increase in electrical efficiency as the beam was increased.

Howard (ed.), Electromagnetic Research Division Quarterly, period ending 30 June 1952 — ORNL-1345 (1952) — p. 7

Editorial note, tabletop extrapolation: On the reference machine at nA the beam power is invisible next to fixed RF losses - the transferable lesson is the metric, not the number: log P_beam/P_RF per run, and chase resonator Q and coupling rather than amplifier watts for efficiency on any small machine.

A negative voltage bias, 1 to 2 kv, is applied to the dees in order to sweep out any ions that may be formed while oscillation is being established.

Howard (ed.), Electromagnetic Research Division Quarterly, period ending 30 June 1952 — ORNL-1345 (1952) — p. 9

Editorial note, tabletop extrapolation: Transferable as a startup practice: a bias supply that sweeps ions out during RF ramp-up is the classical cure for start-up loading (dg-320, dg-680 - polarity differs by machine and both worked). What voltage a small machine needs is found at the machine; the 63-inch's 2-4% of dee voltage is the documented anchor, not a scaling law.

Carbon lips of a new design were installed on the edges of the dees to reduce sparking at the increased dee-to-dee voltage, 400-500 kv, required for operation at the high energy level.

Howard (ed.), Electromagnetic Research Division Quarterly, period ending 30 June 1952 — ORNL-1345 (1952) — p. 7

Editorial note, tabletop extrapolation: The 400-500 kV is MW-era and does not transfer; the material practice is a candidate to test - if the reference machine's 5-13 kV upgrade sparks at the dee gap, carbon edge pieces are the period remedy and trivially machinable. Verify grade choice and watch for carbon dust on insulators; and note ucrl-10654's caveat that carbon loses its bake-in minutes after voltage-off (dg-744).

This additional pumping speed then can be considered as being in parallel with that through the opening at the mouth of the dee.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 129

Editorial note, tabletop extrapolation: Dees are pumping dead-ends by construction, and the ion source dumps its gas inside one: added holes in the dee back or stem shrouds are valuable conductance exactly there - size and place each pattern with an RF-current and field review, a structural check, and a molecular-flow conductance estimate; below-RF-significant hole size is the starting constraint, not the whole analysis.

Cited in: The Vacuum Budget of a Cyclotron

The frequency-sensitive circuit "gates" the phase-sensitive circuit, and the phase-sensitive circuit triggers the deflector.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 168

Editorial note, tabletop extrapolation: The architecture for a timed kick against an extraction gap when frequency and phase are not derived coherently from one reference: coarse condition (frequency, turn count, integrated field) gates, RF phase triggers. A modern phase-coherent synthesizer can supply both from one reference - then a single measurement suffices.

Block 4 is a local oscillator with a frequency about 1 megacycle below the desired deflection frequency P. When the dee-oscillator signal sweeps through point P, the 1-megacycle filter passes an a-c transient.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 168-169

Editorial note, tabletop extrapolation: Classic measurement doctrine - move the precision problem to a low frequency where stability is cheap. A modern mix-down marker inherits the crystal's stability only for the LO term: the IF filter's center drift, bandwidth and threshold timing all enter the marker's error budget, so build that budget rather than expecting crystal accuracy from junk-box filters.

The crystal oscillators, Nos. 3 and 5, will maintain a constant frequency within one part in 10,000.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 169-170

Editorial note, tabletop extrapolation: The stabilization pattern transfers even where the parts are now silicon: put the reference AND the analog discrimination components in one controlled thermal box, because the filter drifting is as fatal as the oscillator drifting - then budget the whole chain (oscillator, filter, mixer, threshold) instead of assuming the oven number covers it.

Unfortunately it is theoretically impossible to filter a transient without introducing time delay. The time delay thus introduced was kept to a minimum.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 170-171

Editorial note, tabletop extrapolation: General fast-timing wisdom for beam-pulse and kick timing chains: every smoothing stage costs latency. Measure the chain's end-to-end latency and compensate the FIXED part in the trigger schedule or delay setting; threshold bias (the historical method) only advances the crossing for a given waveform - it walks with amplitude and slew rate, so calibrate it over the expected pulses.

the time at which the transient is at a peak is somewhat later than the time at which the dee-oscillator frequency is in the center of the filter pass band.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 171-172

Editorial note, tabletop extrapolation: Matters wherever a resonant pickup watches a changing frequency - a synchrotron RF ramp or an FM-tuned marker on a cyclotron: if the ramp rate changes, re-characterize the timing rather than assuming the old calibration.

That alternative was abandoned in view of the susceptibility of high-frequency switching circuits to unforeseen difficulties.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 172

Editorial note, tabletop extrapolation: A complexity-avoidance pattern with 2026 force - blanking a known-bad time window (one line of firmware now) - valid when no wanted events occur in the window and the gate acts early enough that the front end isn't overloaded by the artifact; otherwise the analog filtering earns its complexity.

Probable error in firing time, <1 microsecond. Range of firing frequency, 19 to 21-1/2 megacycles, with provision for changing this.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 174

Editorial note, tabletop extrapolation: Calibrates ambition - microsecond-class event timing off a small RF sample needed no exotic parts in 1952. A modern comparator-plus-MCU implementation should do well against that; measure its jitter rather than assuming orders of magnitude, and copy the architecture, not the hardware.

Fig. 6.3-Typical characteristics of three-fourths scale model ... 150-kw input, 27.5-kw plate dissipation per tube ... The fairly low efficiency, 27 per cent, indicates that it would be desirable to go to six type-880 tubes in the final model

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. PDF p.162 (unnumbered chapter opener, Technical Report No. 6) for the quoted text; the figure is on PDF p.167 = printed p.167

Editorial note, tabletop extrapolation: The transferable method rule - prototype the next machine's dee/stem/liner as a cheap scale model (or full-scale mockup, given the small size) and measure resonance, Q and parasitics before final fabrication; NYO-780 p.29ff records the same practice. Cite both.

equipped with a small coupling loop ... used to load the unwanted mode, which on the three-fourths scale model was about 50 megacycles, in which the oscillator stub forms a capacity-loaded half-wavelength line.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 162

Editorial note, tabletop extrapolation: Both steps are amateur-accessible: find candidate modes cheaply (a scale model or a bench sweep of the real resonator), then load the parasite selectively into a lossy element that leaves the wanted mode alone. Scaling shifts parasitic frequencies, and the final amplifier's loading shifts them again - so verify and re-suppress on the fully assembled system; that matters the moment the LDMOS upgrade raises the reference machine's gap voltages.

The operation of the oscillator determines the variation of capacity with time which will keep the ion phase constant. This variation is not very critical.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 152

Editorial note, tabletop extrapolation: For a small synchrotron's RF ramp the pattern maps with its own tolerances: f(t) and the allowable phase/frequency error come from the magnetic ramp, synchronous orbit and RF-bucket acceptance - the cited looseness belongs to that FM oscillator, not to synchrotron ramps in general; the duty-factor lesson (reset time is pure tax, minimize it within hardware limits) transfers as stated.

From (5) the measurement of dr is essentially a determination of the phase.

Cohen, Spatial Distribution of Current on an Internal Cyclotron Target — ORNL-1348 (1952) — p. 9

Editorial note, tabletop extrapolation: Energy-independent physics: a differential probe (shadowed double tip) or the sectioned-target map gives dr, and with the dee voltage - stated in ONE convention, peak dee-to-dee or dee-to-ground, never mixed - that is a direct measurement of ion RF phase, the quantity a next machine's field-tolerance budget protects. A rare experimental handle on phase for machines with no beam-position monitors.

The cost of the magnet would be increased unreasonably if a gap suitably large for conventional dees were provided. For this reason, a system for acceleration with vertically oriented resonant cavities was adopted.

Oak Ridge National Laboratory, A Proposal for the Mc² Isochronous Cyclotron — ORNL-3540 (1963) — p. 145

Editorial note, tabletop extrapolation: The specific topology (vertical TEM cavities) is 810-MeV-only; the transfer is the coupling: every inch of dee clearance is bought with magnet cost, so dee-gap and magnet-gap must be traded as one system, as in a next machine's gap decision.

chosen for the final design since this is the ordinary coaxial cavity and is more amenable to design ... was chosen as a compromise between voltage-holding ability and transit-time effects.

Oak Ridge National Laboratory, A Proposal for the Mc² Isochronous Cyclotron — ORNL-3540 (1963) — p. 174-176

Editorial note, tabletop extrapolation: Scale-free method: a dee-stem system is likewise a transmission line with machine-fixed dimensions and a few free ones - when sizing the planned higher-voltage dee (the 5-13 kV upgrade), name each free spacing's compromise pair in the design notes the way the source names theirs.

Checking of the model dimensions revealed a construction error of several percent in the spacing near the median plane ... a resonant frequency of 151.3 Mc/s was calculated for the model; this is within 4% of the measured value.

Oak Ridge National Laboratory, A Proposal for the Mc² Isochronous Cyclotron — ORNL-3540 (1963) — p. 177

Editorial note, tabletop extrapolation: Scale-free double duty: a bench mock-up of a next machine's dee/stem before the LDMOS amplifier arrives certifies the calculation and catches build errors - and while it sits on the bench, sweeping for higher-order modes and measuring Q are nearly free additions (dg-664).

Computed power loss in cavity 500 kW; Beam power 160 kW; Contingency 200 kW; total 860 kW

Oak Ridge National Laboratory, A Proposal for the Mc² Isochronous Cyclotron — ORNL-3540 (1963) — p. 180

Editorial note, tabletop extrapolation: The kilowatts are 810-MeV numbers; the structure sizes the planned 100-500 W LDMOS chain honestly - compute the resonator loss (dg-313), add beam and coupling loads, then carry contingency as a NAMED line of the source's ~30% class instead of hiding margin inside each estimate.

Thus, when a spark occurs in the cavity a large resistive load is reflected to the plates of the power amplifier and the tube plate current would decrease.

Oak Ridge National Laboratory, A Proposal for the Mc² Isochronous Cyclotron — ORNL-3540 (1963) — p. 182-183

Editorial note, tabletop extrapolation: Scale-free fault-mode-first design: dees spark at every scale, so choose a next machine's amplifier coupling for arc behavior, not just matched-condition efficiency - establish what YOUR coupling does to the device when the load arcs (some couplings raise device stress instead), then layer the protection accordingly (dg-338, dg-679). Directly relevant to protecting an LDMOS pallet.

Since the dee voltage in the experimental unit was limited to 10 kv, application of injection potentials of over 10 kv resulted in deceleration of ions between the accelerating electrode and the dee.

Howard (ed.), Electromagnetic Research Division Quarterly, period ending 31 December 1951 — ORNL-1269 (1952) — p. 47

Editorial note, tabletop extrapolation: Any source-bias or puller experiment must check the same ordering in ITS geometry: a dc extraction potential that overtops what the RF gap can supply runs the first gap backward. The check is signed potentials and timing at the actual gap - the source's inequality is that machine's instance of it, not a universal bound.

The dee voltage will undoubtedly be limited, though, by the spacing between the dee stems outside the vacuum tank, which is only 1.5" at one point

Howard (ed.), Electromagnetic Research Division Quarterly, period ending 30 September 1952 — ORNL-1383 (1953) — p. 23

Editorial note, tabletop extrapolation: For the LDMOS upgrade toward 5-13 kV dees, walk the whole RF path on BOTH sides of the wall - feedthroughs, stem gaps in air, coupling hardware, creepage across insulator surfaces, and the vacuum-side gaps and multipactor windows - and let field analysis, ratings and conditioning tests say which limit binds first; the cited machine's air-side cap is one historical outcome, not a law.

Since this circuit depends upon the electrical characteristics of the resonant dee system, it cannot be designed until these characteristics are determined.

Howard (ed.), Electronuclear Research Division Semiannual, period ending 20 September 1953 — ORNL-1663 (1954) — p. 18

Editorial note, tabletop extrapolation: The template for the reference machine's LDMOS upgrade - freeze the amplifier and dee-resonator designs, but specify the matching/coupling network only after measuring the real dee system's f0, Q, and shunt impedance on the bench. Ordering the coupling parts first is the classic mistake this rule prevents.

The whole dee system is insulated from ground so that a bias potential may be applied to control ion loading.

Howard (ed.), Electronuclear Research Division Semiannual, period ending 20 September 1953 — ORNL-1663 (1954) — p. 18

Editorial note, tabletop extrapolation: The reference machine already uses dee bias; the design rule for a next machine is to make bias a first-class requirement - insulate the dee-stem support (see the ornl-1884 cantilever-on-insulators execution) rather than retrofitting isolation later.

The removal of the flat shims from the tank increased the magnet gap to 13 1/2 in. and provides sufficient clearance to permit operation of the dees at a potential of 100 kv.

Howard (ed.), Electronuclear Research Division Semiannual, period ending 20 September 1953 — ORNL-1663 (1954) — p. 18

Editorial note, tabletop extrapolation: For a next machine the same ledger applies at 5-13 kV: dee-to-liner spark distance plus dee aperture plus liner clearances must fit inside the gap, and gap given to voltage clearance is field taken from energy - in the gap-dominated, fixed-ampere-turn regime (dg-021's measured caveat on the ideal scaling). Decide voltage and gap together (dg-181).

Beam radius, in. 11 / 20; Proton energy, Mev 1.5 / 4.9; Magnetic field, oersteds 6400; Magnet gap, in. 13.5; Maximum dee-to-dee potential, kv 100; Frequency, megacycles/sec 9.7 (spec table, condensed)

Howard (ed.), Electronuclear Research Division Semiannual, period ending 20 September 1953 — ORNL-1663 (1954) — p. 18

Editorial note, tabletop extrapolation: The nearest professional sibling to a next machine in this collection - same ~0.64 T field class and ~9.7 MHz as the reference machine's 0.59 T / 9 MHz. Use it to sanity-check B-f consistency; note the 100 kV (vs ~1.3 kV) buys energy per turn and fewer turns - less phase slip and interception - while the energy-radius relation stays set by the field.

Dees were simulated by a capacitor connected from the end of each dee stem to ground... Other circuit components were selected to have approximately the same values as those in a full-scale operation.

Howard (ed.), Electronuclear Research Division Semiannual, period ending 20 September 1953 — ORNL-1663 (1954) — p. PDF p. 19 as cited (printed p. 10, section 'VARIABLE-ENERGY HEAVY-PARTICLE CYCLOTRON')

Editorial note, tabletop extrapolation: A bench-scale dee-stem mockup (pipe sections plus padding capacitors) lets the next machine's oscillator/coupling scheme be raced against alternatives for pocket change - the same measure-on-model philosophy as the deferred filament-coupling rule, one report earlier in hardware form.

This circuit consists of a coil and variable capacitor connected in series, plus the inherent resistance of both elements. The magnetic coupling between the dee stems and secondary circuit results in an impedance being reflected into the dee stems from the secondary. ... A resonant frequency varying from 6 megacycles to 12 megacycles was achieved with the particular circuit tested. ... the resonant impedance of the dee stems varies markedly with the frequency due to the comparatively low 'Q' of the secondary circuit.

Howard (ed.), Electronuclear Research Division Semiannual, period ending 20 September 1953 — ORNL-1663 (1954) — p. 19

Editorial note, tabletop extrapolation: Relevant if a next machine ever adds a variable-frequency or remote trim element: any lossy tuning appendage coupled to the dee resonator drags its shunt impedance (hence dee voltage per watt) across the tuning range - minimize tuner loss and measure loaded Q and shunt impedance over the whole range, whatever the tuner's construction.

The error of the control in tuning the oscillator to the frequency of the secondary is of the order of 0.1%.

Howard (ed.), Electronuclear Research Division Semiannual, period ending 20 March 1954 — ORNL-1670 (1954) — p. 24

Editorial note, tabletop extrapolation: A 1954 peak-hold autotune implementable today in a microcontroller: sweep the exciter, record the dee pickup peak, re-sweep and lock. Two scope-of-validity notes: it locks to the CAVITY resonance, not to the beam-synchronous f = qB/(2*pi*gamma*m) - the field still sets that independently; and 0.1% was demonstrated unloaded, so validate peak detection and drift on the beam-loaded resonator before trusting it.

at an r-f load of 100 amp per lineal inch, the temperature rise could be held to less than 10 C by a water flow of only 0.5 gpm.

Howard (ed.), Electronuclear Research Division Semiannual, period ending 20 September 1954 — ORNL-1795 (1954) — p. 23

Editorial note, tabletop extrapolation: For a next machine's shorting planes and tuning bars, compute the actual RF surface current at the contact, then validate the joint thermally at that current and duty - the cited numbers say such joints are buildable, not that 100 A/in is free. The material lesson (plate stainless with copper; bare SS is an RF resistor) is sound skin-effect physics at any scale.

The whole dee system is supported by a cantilever mounting at the outer end of the dee stems. This mounting is supported on insulators in order to permit the application of a bias potential to the dees.

Howard (ed.), Electronuclear Research Division Semiannual, period ending 20 March 1955 — ORNL-1884 (1955) — p. 19

Editorial note, tabletop extrapolation: An attractive pattern for a next machine: one stiff cantilevered dee-stem mount outside the field region, isolated for DC bias, is mechanically simpler than distributed insulated supports. Design the RF side separately - insulating the mount enables bias but does not by itself define the RF return path, so engineer the ground plane, bypassing and bias feed network explicitly, and check insulator loading and flashover.

Dee-to-dee r-f voltage (design), kv 200; Threshold voltage for N5+, kv 110 (Table 3, condensed)

Howard (ed.), Electronuclear Research Division Semiannual, period ending 20 March 1955 — ORNL-1884 (1955) — p. 20

Editorial note, tabletop extrapolation: Margin philosophy consistent with the 63-inch's 75-vs-60 kV acceptance hold (ornl-1339): documented machines bought well over threshold. For the LDMOS upgrade, compute the threshold dee voltage for the intended turn count and buy real headroom - documented precedents cluster around 1.3-2x. What the margin purchases (orbit count, loading headroom, species reach) is the editorial reading, not the table's statement.

the pulses are obtained in a way which makes them insensitive to beam current changes, and b) all reference pulses are smooth and identical in shape.

Fulbright et al., A Fast Neutron Time of Flight System for Use with Cyclotrons — NYO-9360 (1962) — p. 6

Editorial note, tabletop extrapolation: The most directly transferable finding here: the machine's RF is a free, stable timing fiducial at any scale - clock gated counting and TOF off a capacitive sniff of the dee. A fiducial is not a beam-arrival timestamp: beam phase relative to the RF moves with field tuning, loading and cable delays, so calibrate the offset against a real beam signal - and re-calibrate after retuning - before treating RF zero-crossings as beam time.

The output pulses are made about 10 volts high. Their rise time is of the order of 5 ns or less. ... When the cyclotron is operating at about 10 mc the shortest rise time available is about 3 ns, according to sampling oscilloscope observations.

Fulbright et al., A Fast Neutron Time of Flight System for Use with Cyclotrons — NYO-9360 (1962) — p. PDF 8 (printed 4) for the antenna and harmonic-mixture sentences; PDF 9 (printed 5) for the 10 V / 5 ns / 3 ns figures; PDF 10 (printed 6) for the retune time

Editorial note, tabletop extrapolation: Buildable on the reference machine: loose capacitive pickup plus stub-phased harmonic mixing sharpens the oscillator's waveform into a fast edge with zero active electronics at the pickup - noting a passive stub network can only re-phase and weight harmonics ALREADY in the picked-up signal (an oscillator's tank waveform has them; a purified sine does not). Check the pulse shape after every retune, and measure the actual 10-90% rise rather than assuming the vintage figure.

stop trigger pulses emerge only after an event occurs in the neutron detector.

Fulbright et al., A Fast Neutron Time of Flight System for Use with Cyclotrons — NYO-9360 (1962) — p. 8

Editorial note, tabletop extrapolation: The reversed (common-stop) architecture inverts the time axis and slashes unnecessary converter starts and their dead time (pileup in the detector chain is its own problem). With a modern TDC or digitizer you can instead timestamp both the detector and RF streams continuously and form differences offline - the gated arrangement remains the right shape for TAC-style hardware.

In our case reducing the frequency of beam pulses to about 3 mc can virtually eliminate the problem.

Fulbright et al., A Fast Neutron Time of Flight System for Use with Cyclotrons — NYO-9360 (1962) — p. 16

Editorial note, tabletop extrapolation: Check overlap arithmetically for the actual spectrum and flight path - t[ns] ~ 72.3*L[m]/sqrt(E[MeV]), so even an all-sub-MeV spectrum overlaps at a 10 MHz rate over a 1 m path, and D-D work adds multi-MeV neutrons on a sub-MeV machine. The subharmonic plate pair is a genuinely cheap cyclotron chopper for periodic bunch rejection and duty-cycle control - single-bunch selection needs a gating scheme beyond a sinusoidal drive - and the odd/even zero-crossing subtlety is real circuit physics worth teaching.

In order to simplify tuning procedures the scaler system was designed with a minimum of tuned circuits; there is only one, the tank circuit associated with the beam deflection plates.

Fulbright et al., A Fast Neutron Time of Flight System for Use with Cyclotrons — NYO-9360 (1962) — p. 17

Editorial note, tabletop extrapolation: Every tuned circuit is a knob someone must retune at every frequency change - minimize them by design. On timing: the cited system took its precision edge directly from the oscillator, a sound default; a modern divider or PLL can carry timing when its phase error and jitter are characterized against the experiment's budget - the rule is budget-the-jitter, not never-divide.

Performance of the model is considered sufficiently satisfactory to proceed with the full scale design and construction based on the model dimensions.

Anderson, Half-Scale Model Tests on the Three Quarter Wave R.F. System — UCRL-31 (1947) — p. 16

Editorial note, tabletop extrapolation: A next machine's dee/stem/tank is already benchtop-sized, so the transferable form is the mockup itself — a cheap RF-only copy (no vacuum) of the dee-liner geometry, swept with a VNA before the vacuum parts are machined. Same lineage as UCRL-64 and MDDC-1045 already in this collection.

Cited in: Choosing Your Machine

Only the radio frequency circuit was simulated in the model, the vacuum system and purely mechanical equipment was not included. Insulation required for the application of bias voltage to the dee and condenser rotor was not included as it had no radio frequency function.

Anderson, Half-Scale Model Tests on the Three Quarter Wave R.F. System — UCRL-31 (1947) — p. 7

Editorial note, tabletop extrapolation: License to mock up the next machine's RF cavity in bare copper/aluminum on a bench plate - no chamber, no pumps - provided every electromagnetic boundary that shapes the mode is reproduced: RF-current surfaces (liner included), coupling structures, and any dielectric near high fields. A bare-metal model validates resonance and field geometry; Q, loss and breakdown under vacuum still need the real thing.

For 30 kv on the full scale system the above power input figures become 146 kw at 9.25 mc, 132 kw at 12 mc, 146 kw at 15 mc, and 98 kw at 23 mc for continuous operation.

Anderson, Half-Scale Model Tests on the Three Quarter Wave R.F. System — UCRL-31 (1947) — p. 15

Editorial note, tabletop extrapolation: The V^2 term is the live part for power budgeting: measured drive power at a safe low dee voltage extrapolates as (V_target/V_test)^2 on the SAME matched, linear, unloaded cavity - so a 1500-V measurement anchors the 5-13 kV LDMOS requirement, with beam/plasma loading, thermal drift of losses and amplifier efficiency budgeted on top, and the extrapolation ending where multipactor or breakdown begins.

These were the capacity presented to the dee by the dummy dee, the minimum capacity of the rotor, and the inductance at the throat of the dee.

Anderson, Half-Scale Model Tests on the Three Quarter Wave R.F. System — UCRL-31 (1947) — p. 10

Editorial note, tabletop extrapolation: Direct checklist for why a tank on the reference machine or a next machine does not resonate where the lumped-element estimate says — dummy-dee proximity, feedthrough/trimmer minimum C, and stem-to-dee transition inductance are the three knobs.

the insertion of the dummy dee had dropped the upper frequency limit from 48.8 to 44.5 mc, and the lower limit from 19.9 to 18.8 mc

Anderson, Half-Scale Model Tests on the Three Quarter Wave R.F. System — UCRL-31 (1947) — p. 9

Editorial note, tabletop extrapolation: Final RF tuning of a next machine's cavity must be done with dummy dee, source structure, and probes installed - the model's single grounded dummy dee moved the band edges ~9%, and each added structure perturbs by its own amount: measure or simulate the shift for the actual geometry rather than budgeting any particular percentage in advance.

a shorted stub - a section of transmission line less than a quarter wave length at 50 mc - was connected to each side of the dee.

Anderson, Half-Scale Model Tests on the Three Quarter Wave R.F. System — UCRL-31 (1947) — p. 9

Editorial note, tabletop extrapolation: The recovery plan if a next machine's fixed-frequency cavity misses its target after assembly. Both fixes tax drive power, and the directions dictate the design bias: aim the design HIGH in frequency if you want to trim with the cheaper capacitive side (which only moves frequency down), or low if you accept stub-trimming up. The cited shift/power figures are that cavity's calibration, not guaranteed ranges.

This region is a current maximum point at the highest frequency and most sensitive to volume or inductance.

Anderson, Half-Scale Model Tests on the Three Quarter Wave R.F. System — UCRL-31 (1947) — p. 10

Editorial note, tabletop extrapolation: On a small machine the dee-stem-to-chamber-wall clearance is the candidate critical region - it plausibly sets both the resonant frequency and where I^2R heating concentrates. Confirm with an eigenmode/surface-current calculation (or low-power RF measurement with a thermal camera) for the actual cavity, then machine that region to drawing rather than shimming by eye.

The dee voltage must be at least twice the d.c. plate voltage. 2. The oscillator must be stable enough to sustain an arc drawn from the dee face (simulating discharges in that region). ... 4. The phasing capacity, as calculated in MacKenzie's report ..., should be as near [the calculated value] as possible.

Anderson, Half-Scale Model Tests on the Three Quarter Wave R.F. System — UCRL-31 (1947) — p. 12

Editorial note, tabletop extrapolation: The requirement transfers as a criterion, not a procedure: the planned LDMOS amplifier must demonstrably survive dee-side arcs before it is trusted in vacuum, where conditioning sparks are guaranteed. For solid-state that means proving the protection chain - VSWR trip, drain clamping, fast drive-cut (dg-338, dg-679) - against controlled fault tests, not drawing an open arc onto an unprotected amplifier the way the 1947 tube crews could.

A deviation of an inch or two one way or the other will cause this response to rise or fall at either end of the range.

Anderson, Half-Scale Model Tests on the Three Quarter Wave R.F. System — UCRL-31 (1947) — p. 13

Editorial note, tabletop extrapolation: Even a fixed-frequency amateur system inherits this through the amp-to-dee coax and its stray resonances: sweep the ASSEMBLED feed system, not just the cavity, and choose line lengths from the measured input impedance and matching bandwidth at the operating frequency. The cited inch-scale sensitivity belongs to that swept resonant feedline - your system's sensitivity scale comes out of your sweep.

the original ones used were resonant at 18 mc, which may account for a sharp drop observed in the dee voltage ... The coils were rewound and made resonant at 60 mc after which the voltage drop was no longer noticed.

Anderson, Half-Scale Model Tests on the Three Quarter Wave R.F. System — UCRL-31 (1947) — p. PDF p.13 (printed p.-10-)

Editorial note, tabletop extrapolation: Filament, bias, meter, and interlock leads entering the tank all need chokes whose behavior is MEASURED across the operating band - impedance or insertion loss over the whole band, not just the self-resonant frequency - because a choke resonant near the operating frequency silently loads the dee.

Ratio Max-capacity/Min-capacity = 1370/50 = 27.6

Anderson, Half-Scale Model Tests on the Three Quarter Wave R.F. System — UCRL-31 (1947) — p. 14

Editorial note, tabletop extrapolation: Same differential technique as Koeth's Rutgers dee-capacitance note in this collection: an LCR meter plus one disassembly step estimates the selected lumped capacitances in a tank model - subject to fixture and stray-capacitance errors, which set how many elements one subtraction chain can honestly resolve.

the errors in readings should be assumed to be +/- 5 to 10 percent. ... For power measurements, a Leeds and Northrup optical pyrometer, Cat. #8622-C, was used to observe plate dissipation in the triodes. ... In using the optical pyrometer, one spot on one plate of a triode was selected as the comparison point. The excitation was removed by connecting the plate line to the oscillator housing so that no r.f. currents would flow and all the power input would appear in the plates of the triodes.

Anderson, Half-Scale Model Tests on the Three Quarter Wave R.F. System — UCRL-31 (1947) — p. 8

Editorial note, tabletop extrapolation: The thermal-reference trick survives translation with a defined reference plane: calorimetry on the LDMOS heatsink (or dee cooling loop) calibrated at DC gives THE HEAT INTO THAT PATH - write the full power balance (P_RF_out = P_DC - P_device - other paths) with matched thermal boundary conditions and steady state before quoting an output power; and publish instrument error bars the way Anderson did.

the inductance inherent in the 304-TL triodes is large compared with that in the 9C21 triodes to be used in the final oscillator. ... The power measurements at this stage in the experiments were found to be very inaccurate due to differences in plate capacity on the two 304-TL triodes and the consequent difference in distribution of r.f. currents.

Anderson, Half-Scale Model Tests on the Three Quarter Wave R.F. System — UCRL-31 (1947) — p. 12

Editorial note, tabletop extrapolation: When bench-testing a next machine's RF with a stand-in amplifier or without the real chamber wall, write the fidelity caveats into the test log - the model predicts the cavity, not the parts that were substituted. (The filament-line impedance discontinuity previously listed here is dropped pending re-read - the scan discusses filament-line length effects but not that specific claim.)

volts per turn substantially lower than the designed 280 kev/turn would result in sharp reduction of both extraction efficiency and optical quality.

Blosser & Gordon, Computational Study of a Resonant Extraction System for a 3-Sector Cyclotron — MSUCP-9 (1961) — p. 45

Editorial note, tabletop extrapolation: The quantitative ancestor of 'dee volts buy extraction': the reference machine's uncalibrated ~1.3 kV dee is one reason it is internal-beam-only, and a next machine's 5-13 kV target is what would make an extraction scheme thinkable - thinkable, not feasible, until the turn separation (delta_r ~ r*delta_E/2E), phase width, septum clearance, tune and bump design are actually computed.

The sinusoidal voltage, it is seen, shifts the final position of the beam spot but has almost no effect on the distortion.

Blosser & Gordon, Computational Study of a Resonant Extraction System for a 3-Sector Cyclotron — MSUCP-9 (1961) — p. 40

Editorial note, tabletop extrapolation: A permission slip for CYCLOPS-lite staging — start with constant energy gain per gap to get the radial dynamics right, then add cos(phi) gain and phase slip as a second-stage refinement, checking that conclusions survive.

Table 1. k/h = 0.1: at x/h = 0, E/(V0/h) = 0.99388 [values verified against page image]

Beal, Computation of Electric Field and Potential of an Idealized Dee Geometry — MSUCP-12 (1961) — p. 11

Editorial note, tabletop extrapolation: Sets the ceiling on CENTERLINE gap field for a dee redesign: with a 1-inch aperture (h = 0.5 in) and 2.5 kV dee-to-dummy, the median-plane peak cannot exceed ~2 kV/cm however tight the gap. Two cautions: local surface fields at electrode edges run above the centerline value - breakdown cares about those (dg-353) - and widening the aperture trades centerline field for beam height by the table's factors, not one-for-one at every k/h.

Table 1, k/h = 0.1: V/V0 = 0.73760 at x/h = 1.0, 0.94468 at 2.0 [verified against page image]

Beal, Computation of Electric Field and Potential of an Idealized Dee Geometry — MSUCP-12 (1961) — p. 11

Editorial note, tabletop extrapolation: Transit-time factors and gap-crossing phase errors must be computed on this extended profile - and whether a delta-kick model is adequate is the transit parameter's call: evaluate omega*L_eff/v for the actual first-turn velocities and the ~2h-long field region, and let that number, not a blanket assumption, decide when the distributed kick is needed.

Table 1, k/h = 2.0: E/(V0/h) = 0.37823 at x/h = 0, maximum 0.38966 at x/h = 1.2 [verified against page image]

Beal, Computation of Electric Field and Potential of an Idealized Dee Geometry — MSUCP-12 (1961) — p. 16

Editorial note, tabletop extrapolation: Kills the tempting E = V_dee/gap for FIELD estimates on a next machine's geometry, where gap and aperture are the same order (k/h ~ 1) and neither limiting approximation holds - use the formulas or tables for the profile. Energy gain is a different question: absent transit-time effects the work across the gap is q*V0 whatever the profile; the profile changes transit-time factors and where field concentrates - and the surface fields at electrode edges, which the breakdown margin actually cares about (dg-353, dg-1028).

Commercial mu metal shields, if properly used, will normally provide sufficient shielding against magnetic fields. To eliminate the effects of RF fields, aluminum foil or screening can be used.

Martin (ed.), Accelerator Radiation Protection — AD-755510 / USA-NLABS-TR-73-7, US Army Natick Laboratories (1972) — p. 128

Editorial note, tabletop extrapolation: Written for exactly such a bench: a scintillator PMT near a 0.6 T magnet's fringe field and a 9 MHz (soon LDMOS) transmitter. 'Properly used' is load-bearing - mu-metal saturates in strong fields and PMT gain moves at millitesla - so position the PMT where the fringe field is already small, shield, and verify gain with a check source in place; confirm RF quieting with the transmitter actually running. The Keithley 617 grounding lore in the reference machine's as-builts is this rule independently rediscovered.

The capacitor housings have separate vacuum systems using turbomolecular pumps. RF feed through insulators separate them from the main cyclotron vacuum system.

Rainwater et al., The Columbia University Nevis Synchrocyclotron Major Modification — NEVIS-189 / R-774 / CU-295 (1971) — p. 10

Editorial note, tabletop extrapolation: Scales down as a case-by-case method: a sealed partition (like Nevis's insulator barrier) actually isolates the gas load; an OPEN differentially pumped appendage - the reference machine's diff-pumped source region - only reduces transfer through its conductance. Pick per mechanism from a conductance and gas-load estimate, and remember debris control is geometry, not pumping.

the rotors are at low RF due to their < 0.010 in. high capacitance face gaps to ground

Rainwater et al., The Columbia University Nevis Synchrocyclotron Major Modification — NEVIS-189 / R-774 / CU-295 (1971) — p. 10

Editorial note, tabletop extrapolation: The capacitive-shunting method transfers to rotating RF machinery (choppers, tuners) - by calculation, not copying: work out the gap capacitance (area and gap, not gap alone), the induced rotor voltage and displacement current at the actual frequency and power, and the field/breakdown margins in vacuum. The rotating-capacitor FM tuner itself is synchrocyclotron-specific and does NOT transfer to a fixed-frequency tabletop machine.

The basic variation of line Zo along the resonator tends to minimize the capacitor Cmax/Cmin ratio needed. Inductance effects in the structure at the RF frequency considerably increase the effective Cmax value. It is expected that the full scale capacitors will each have Cmax = 6.5 nF and Cmin = 1.3 nF (measured at 1000 Hz).

Rainwater et al., The Columbia University Nevis Synchrocyclotron Major Modification — NEVIS-189 / R-774 / CU-295 (1971) — p. 9

Editorial note, tabletop extrapolation: FM machinery itself does not transfer, but the impedance-profiling option applies to any tunable tank or swept/trimmed cavity: model the resonator as a transmission line and let the optimization pick the profile - Nevis's own is nonmonotonic, so 'taper' is the idea, not the shape.

a half-wave resonator permits the rotating capacitors to be located outside the main vacuum chamber for good shielding from both the magnetic field and radiation

Rainwater et al., The Columbia University Nevis Synchrocyclotron Major Modification — NEVIS-189 / R-774 / CU-295 (1971) — p. 10

Editorial note, tabletop extrapolation: The placement principle transfers: keep variable capacitors, trimmers and drive mechanisms of a next machine's tank outside the pole gap and chamber, where field, beam spray and pumpdown cannot reach them - where the geometry allows it.

The design has used a 1/2 scale model, in conjunction with detailed computer calculations, to establish all parameters which can be varied

Rainwater et al., The Columbia University Nevis Synchrocyclotron Major Modification — NEVIS-189 / R-774 / CU-295 (1971) — p. 9

Editorial note, tabletop extrapolation: At tabletop size the "scale model" is the full-size mockup on the bench — cold-test a next machine's dee/stem with a VNA before power exists; the mode-spectrum audit transfers verbatim.

The dee resonator will be dc floating so a negative bias of amount sufficient to control multipacting can be applied.

Rainwater et al., The Columbia University Nevis Synchrocyclotron Major Modification — NEVIS-189 / R-774 / CU-295 (1971) — p. 10

Editorial note, tabletop extrapolation: Directly relevant at a next machine's planned 5-13 kV dees, where multipactor bands are widest: a 1971 operating-lab remedy with a concrete magnitude to scale from. Bias works by breaking the multipactor resonance condition; what trajectories do in detail depends on the local fields, so 'sufficient to control' is found empirically - exactly as Nevis wrote it.

a slow linear reduction (turn off) of the RF amplitude there will result in a near adiabatic spreading out of the phase angle

Rainwater et al., The Columbia University Nevis Synchrocyclotron Major Modification — NEVIS-189 / R-774 / CU-295 (1971) — p. 5

Editorial note, tabletop extrapolation: Swept-frequency machinery, not fixed-frequency CW territory - the design space it illustrates (adiabatic capture, slow parameter ramps judged against the phase-oscillation period, not a fixed microsecond count) belongs to any future synchro- or synchrotron-class RF program.

The Q of the model will be 0.7 times the Q of the actual installation and so will require 1.4 times as much power for a given dee voltage.

MacKenzie, Preliminary Report on the “Three Quarter Wave” R.F. System for Frequency Modulated Cyclotrons — AECD-1850, University of California (1947) — p. 6

Editorial note, tabletop extrapolation: Bench-model a dee-stem or resonator geometry at reduced size before cutting full-size copper, applying the sqrt(scale) Q correction to power comparisons - and determine coupling separately, from impedance or measured external Q: the power ratio says nothing directly about what a tap or loop must pick up.

It was not excited satisfactorily due to the fact that at 100 megacycles the transit time effects were quite noticeable on the fundamental mode.

MacKenzie, Preliminary Report on the “Three Quarter Wave” R.F. System for Frequency Modulated Cyclotrons — AECD-1850, University of California (1947) — p. 6

Editorial note, tabletop extrapolation: Cold measurements scale approximately - eigenfrequencies and field patterns follow geometry, while Q, losses, contacts and probe loading need corrections or direct measurement. Any POWERED model test needs a driver checked for transit angle and loading at the model frequency; otherwise the model exhibits modes the real system never sees, and vice versa.

dimensions can be calculated fairly exactly whereas in the system shown in Figure 5 one must depend on model tests (which are safer anyway).

MacKenzie, Preliminary Report on the “Three Quarter Wave” R.F. System for Frequency Modulated Cyclotrons — AECD-1850, University of California (1947) — p. 6

Editorial note, tabletop extrapolation: Transmission-line formulas ignore end effects, bends, and support hardware; for any resonator whose geometry is not a textbook line, a cheap model measurement outranks the calculation it checks.

excited by a separate oscillator ... It was suppressed with 2 wavetraps slightly staggered in tuning to cover a small frequency band ... A total of 6 wavetraps sufficed to suppress all unwanted modes throughout the proton range. The parasitic modes were not completely eliminated, however, when the dee was shorted, as would occur in a discharge.

MacKenzie, Preliminary Report on the “Three Quarter Wave” R.F. System for Frequency Modulated Cyclotrons — AECD-1850, University of California (1947) — p. 7

Editorial note, tabletop extrapolation: Sweep the assembled dee/stem/liner system with a signal generator and probe before first power-up; every resonance within the amplifier's gain bandwidth is a candidate parasitic. Repeat the survey for fault-like boundary conditions - a dee spark momentarily retunes the system into modes the clean census missed, exactly the source's shorted-dee exception.

It was found that the parallel mode was discouraged by grounding the supports ... two of them require that large currents flow in the rotor supports, which can be made fairly high resistance. These modes are therefore not excited in favor of the much higher Q correct mode.

MacKenzie, Preliminary Report on the “Three Quarter Wave” R.F. System for Frequency Modulated Cyclotrons — AECD-1850, University of California (1947) — p. 7

Editorial note, tabletop extrapolation: Mode-selective damping - resistance placed at a current maximum of the unwanted mode and a current null of the wanted one - is a powerful alternative to tuning the parasite out of band. Verify with a current map that the wanted mode's null is real (an imperfect null costs Q), and check the resistive element's dissipation and temperature at power.

the insulators will be subjected to about 3 times the rotor voltage to ground. This is because the long metal supports act as open transmission lines

MacKenzie, Preliminary Report on the “Three Quarter Wave” R.F. System for Frequency Modulated Cyclotrons — AECD-1850, University of California (1947) — p. 8

Editorial note, tabletop extrapolation: Check the electrical length of every support, cooling line, and instrument stalk inside the RF volume against its actual return path and termination (loaded lines behave differently from open ones): a mechanically convenient standoff can sit at a voltage antinode and flash over at dee voltages its rating should easily hold. The 3x is MacKenzie's installation, not a universal factor - model or measure your own.

The oscillating circuit actually is a long folded transmission line consisting of the two rows of meshed teeth.

MacKenzie, Preliminary Report on the “Three Quarter Wave” R.F. System for Frequency Modulated Cyclotrons — AECD-1850, University of California (1947) — p. 16

Editorial note, tabletop extrapolation: The diagnostic transfers as a leading suspect, not a verdict: a sharp frequency-specific dead spot MAY be a resonant conductor assembly (screen, liner seam, feedthrough array) - confirm with low-power sweeps, probing or damping tests before modifying the structure, since matching faults, mode coupling and measurement artifacts produce nulls too. When confirmed, fix by shortening or breaking up the structure, not by driving harder.

if the frequency of the transverse mode is still higher than the fundamental when the teeth are fully meshed, then the transverse frequency will always lie above the fundamental for any partially meshed position.

MacKenzie, Preliminary Report on the “Three Quarter Wave” R.F. System for Frequency Modulated Cyclotrons — AECD-1850, University of California (1947) — p. 16

Editorial note, tabletop extrapolation: For any tunable element (trimmer panel, movable shorting plane): where analysis or a coarse sweep establishes that the mode separation varies monotonically with travel, one measurement at the converging extreme clears the range; otherwise sweep the full travel and watch for additional or avoided crossings.

over about a 2 to 1 frequency shift, the voltage on the 1/4 wave-shorted line (which will be referred to as the "stub" line) is practically the same as the dee voltage.

MacKenzie, Preliminary Report on the “Three Quarter Wave” R.F. System for Frequency Modulated Cyclotrons — AECD-1850, University of California (1947) — p. 3

Editorial note, tabletop extrapolation: Even a fixed-frequency machine drifts with thermal expansion and plasma loading, and feeding at a voltage-stable point of the resonator helps - but a stable voltage RATIO is not constant drive impedance: detuning, Q and plasma loading still move what the amplifier sees, so measure the input impedance (or S11) across the expected drift and loading range before promising the amplifier anything.

start with the tap at the end of the stub line and then move toward the shorted end until the tube draws rated plate current at rated voltage.

MacKenzie, Preliminary Report on the “Three Quarter Wave” R.F. System for Frequency Modulated Cyclotrons — AECD-1850, University of California (1947) — p. 11

Editorial note, tabletop extrapolation: The walk-the-tap idea transfers as a method of converging on coupling empirically rather than committing to a computed position - executed safely: find the initial setting at low power or with a VNA, move taps only de-energized, approach the operating point with current limiting, and watch plate current AND dissipation AND reflected power together - rated plate current alone is one indicator, not proof of match, and the line's high-impedance end carries hazardous RF voltage.

End effects and bends in the line can cause this much variation. The conclusion is that there should be some possibility of varying the line length by a small amount

MacKenzie, Preliminary Report on the “Three Quarter Wave” R.F. System for Frequency Modulated Cyclotrons — AECD-1850, University of California (1947) — p. 11

Editorial note, tabletop extrapolation: Design connection lines and stubs with a sliding section or trombone whose travel comes from a tolerance analysis (component-value uncertainty, bends, end effects) or a prototype sweep - the calculation gets you to the right neighborhood and the adjustment does the rest.

the shift is reduced by making the filament grid capacity large, so that the out of phase r.f. current will be large compared with the in phase electron emission current. ... Hence we might expect total phase shifts around 25° ... this shift of 25° can not be increased very much without seriously impairing efficiency.

MacKenzie, Preliminary Report on the “Three Quarter Wave” R.F. System for Frequency Modulated Cyclotrons — AECD-1850, University of California (1947) — p. PDF p. 12 (printed 11) for the card's current quote; PDF p. 14 (printed 13) for the ~25° limit

Editorial note, tabletop extrapolation: The mechanism matters for any self-excited tube oscillator on a dee - drive phase error costs efficiency - and padding the input capacity is a candidate fix, not a free one: the added reactive current changes loading, bandwidth and possibly parasitic resonances, so verify the full input network after the change. Check total drive phase with an incident/reflected-wave measurement.

The 1/2 scale model uses about 400 watts input to the oscillator at 48 megacycles and 600 watts input at 18 megacycles to produce 1500 volts on the dee.

MacKenzie, Preliminary Report on the “Three Quarter Wave” R.F. System for Frequency Modulated Cyclotrons — AECD-1850, University of California (1947) — p. 16

Editorial note, tabletop extrapolation: Dee power scales as voltage squared: measure watts-per-volt-squared on the bench and the amplifier requirement for any target voltage falls out. Mind the quantity - the model figures are OSCILLATOR INPUT, so the scaled 28-42 kW carries the model oscillator's efficiency inside it: separate wall loss from drive-chain overhead when budgeting a modern amplifier (dg-313, dg-316), and budget for joint quality and surface material shifting Q.

the R. F. dee voltage was lowered to approximately 50% of its normal value which is less than the threshold voltage.

Cyclotron Staff, Report of Cyclotron Operation 1 July – 31 December 1969 — NRL Memorandum Report 2103, Naval Research Laboratory (1970) — p. 23

Editorial note, tabletop extrapolation: The concept transfers as an experiment, not a guarantee: measure the machine's own beam-versus-dee-voltage curve first (reduced RF can merely move the loss radius inward rather than extinguish ions), verify with a detector that the gated state is beam-off to the level the measurement needs, and check where the residual beam goes. Where true interruption matters, gate the source. Stepping the regulator's dc reference is the clean actuator either way.

The filament voltage of the 6949V1 must be raised slowly from zero to the normal operating value to prevent filament current from exceeding a value of 1,700 amperes, even momentarily.

Cyclotron Staff, Report of Cyclotron Operation 1 July – 31 December 1969 — NRL Memorandum Report 2103, Naval Research Laboratory (1970) — p. 24

Editorial note, tabletop extrapolation: Scales down to any transmitting tube or big thoriated filament: follow the tube maker's warm-up and inrush limits with a soft-start rated for the actual current (variac ramp; an NTC only where its rating and cool-down behavior fit). Guarding against the loose-socket failure (a dropout then full voltage on a cooled filament) is sound engineering - implement it as a properly coordinated undercurrent trip with startup inhibit, as a design addition rather than NRL doctrine.

The four PAA tuning capacitors are now coupled together by a heavy-duty chain driven by a single large servo motor with one translator. No trouble has been experienced since this modification. Formerly, each of the four capacitors was driven by its separate servo motor with a pair of servo motors being fed by one of the two translators. This had resulted in capacitors being driven to unequal capacities upon the loss of a signal from a translator for any of several reasons. This then necessitated the removal of the capacitors to reset them for equal capacity tracking which is required for equal sharing of the RF current and for maximum tuning range.

Cyclotron Staff, Report of Cyclotron Operation 1 July – 31 December 1969 — NRL Memorandum Report 2103, Naval Research Laboratory (1970) — p. 24

Editorial note, tabletop extrapolation: Wherever two adjustments must hold a FIXED mechanical relationship (paired trimmers, symmetric shorting planes), a shaft, chain, or belt enforces the constraint by construction, with backlash and stretch as the residual error terms; keep independent trim where the relationship must be calibrated rather than fixed - software matching isn't doomed, but it reintroduces the desync failure class the chain removed.

The output voltage of the radio-frequency oscillator for the cyclotron proved to vary with frequency and to contain undesired frequency components. At some particular operating frequencies, the undesired frequencies appeared as modulation of the dee voltage and could not be eliminated. These problems were solved by replacing the oscillator with a frequency synthesizer. ... The modulation on the dee voltage, defined as the peak-to-peak ripple riding on the RF voltage as a percentage of the peak RF value, has recently been reduced to about 0.5% from 1.5%.

Cyclotron Staff, Report of Cyclotron Operation 1 July – 31 December 1969 — NRL Memorandum Report 2103, Naval Research Laboratory (1970) — p. 25

Editorial note, tabletop extrapolation: Dee-voltage ripple modulates per-gap energy gain (and, through phase slip, orbit phase where the machine is off-isochronous); put the envelope from a calibrated RF pickup on a scope, log the percentage, and remember the excitation source - a cheap generator's spurs included - is a candidate cause before blaming the amplifier or resonator.

Changes in the cooling water path for the 6949V1 anode increased the flow rate sufficiently that the allowable anode dissipation was doubled. This increased anode dissipation permits operation with higher dee voltages at the higher frequencies with a margin of safety for detuning of the anode circuit. ... we increased the flow rate to the 6949 tube plates from 42 gpm to 60 gpm by the addition of a 4-inch return pipe to separate the high pressure and low pressure water loops ... In an attempt to decrease future outages due to water pump failure, the mechanical and structural installation of a standby 200HP, 1400 gpm, 150 psi, demineralized water pump was completed with associated plumbing that places it in a parallel loop with the existing low pressure demineralized pump.

Cyclotron Staff, Report of Cyclotron Operation 1 July – 31 December 1969 — NRL Memorandum Report 2103, Naval Research Laboratory (1970) — p. 24, 29

Editorial note, tabletop extrapolation: When an amplifier cannot hold rated dissipation, check hydraulic head losses in shared manifolds before derating the tube; and duplicating a single-point-of-failure pump is a reliability purchase the outage ledger justifies - engineered in, with isolation valving and controls, not just teed into the pipe.

The holder ring was split to prevent eddy currents in the ring from rf (Ramsay, discussion of "Thick Targets for In-Beam Hyperfine Structure Study")

Fifth Annual Conference of the International Nuclear Target Development Society — LA-6850-C, Los Alamos Scientific Laboratory (1977) — p. 201

Editorial note, tabletop extrapolation: An internal target probe near the dee gap lives inside the machine's own RF field; a closed metal frame is a shorted turn that heats and perturbs. One saw cut interrupts the loop PROVIDED nothing bridges it - target foil, conductive deposits, or mounting hardware across the gap re-close the turn, and a narrow gap still passes some capacitive current - so verify RF heating after assembly.

in cyclotrons using a simple dee system as the tank circuit difficulties are encountered in getting the oscillator to break into full oscillation.

Fulbright, The Sparker, a Device to Overcome the Multipactor Difficulty in Starting the Oscillator of a Cyclotron — NYO-9359, University of Rochester (1961) — p. 2

Editorial note, tabletop extrapolation: DIRECT: this names the exact configuration of the reference machine - a simple dee system as the tank circuit - and matches its documented pattern of RF amplifiers failing to bring the dee to voltage. Multipactor loading in the ~100 V band is the report's named mechanism and a testable CANDIDATE cause, not a confirmed diagnosis: the bias and drive-through cures (dg-1274) double as the discriminating experiments.

multipactor loading, which occurs with voltages of the order of a hundred, cannot build up sufficiently to prevent the rise of voltage through the multipactor region.

Fulbright, The Sparker, a Device to Overcome the Multipactor Difficulty in Starting the Oscillator of a Cyclotron — NYO-9359, University of Rochester (1961) — p. 2

Editorial note, tabletop extrapolation: The decision menu for any machine that stalls in the multipactor band: bias, drive-through, or impulse shock. On a small machine the driven start maps to an external exciter ahead of the power stage; the bias cure maps to a DC offset on an insulated dee (dg-320, dg-805), with the magnitude found empirically.

The dee biasing scheme was considered too awkward to apply, chiefly because the variable frequency requirement had already led to a rather complicated mechanical design.

Fulbright, The Sparker, a Device to Overcome the Multipactor Difficulty in Starting the Oscillator of a Cyclotron — NYO-9359, University of Rochester (1961) — p. 2

Editorial note, tabletop extrapolation: Transferable decision pattern: on a machine whose dee stem is grounded through the tank structure, retrofitting DC bias means rebuilding the stem insulation, so Rochester's choice of an impulse starter is the additive option. Additive is not hazard-free: a shock starter is a high-voltage pulser coupled into an RF vacuum structure and needs a rated feedthrough, insulation and current limiting, grounding, an interlock, and a check for RF coupling and unintended arcs. Compare the two cures by the actual RF/HV insulation and safety design, not by port count. [Corrected 2026-08-23: earlier note said the starter "touches nothing but a spare port".]

the dee circuit begins to oscillate with a dee voltage amplitude of several hundred volts. The oscillator then begins to carry the voltage on up to its full value.

Fulbright, The Sparker, a Device to Overcome the Multipactor Difficulty in Starting the Oscillator of a Cyclotron — NYO-9359, University of Rochester (1961) — p. 3

Editorial note, tabletop extrapolation: One loop, one capacitor, one spark gap, one HV supply - a genuinely cheap cure for a stalled self-excited start. The transferable insight is that the kick need only clear the loading band, not deliver operating power; what that band and required amplitude ARE on a given resonator is a measurement, not an inheritance from the 27-inch.

Cited in: Driving the Dee: RF Coupling

The spark gap is adjusted so that the sparking rate is roughly two per second. Ordinarily a single spark will cause oscillation to commence.

Fulbright, The Sparker, a Device to Overcome the Multipactor Difficulty in Starting the Oscillator of a Cyclotron — NYO-9359, University of Rochester (1961) — p. 3

Editorial note, tabletop extrapolation: A sub-joule impulse sufficed on a 27-inch machine; what a smaller system needs follows from its dee capacitance, coupling efficiency and the voltage the kick must reach - calculate or measure it rather than scaling by size. The 30 kV charger is the one nontrivial part, and it must be a properly engineered, current-limited supply with the right polarity and isolation - a bare NST or flyback is a starting component, not the finished charger.

automatically turned on when the oscillator power is on and there is no dee voltage, but which is automatically turned off as soon as dee voltage appears.

Fulbright, The Sparker, a Device to Overcome the Multipactor Difficulty in Starting the Oscillator of a Cyclotron — NYO-9359, University of Rochester (1961) — p. 3

Editorial note, tabletop extrapolation: DIRECT automation pattern: gate the starter on (RF enabled) AND (dee pickup below threshold) - a dee voltage pickup is standard monitoring hardware, and where one exists it is exactly the signal needed. The same gate makes stalls detectable: a starter that keeps refiring means the machine is not coming up, so alarm on repeated firings, with the rate threshold chosen at the machine.

Because the loop is oriented at right angles to the axis of the cavity, the RF voltage induced in the loop is very small, even with full dee voltage.

Fulbright, The Sparker, a Device to Overcome the Multipactor Difficulty in Starting the Oscillator of a Cyclotron — NYO-9359, University of Rochester (1961) — p. 3

Editorial note, tabletop extrapolation: General principle for any starter or diagnostic coupling on a resonator: orient it weakly coupled to the operating mode - remembering reciprocity: a true null for pickup is a null for drive through the same port, so the impulse works through the residual coupling (and other current paths), which is fine because the required kick is small. Verify the coupling both ways, and rate the spark circuitry for the transients it will still see.

the envelope of the oscillations was found to fall smoothly until the dee voltage had fallen to a value roughly 1/3 its maximum, then for a short time to drop steeply, then afterward to decay slowly once again.

Fulbright, The Sparker, a Device to Overcome the Multipactor Difficulty in Starting the Oscillator of a Cyclotron — NYO-9359, University of Rochester (1961) — p. 4

Editorial note, tabletop extrapolation: A free diagnostic worth running: ring the dee (impulse or drive-and-release), scope the pickup envelope through a calibrated divider, and look for a kink - a steep-decay segment is a candidate multipactor band on YOUR machine. Corroborate with pressure and conditioning dependence before labeling it multipactor (other nonlinear losses kink envelopes too), and don't transfer the 1/3 ratio - localize your own band and compare it with the operating voltage.

Cited in: Driving the Dee: RF Coupling

Changing the tuning of the grid circuit changed the amplitude of spark-induced dee oscillation severalfold, which seems indicates the flow of considerable capacitative current through the oscillator tube.

Fulbright, The Sparker, a Device to Overcome the Multipactor Difficulty in Starting the Oscillator of a Cyclotron — NYO-9359, University of Rochester (1961) — p. 4

Editorial note, tabletop extrapolation: Two consequences, one caution: every branch circuit hanging on the resonator participates in the ring, so commission the starter at the operating tune, not on the bench. And the tube's passive capacitances were part of the tested path - a solid-state driver changes that path AND is far less transient-tolerant, so model the coupling with the PA's output network, isolate or disconnect the devices for first tests, and check transient ratings before calling the method transferred.

The ringing frequency of the current in the sparker loop was found to be about 12 mc, independent of the oscillator conditions. The amplitude of ringing is found to decay 50% in about 3 cycles.

Fulbright, The Sparker, a Device to Overcome the Multipactor Difficulty in Starting the Oscillator of a Cyclotron — NYO-9359, University of Rochester (1961) — p. 4

Editorial note, tabletop extrapolation: Sets expectations honestly: the shock cures the multipactor stall, not bad vacuum or a detuned feedback network - if a spark fails to start the machine, work the fault list (pressure, tune, outgassing state). Whether one fixed sparker covers a whole tuning range is a startup test at the band edges, not an assumption (trivially satisfied at fixed frequency).

partly because it was more convenient in our case since the dee chamber is rather crowded, and partly because we thought that the RF pickup problem would cause less trouble with inductive coupling.

Fulbright, The Sparker, a Device to Overcome the Multipactor Difficulty in Starting the Oscillator of a Cyclotron — NYO-9359, University of Rochester (1961) — p. 4

Editorial note, tabletop extrapolation: A useful trade note, not a theorem: in a small chamber where every square inch near the dee is contested, try a loop near the dee stem (outside the beam region) first - then MEASURE steady-state pickup and impulse coupling before fixing the location; whether inductive actually beats capacitive depends on the local field geometry and the mode.

The skin is of electrolytic high conducitvity copper with 1/4, 3/8, and 5/8" copper tubes silver soldered on the back side for water cooling.

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (1951) — p. 58

Editorial note, tabletop extrapolation: The construction vocabulary transfers as a menu, not a mandate: EHC copper skin with cooling sized from computed RF loss (a tabletop dee at tens of watts may need none), silver-plated joints where measured contact resistance warrants, high-pressure sliding contacts only on genuinely movable RF joints, and split-for-repair weighed against the RF seam it adds. Same contact-pressure concern as the nyo-9683/ornl-2648 sliding-contact rules when a movable short exists.

upon considering the approximations necessarily made in this type of analysis, the figure of 150 kw maximum r-f power was selected.

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (1951) — p. 75

Editorial note, tabletop extrapolation: DIRECT scaling method for the LDMOS upgrade: measure the dee system's Q and C, compute watts per kV from P = V^2/(4QX) (equivalently V^2/(2*R_shunt)), then add margin for what the lumped model misses - beam loading, coupling loss, arcs, duty cycle. UW's own practice sized 150 kW against a ~52 kW computed requirement, roughly 3x, 'upon considering the approximations'; let your margin come from your own unknowns inventory, with theirs as the precedent.

This method should be easiest of the methods used to assure oscillation at the proper frequency with the dees operating 180 degrees out of phase.

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (1951) — p. 76

Editorial note, tabletop extrapolation: For a one-dee-plus-dummy machine the mode problem collapses. For any driven system, verify which resonance the amplifier locks to - a network-analyzer sweep plus a phase comparison between dee pickups distinguishes the modes - because the wrong one accelerates nothing.

Electron oscillations in the vicinity of the dees and dee stems at low r-f voltages tend to absorb energy and prevent the oscillations from building up.

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (1951) — p. 75

Editorial note, tabletop extrapolation: The corpus's driven-start cure (mddc-1045 tickler; nyo-9359's catalogue) as a 1951 DESIGN feature rather than a retrofit, including the half-frequency/doubler isolation trick that spares a changeover switch. Directly relevant to the reference machine's dee-voltage buildup pathology: any LDMOS drive chain is inherently a driven start, but only if it can push watts through the multipactor loading band without foldback or protection tripping - and that band's voltage is geometry-, frequency-, pressure- and surface-dependent, so measure it on the actual dee. [Note revised 2026-08-23: the earlier note quoted '~100 V' for the band as if it were a design constant.]

there are many uncertainties in the exact determination of the constants of the equivalent circuit ... the calculated values ... serve well as a guide

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (1951) — p. 82

Editorial note, tabletop extrapolation: A tabletop resonator IS the scale model — build the dee/stem mockup on the bench, measure f and Q before committing to vacuum hardware, and trust lumped calculations as guides not gospel. Berkeley used the same quarter-scale method on the 88-inch (ucrl-9435), which also confirms the Q-degradation-at-joints lesson (ornl-2648).

the plate is operated at d-c ground potential so that no insulation is required in the water lines.

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (1951) — p. 85

Editorial note, tabletop extrapolation: Solid-state amps moot the HV plumbing, but two doctrines survive: pick the grounding scheme that minimizes what the coolant circuit must insulate - DC-grounding the plate removed the DC insulation requirement, while RF potentials, leakage control and water quality stay on the checklist - and use source impedance (here transformer reactance) as passive inrush protection where a component's own rating allows it.

measured by means of a saturable reactor ... The dee voltmeters are of the series type coupled ... by a small capacity between the probe and a copper paddle soldered to the dee edge.

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (1951) — p. 86

Editorial note, tabletop extrapolation: The capacitive-paddle dee voltmeter is the instrument Koeth calibrated on the Rutgers 12-inch and the missing calibration behind the reference machine's ~1.3 kV: a soldered paddle + defined-gap probe + diode peak detector, calibrated IN SITU against an RF-RATED reference at the operating frequency - and recalibrated after any geometry, frequency, detector or cabling change (dg-307's Houghton data show the factor moves with frequency). The saturable-reactor trick survives as the Hall/fluxgate-sensor principle - never bring an HV node to the meter; a bare shunt is not isolated, it needs a rated isolation amplifier.

On the basis of cost it was decided to omit this refinement.

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (1951) — p. 90

Editorial note, tabletop extrapolation: The decision pattern - name the deleted protection, name what stands in for it, keep a commissioning-only resistor in the drawer - is reusable as an engineered, recorded risk acceptance, not a license: verify the stand-ins actually bound the fault energy for YOUR stored energy and clearing time (a 6-cycle breaker passes ~0.1 s of fault current), and re-examine the acceptance at each upgrade. Contrast ucrl-9435, where the 88-inch - with 20x the stored energy - bought the full hard-tube-modulator protection instead. Scale decides.

a minimum of 80 kv dee to ground r.f. potential is necessary in order that the ions do not enter the region of decelerating phase at any time within the dees.

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (1951) — p. 116

Editorial note, tabletop extrapolation: Two transferable ideas for any future extraction study: run the phase-floor analysis BEFORE cutting metal (the computation this collection's deflector cluster expects), and consider using the machine's existing RF field for deflection with DC as supplement - after resolving the geometry from the re-read, since a deflection field needs a potential difference and the as-summarized grounded-plate-vs-grounded-dee-edge description cannot be right as written.

(b) the multipactoring problem, common in the field of particle accelerators, rarely occurs in other industrial applications

Smith, The RCA 6949 as a Self-Excited Cyclotron Oscillator — UCRL-9435, Lawrence Radiation Laboratory (1960) — p. 7

Editorial note, tabletop extrapolation: The checklist for adapting any industrial or ham RF gear (an LDMOS pallet included) to a cyclotron: add spark protection, add a multipactor start plan, and only then worry about power. Fixed-frequency tabletop machines are spared only (c).

The threshold of secondary emission is about 150 electron volts for most surfaces; consequently, multipactoring becomes possible when the voltage across the dees reaches this value.

Smith, The RCA 6949 as a Self-Excited Cyclotron Oscillator — UCRL-9435, Lawrence Radiation Laboratory (1960) — p. 4

Editorial note, tabletop extrapolation: DIRECT: a small machine's dee voltage passes through the ~100-150 V-class region on every start - whether multipactor actually lights there depends on the gap-frequency resonance and the surfaces' secondary yields, which is why some machines never see it. Completes this collection's cure set: mddc-1045 (bias + tickler), nyo-9359 (impulse start), ucrl-64 (volume reduction + bias).

It usually involves permitting the dee to spark several hundred thousand times. Afterwards, it will usually hold many times the voltage that it would initially.

Smith, The RCA 6949 as a Self-Excited Cyclotron Oscillator — UCRL-9435, Lawrence Radiation Laboratory (1960) — p. 4

Editorial note, tabletop extrapolation: For the 5-13 kV dee upgrade, plan a conditioning campaign rather than reading early sparking as failure - a supervised one: compute the actual stored and delivered fault energy first, current-limit and arc-detect, set the auto-recycle behavior from that arithmetic, monitor temperatures, and inspect between sessions. Corroborates the ornl-2648/nyo-9683 conditioning rules and quantifies the count.

Vacuum switches connected in the three-phase, 16.6 kv ac lines feeding the rectifier ... open within 10 msec plus the time to the first current zero ... In this service it will open the anode circuit within 10 usec of a fault.

Smith, The RCA 6949 as a Self-Excited Cyclotron Oscillator — UCRL-9435, Lawrence Radiation Laboratory (1960) — p. PDF p. 6 (printed -6-) for the layer arrangement; PDF p. 7 (printed -7-) for the regulation and termination items

Editorial note, tabletop extrapolation: The modern translation, mapped by FUNCTION rather than spec-for-spec: an LDMOS drain supply wants a fast electronic disconnect (the hard-tube modulator's descendant), a slower breaker layer, and snubbing on the dc feed - each layer rated against the actual stored energies and fault modes of the build (dg-330, dg-679, dg-1371).

In this type of system the resonator is the frequency-determining element of the system; hence it is called a self-excited oscillator.

Smith, The RCA 6949 as a Self-Excited Cyclotron Oscillator — UCRL-9435, Lawrence Radiation Laboratory (1960) — p. 4

Editorial note, tabletop extrapolation: The live architecture decision for a next machine. An LDMOS chain driven by a synthesizer is a MOPA — it inherits ornl-2403's virtues (frequency authority, instrumentation) AND the self-excited literature's start-up disease (nyo-9359): the synthesizer holds frequency while multipactor holds the dee at zero. Smith's phase-discipline logic (feedback phase correct across the whole operating range) is the checklist item either way. High-SWR argument p.6.

Cited in: Driving the Dee: RF Coupling

At the maximum particle energy, the beam requires 60 kw of power.

Smith, The RCA 6949 as a Self-Excited Cyclotron Oscillator — UCRL-9435, Lawrence Radiation Laboratory (1960) — p. 5

Editorial note, tabletop extrapolation: The four-line budget is the right form at any scale. A tabletop version: watts of copper loss (dg-313), a beam line computed from ITS current and energy - 1 nA at 500 keV is 0.5 mW, 10 uA at 1 MeV is 10 W, small only until the source improves - a stray-ion line that follows source gas and RF (measurable as the loading difference with the source on vs off), and a misc line that is mostly coupling and radiation.

The circuit elements of the rf system were adjusted so that the first two higher modes would not be excited by an oscillator harmonic.

Smith, The RCA 6949 as a Self-Excited Cyclotron Oscillator — UCRL-9435, Lawrence Radiation Laboratory (1960) — p. 5

Editorial note, tabletop extrapolation: For a fixed-frequency machine: sweep the dee system on a VNA, list the modes WITH their widths and couplings, and check them against the drive's measured harmonic spectrum - detune offenders with a strap or stub before blaming the amplifier for instability. Same mode-vs-harmonic discipline as the msucp-9 and ornl-2648 lines.

For accelerator applications, a tube should have a sufficiently heavy grid to absorb several joules of energy in an area determined by the cross section of the spark.

Smith, The RCA 6949 as a Self-Excited Cyclotron Oscillator — UCRL-9435, Lawrence Radiation Laboratory (1960) — p. 6

Editorial note, tabletop extrapolation: The solid-state translation: LDMOS devices have finite ESD, avalanche and mismatch ratings rather than a tube grid's joules of thermal mass, so the ruggedness must live in the coupling network - series blocking, clamping, fast drive-cut (dg-338, dg-758). A dee-side fault arrives first at the OUTPUT network, which is where the protection belongs.

The rf-dc interlock compares the dee voltage with the amount of oscillator anode dc. If the ratio is too low, indicating the presence of an arc, the fault detector opens the anode circuit and recycles

Smith, The RCA 6949 as a Self-Excited Cyclotron Oscillator — UCRL-9435, Lawrence Radiation Laboratory (1960) — p. 7

Editorial note, tabletop extrapolation: DIRECT and cheap: a comparator on the dee-voltage-to-drive ratio with a drop-and-retry turns dee sparks from session-enders into log entries - the ratio form matters, because absolute thresholds miss arcs that still draw full power. Two amendments for a tabletop copy: cap the retry count and latch out on repeated faults, since an endless auto-recycle would keep re-feeding a failed feedthrough or persistent arc; and if forward power stands in for anode dc, validate the arc signature on the actual amplifier - it is not the same quantity Smith's ratio used.

The signal from the rf-dc interlock is slowed down by an RC circuit, so that the discharge will persist for about a millisecond. ... Experience indicates that 1 msec is about the right delay.

Smith, The RCA 6949 as a Self-Excited Cyclotron Oscillator — UCRL-9435, Lawrence Radiation Laboratory (1960) — p. PDF p. 7 (printed -7-)

Editorial note, tabletop extrapolation: A protection spec you cannot derive from electronics alone: the dwell is chosen so each spark finishes cleaning the spot that caused it. The compromise transfers; the number does not - Smith's ~1 ms suits his machine's stored energy and electrode scale, so a tabletop supply picks its own dwell from its fault energy, starting shorter and lengthening only if conditioning stalls. Amplifier-device faults still trip as fast as the electronics allow: two speeds, two purposes.

the resonator has to be vacuum-tight, automatically making it rf-tight.

Smith, The RCA 6949 as a Self-Excited Cyclotron Oscillator — UCRL-9435, Lawrence Radiation Laboratory (1960) — p. 8

Editorial note, tabletop extrapolation: Comforting for a residential machine, with 'somewhat' doing real work: the metal chamber contains the dee's RF well, and the leakage paths are feedthroughs, viewports, gauge ports and the amplifier chain - gasket and shield those, then VERIFY with a receiver walk-around. Quiet neighbors' radios are a measurement, not a promise.

Maximum operating conditions for the RCA 6949 for the 88-in. cyclotron

Smith, The RCA 6949 as a Self-Excited Cyclotron Oscillator — UCRL-9435, Lawrence Radiation Laboratory (1960) — p. 10

Editorial note, tabletop extrapolation: The ratio HABIT transfers, the numbers are this tube's: work out the equivalent operating-point ratios for the actual device from its own datasheet and measurements, and treat large departures from the device's own expected ratios as a prompt to look for mistuning, parasitics or multipactor loading - among other causes (topology, matching and the efficiency definition all move the numbers).

Es ist nämlich leichter, das Magnetfeld von 185 mT auf 370 mT zu erhöhen als die Frequenz von 2,82 MHz auf 5,64 MHz [tr.: easier to raise B from 185 to 370 mT than f from 2.82 to 5.64 MHz]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 37-39

Editorial note, tabletop extrapolation: A fixed-frequency resonator plus a 2:1 field range covers both hydrogen species IF the machine works at both fields - field quality, source output and capture must each hold at both points, so verify rather than assume. Two peaks at B and 2B are consistent with H+/H2+ but not unique to them (q/m degeneracy, dg-1432); use them as a species INDICATION to confirm.

Dies ist auf die bessere Abstimmbarkeit des HF-Systems bei der kleineren Frequenz zurückzuführen [tr.: due to the better tunability of the RF system at the lower frequency]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 39

Editorial note, tabletop extrapolation: When species choice leaves a frequency option open, tunability is a legitimate tiebreaker - established by trying both on YOUR network, not by a frequency ceiling: evaluate component Q, circulating current and voltage stress at each candidate. Documenting lead inductance and stray capacitance pays regardless of frequency.

Aus Gründen der Spannungsfestigkeit der Durchführung ist U0 ≤ 3000 V [tr.: because of the feedthrough voltage rating, U0 <= 3000 V]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 42

Editorial note, tabletop extrapolation: A 5-15 kV dee upgrade is an insulation-coordination problem across the WHOLE RF path - feedthrough, stem supports, matching capacitors, connectors, plus contamination and conditioning state - with the feedthrough a frequent but not guaranteed weakest link. Specify every element for peak RF plus any DC bias, in vacuum, with tracking margin.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

Diese beträgt nach aktuellen Messungen ca. 330 kΩ [tr.: according to current measurements this is about 330 kOhm]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 42, 44

Editorial note, tabletop extrapolation: The scaling explains why a 100-500 W amplifier class suits a 5-13 kV dee - sized with margin: P_source >= U0^2/(2*R_p*eta) with measured end-to-end efficiency eta (matchbox, feedline and base-load losses all sit between amplifier and dee), and the larger dee's own R_p measured, not borrowed from this machine.

Der verwendete Transceiver, ein ICOM M 600, liefert in der Betriebsart H3E eine sinusförmige Spannung (Amplitude ≈ 70 V) im Frequenzbereich von 0,5–35 MHz mit einer abgegebenen Leistung von ungefähr 45 W an 50 Ω Ausgangsimpedanz. ... Das Widerstandsnetzwerk der Eingangsstufe stellt dabei eine Grundlast für den Transceiver dar. Dieser würde sonst [...] abschalten [tr.: the transceiver used, an ICOM M 600, delivers in H3E mode a sinusoidal voltage (amplitude ~70 V) over 0.5-35 MHz with about 45 W into 50 ohm output impedance ... the input resistor network is a base load; otherwise the transceiver shuts down]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 44-45

Editorial note, tabletop extrapolation: The load-requirement lesson generalizes as a check, not a law: characterize the chosen amplifier's required load, mismatch tolerance and protection behavior (an LDMOS deck without foldback dies where the ICOM merely shuts down), and budget a dummy-load fraction plus a VSWR interlock so a detuned dee - a plasma flash, say - cannot damage the final stage.

muss die niedrige Ausgangsimpedanz (50 Ω) der HF-Quelle an die hohe Eingangsimpedanz (330 kΩ) angepasst werden. Außerdem ist die Ausgangsspannung von 70 V auf 3000 V zu transformieren. Beide Aufgaben werden von der Koppelstufe oder Matchbox erledigt. ... C1 bildet mit L einen Filterkreis, der auf die Eingangsimpedanz von 50 Ω abgestimmt ist, während L mit C2 die Impedanz Z = 330 kΩ des Zyklotrons erzeugt. Und bei diesem Impedanzmatching wird gleichzeitig die Eingangsspannung von ca. 70 V auf 2–3 kV am Ausgang erhöht. ... Eine optimales Matching des Pi-Filters ist dann gegeben, wenn die reflektierte Leistung Null ist [tr.: the source's low 50-ohm output impedance must be matched to the high 330-kohm input impedance (a recent measurement gives ~330 kohm for the cyclotron), and the 70 V output stepped up to 3000 V - both jobs done by the coupling stage or matchbox; C1 with L forms a filter circuit tuned to the 50-ohm input while L with C2 produces the cyclotron's 330-kohm impedance, the input voltage rising from ~70 V to 2-3 kV at the output; the pi filter is optimally matched when the reflected power is zero]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 44-45

Editorial note, tabletop extrapolation: Two independent readouts are the honest minimum for tuning: reflected power at the input AND a calibrated dee-voltage pickup at the output - zero reflected power alone proves the power went in, not that it reached the dee rather than the base load or network losses. The output-side capacitor must be RF-rated (the book's own footnote: an HF-tauglicher capacitor to avoid flashover), since kilovolts appear across it.

Mit Hilfe eines Relais kann die Spule mit L = 24 µH in Serie zu der 8 µH-Spule [geschaltet werden] ... Zieht das Relais an und schließt den Kontakt, wird die 24 µH-Spule kurzgeschlossen, so dass nun nur noch die Induktivität von 8 µH wirksam ist. ... kann für diese Umschaltung kein Schalter verwendet werden, vielmehr muss sie mit Hilfe eines Vakuumrelais erfolgen [tr.: a relay puts the 24 uH coil in series with the 8 uH coil; when the relay closes, the 24 uH coil is short-circuited so only 8 uH remains effective; no ordinary switch may be used for this switching - a vacuum relay is needed]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 45-46

Editorial note, tabletop extrapolation: A 4:1 inductance ratio gives the 2:1 frequency ratio at nominally constant capacitance, covering H+ and H2+ on one network - as an ideal-LC starting point: relay contact capacitance and lead inductance shift both points, so retune and re-measure at each setting, and rate the relay for the RF voltage and current at its node.

Über sie kann eine zusätzliche „Saugspannung“ an das Dee angeschlossen werden [tr.: through it an additional extraction voltage can be applied to the dee]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 46

Editorial note, tabletop extrapolation: A DC extraction bias shifts when ions leave the slit relative to the RF phase - a real tuning knob. Determine its magnitude from ion-optics measurement or simulation on the actual source (the book states the provision, not a value), and rate the feedthrough and insulation for the maximum instantaneous RF-plus-DC sum, which also moves the bremsstrahlung end-point.

Da ein Dee wie die Vakuumkammer selbst auf Masse liegt, kann dieses Dee verkürzt werden [tr.: since one dee is at ground like the chamber, it can be shortened]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 46

Editorial note, tabletop extrapolation: Single-dee-plus-dummy gives half the energy gain per turn of an ideal push-pull pair at the same per-electrode amplitude, in exchange for one feedthrough and one resonator - a trade that favors simplicity on most small builds; state the amplitude convention whenever quoting the factor of two.

ωHF = k · ωZyk = k · v/r = k · (q/m) B mit k = 1; 3; 5; ... [tr.: RF frequency equals an odd multiple of the cyclotron frequency]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 24-25

Editorial note, tabletop extrapolation: Third-harmonic operation (k = 3) lets a 0.2 T magnet accelerate protons with a 9 MHz resonator, at the cost of a narrower phase window per crossing; it is the formal basis of the sub-harmonic peaks in I(B) spectra (dg-1424).

The El Cerrito Cyclotron used only one dee, and did not employ a 'dummy dee,' but rather held the chamber itself at ground. ... The system was operated at 1,600 watts and could provide a maximum of 2,000 watts to the electrodes. ... with the new vacuum chamber a beam of 7 microamperes was produced.

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 15

Editorial note, tabletop extrapolation: Deleting the dummy dee simplifies the in-chamber assembly at the cost of a less-defined gap field; the precedent documents that the geometry can work at the microampere scale - it does not promise that current class, which came from the whole machine, not the electrode choice alone.

The RF was provided by a ham radio transceiver, using an oven controlled crystal.

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 16

Editorial note, tabletop extrapolation: Oven-controlled crystal stability addresses the drift side of resonance keeping, and ham gear is well-documented and repairable - as the frequency-stable SOURCE/exciter; what amplification, matching and electrode voltage sat downstream isn't in this sentence, so size the rest of the chain from its own requirements before crediting amateur gear with the whole job.

A dee and dummy dee system was used with the electrodes separated by approximately 1 mm.

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 16

Editorial note, tabletop extrapolation: A millimetre-class gap maximizes gap FIELD per volt and can improve the transit-time factor - the ideal energy gain per crossing stays q*deltaV regardless - while tightening alignment, flatness and holdoff tolerances (field enhancement rises as the gap closes). One documented small end of the range, not an established bound; choose the gap from the transit-time and holdoff calculation (dg-1396).

the assembly was supported by a 1.3 cm thick copper rod that also connected the dee to the RF matching transformer

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 17

Editorial note, tabletop extrapolation: Making the RF feed a structural member gives a rigid connection and can save a penetration - count your own: an internal support needn't pierce the wall at all, and low loop inductance comes from the LENGTH and return-path geometry, not rod thickness. The 1.3 cm is Rutgers' as-built datum; size a new rod from RF current, mechanical load and the actual loop.

[The RF] signal was produced using a HP8656B signal source, which had greater frequency resolution than the HP8165, and an ENI NMR-300L solid state amplifier. Its maximum output was 2,500 W, but was usually operated at 50 W with satisfactory results.

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 17

Editorial note, tabletop extrapolation: Tens of watts sufficed for a 30.5 cm, above-1-T machine with a resonant matching network - at ITS reported operating conditions; the 50x headroom was available, and whether more drive would have bought more beam is not in the record. A useful anchor for amplifier shopping: buy the headroom, expect to run far below it.

The oscillator used an HP8165 digital programmable RF signal source, which offered an easy method of tuning the frequency. ... [Later the] signal was produced using a HP8656B signal source, which had greater frequency resolution than the HP8165.

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 17

Editorial note, tabletop extrapolation: Resonance hunting rewards fine, repeatable frequency steps - the documented upgrade was FOR resolution, so check any candidate source's step size against the measured resonance width (Q of the loaded resonator) before buying; whether the first unit's resolution actually limited tuning is our inference from the upgrade, not the thesis's statement.

The capacitance of the dee's was not measured before building the resonating circuit, rather trial and error was used to tune the circuit. ... [Houghton:] The capacitance of the dee and chamber of the Houghton College cyclotron has been determined to be 79 pf.

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 18

Editorial note, tabletop extrapolation: A capacitance measurement on the assembled stack converts resonator design from blind cut-and-try into calculation-plus-trim: include estimated lead/feedthrough parasitics (tens of pF scale means they matter), choose the initial inductance from the formula, and still provide adjustment range - installed resonance always lands off the paper value.

For a deuteron in an accelerating potential of 1,000 volts, the energy limit is 1.94 MeV, for an accelerating potential of 10,000 volts, the limit is 6.13 MeV, and for an accelerating potential of 20,000 volts, the limit is 8.67 MeV. ... the effects of relativity can be countered by more than just increasing the electrode voltage, it can also be mitigated by adjusting the shape and strength of the magnetic field. The actual relativistic limit for magnetic resonators accelerating protons is closer to 25 MeV.

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 28

Editorial note, tabletop extrapolation: For sub-MeV machines relativity is far from limiting even at 1 kV dees on any convention - both the thesis's numbers and the halved re-derivation agree on that. If energies ever approach the MeV scale, dee voltage and field shaping are BOTH levers, per the thesis's own remark.

The capacitance of the dee and chamber of the Houghton College cyclotron has been determined to be 79 pf. If the maximum magnetic field of 1.127 T is used then the frequency of orbit for singly ionized helium is 4.32 MHz, and thus the inductance, using (23), must be 17.2 uH. In this system the maximum energy for singly ionized helium is 77.2 keV. For doubly ionized helium, the frequency in the same magnetic field is 8.63 MHz, so the inductance is 4.29 uH, and the maximum energy is 309 keV.

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 46

Editorial note, tabletop extrapolation: A rare published electrode-system capacitance anchor for microhenry-scale resonator sizing at this machine class - noting the energy quadrupling with charge state at fixed field (the implied orbit radius is ~7.1 cm), that 79 pF is build-specific, and that the installed resonance still needs the parasitics-and-trim treatment (dg-1462).

In order to avoid sparking in the gaps in the cyclotron chamber, the voltage supplied by the amplifier must be carefully chosen.

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 45

Editorial note, tabletop extrapolation: With a high-Q resonator the dee voltage is set indirectly, so the spark limit must be designed in rather than discovered: use the measured or modeled loaded transfer function from amplifier to dee, verify with a calibrated pickup (dg-307/dg-1356), and back it with arc detection - the branch-current subtlety is exactly where a naive I*X_C sizing goes wrong.

The power in the primary coil of the transmatch is monitored by a Bird 43A RF power meter, and supplied by the ENI 155LCRH RF power amplifier. The RF signal is provided by the HP 33120A function [generator]

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 47

Editorial note, tabletop extrapolation: A bench function generator + lab RF amplifier + ham-style through-line wattmeter is a complete drive-and-monitor chain from commodity gear. Meter honestly: a directional wattmeter at the transmatch primary reads forward power at that point - net delivered power is forward minus reflected, and network losses sit downstream of the meter, so pair it with the dee-voltage pickup (dg-1392's two-readout rule).

With an improved matchbox, two cyclotron frequencies of 2.82 MHz and 5.64 MHz are available.

Wolf & Prechtl, COLUMBUS — A Small Cyclotron for School and Teaching Purposes — THPO001, Proceedings of Cyclotrons2022 (2022) — p. 1

Editorial note, tabletop extrapolation: Two-frequency matching lets a small machine serve a light ion and its molecular ion, or run one ion at half field: at the fundamental, 2.82 MHz pairs with H+ at 185 mT or H2+ at 370 mT, 5.64 MHz with H+ at 370 mT (f = qB/2*pi*m). The paper states availability; which pairings were demonstrated as beam operating points, and the switching mechanics (COLUMBUS's own book documents a vacuum-relay inductor switch, dg-1393), need their own evidence per machine.

The RF-power-source is a short-wave transceiver for marine radio. It provides an AC voltage of 50-70 Veff at frequencies from 500 kHz to 35 MHz. The available power is 120 W. … As well as an impedance converter the matchbox is also an RF-transformer transforming the 50 - 70 V output voltage of the power-source up to 2000-3000 V voltage, which is needed for the acceleration of the protons.

Wolf, Frank & Held, COLUMBUS — A Small Cyclotron for School and Teaching Purposes — WE1PB03, Proceedings of Cyclotrons2013 (2013) — p. 2

Editorial note, tabletop extrapolation: The transmitter's rated power is a design-era catalog figure; the usable continuous carrier in the modulation mode actually chosen should be verified on the bench before the RF power budget is frozen.

A directional-coupler in the input-circuit of the matchbox makes it possible to control and minimize the reflections back into the RF-source and a RF pick-up, i.e. Fig. 6, in the output-circuit allows to check whether the cyclotron is tuned to the cyclotron-frequency of 5.63 MHz

Wolf, Frank & Held, COLUMBUS — A Small Cyclotron for School and Teaching Purposes — WE1PB03, Proceedings of Cyclotrons2013 (2013) — p. 2

Editorial note, tabletop extrapolation: Two independent indications, reflected power at the input and detected RF at the dee side, help separate matching problems from resonance problems during tune-up - though both respond to coupling and resonance, so neither is unambiguous alone, and the pick-up reads amplitude: the drive frequency itself should be known independently (a counter is cheap) and compared against qB/2πm.

The frequency (f1) of the cyclotron r.f. supply was measured to five significant figures with a BC-221 frequency standard. The BC-221 was periodically calibrated against the frequencies of the radio station WWV.

Burns, Experimental Program with the Iowa State University Undergraduate 1.5 Mev Cyclotron — Proceedings of the Iowa Academy of Science 68(1), 483–491 (1961) — p. 3

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: frequency metrology by transfer from a broadcast standard, achieved with surplus gear. Modern counters exceed this trivially, but the lesson stands — calibrate the frequency reference and treat frequency as the best-known quantity in the resonance relation. Derive the accuracy actually needed from the allowed accumulated phase slip, and remember absolute field/energy bookkeeping needs the field map and orbit geometry too, not frequency alone.

IUAC, New Delhi, India, operates accelerators with RF structures in the range of 12.125-97 MHz, in both normal and superconducting modes ... this controller has been tested as a Sawtooth Waveform Generator for the Multi-Harmonic Buncher (MHB), as a generator-driven (GDR), and as a self-excited loop (SEL)-based LLRF for various RF cavities at IUAC ... It is a compact, frequency-reconfigurable, standalone device controlled by an EPICS IOC ... The main feature of our design is the hardware configuration, which remains the same regardless of the cavity type, without the need for FPGA reprogramming. In addition to the LLRF algorithm, the same FPGA contains logic for the motorized Frequency Tuner Control, considerably lowering the system's cost ... The major blocks of the system as shown in the overall physical block diagram (Fig. 1a) are a wideband Analog Front-End (AFE), microcontroller programmed PLL Multiplier, and a SoC-FPGA-based digital board.

Sharma, Kar, Dabas, Sahu, Singh, Mathur, Satyanarayana & Venkatramanan, Design and Testing of a Universal Embedded Feedback Controller for RF Cavities — MOP6698, Proceedings of IPAC2026 (2026) — p. 1, 2

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: one reconfigurable digital controller replacing a zoo of structure-specific analog LLRF chassis is exactly the maintainability trade a small lab faces. Folding the mechanical tuner drive into the same FPGA as the feedback loop removes a separate controller box — the motor's power stage still exists, but its logic does not need its own electronics.

this mode also features a PWM-controlled motorized frequency tuner in the same FPGA ... for TT cyclotron, the operational frequency is 18.2 MHz ... For the TT-cyclotron (Fig. 5a), this controller in GDR mode has been operated with a frequency tuner up to 200W RF power ... This instrument is currently under rigorous testing at IUAC and will undergo production once found suitable for beam acceleration.

Sharma, Kar, Dabas, Sahu, Singh, Mathur, Satyanarayana & Venkatramanan, Design and Testing of a Universal Embedded Feedback Controller for RF Cavities — MOP6698, Proceedings of IPAC2026 (2026) — p. 2, 3

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: closed-loop RF control demonstrated at 200 W on a pre-beam machine documents the staged commissioning a professional program uses — prove the loop before raising power. The 18.2 MHz operating frequency is consistent with proton fundamental-mode operation in the 1.2 T field of the same machine's magnet tender (f = qB/2πm gives about 18.3 MHz at 1.2 T) — a cross-source consistency check, not a measured beam frequency.

Long-term RMS stability of ~1% in amplitude and a < ±0.4∘ in phase locks have been obtained ... [Table 1, long-term performance:] MHB-DPLL — phase ± 0.40∘; GDR — ± 0.5%, ± 0.45∘; SEL-AP — ± 1.2%, ± 0.35∘ ... The loop allows phase corrections of up to 35∘ and amplitude corrections of ±3 dB, as verified using an additional phase shifter and attenuator.

Sharma, Kar, Dabas, Sahu, Singh, Mathur, Satyanarayana & Venkatramanan, Design and Testing of a Universal Embedded Feedback Controller for RF Cavities — MOP6698, Proceedings of IPAC2026 (2026) — p. 1, 3

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: sets a benchmark for what percent/sub-degree RF regulation looks like from a compact digital controller — and, more transferably, shows how to verify a loop's correction range by deliberately injecting known phase and amplitude disturbances. Bench figures of this style are the right pre-beam acceptance evidence for any home-built dee drive.

this mode also features a PWM-controlled motorized frequency tuner in the same FPGA ... It compares the phase error (between the FWD signal and the PU signal) with a threshold value and, based on that, it decides the direction of motion of the tuner

Sharma, Kar, Dabas, Sahu, Singh, Mathur, Satyanarayana & Venkatramanan, Design and Testing of a Universal Embedded Feedback Controller for RF Cavities — MOP6698, Proceedings of IPAC2026 (2026) — p. 2

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: the forward-versus-pickup phase comparison is the classic resonance-tracking criterion, stated here in an implementable threshold-and-direction form suitable for a microcontroller and a stepper on a trimmer capacitor. Separating slow mechanical tuning from the fast electronic loop is the standard division of labour worth copying — and the on-resonance phase setpoint must be calibrated for the actual coupling, pickup placement and cable delays, not assumed to be zero.

Several implementations invoke backplane-based methods, such as VME, cPCI, and microTCA. These solutions are often costly, bulky, and difficult to adopt due to a customized design goal. Standalone, non-crate-based systems provide a more versatile, fast, and cost-effective alternative ... The local oscillator signal for the mixer is generated by a Si5356-based I2C-programmable PLL multiplier, synchronized with an external reference signal. Apart from the LO signal, it is used to generate a 125 MHz system clock signal for the FPGA ... This board [13] houses the main signal processing algorithm ... [reference 13:] Red Pitaya, "Red pitaya STEMlab 125-14" ... A lightweight digital PLL (DPLL) ... helps the Si5356-based PLL multiplier mitigate long-term sub-millihertz-level errors which were experimentally observed and caused by accuracy issues with the manual setting of its phase increment word

Sharma, Kar, Dabas, Sahu, Singh, Mathur, Satyanarayana & Venkatramanan, Design and Testing of a Universal Embedded Feedback Controller for RF Cavities — MOP6698, Proceedings of IPAC2026 (2026) — p. 1, 2, 4

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: a national accelerator centre building its cyclotron LLRF around a hobbyist-priced software-defined-radio board shows amateur-accessible hardware can anchor serious RF field control at these frequencies — as one component of a system whose performance also hangs on the analog front end, clock reference, firmware and interlocks. The DPLL fix for the clock chip's long-term drift (sub-millihertz-level, from manual phase-increment setting) is a practical gotcha worth knowing before trusting a cheap synthesizer unsupervised.

The development includes a broadband solid state RF power amplifier up to 2 kW CW, Impedance matching network (IMN) and GDR based Digital LLRF Controller. The aim of the RF system is to generate and maintain high RF voltage across Dee-Dummy Dee to accelerate the particles from the ion source of Cyclotron.

IUAC, Annual Report 2024–25, Chapter 3 — Research Support Facilities (table-top cyclotron RF system) — p. 18

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: the amplifier-IMN-dee chain with a digital feedback controller is the modern minimal RF architecture for a small cyclotron, and the dee/dummy-dee (single-dee) geometry matches common amateur practice. The 2 kW CW is this amplifier's rated maximum, not a derived drive requirement — the power a given machine needs follows from its dee voltage, shunt impedance, coupling and losses, so treat the rating as one professional team's headroom choice for an MeV-class teaching machine.

Frequency is fine tunes with vacuum variable capacitor. A capacitive pick-up built-in the Cyclotron chamber is used as feedback in order to control and maintain the RF voltage and frequency of the system using a digital LLRF controller and a motorized tuner.

IUAC, Annual Report 2024–25, Chapter 3 — Research Support Facilities (table-top cyclotron RF system) — p. 18

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: building the capacitive pick-up into the chamber from the start — rather than improvising one later — is the design habit to copy: early provision simplifies every scheme that reads the cavity field from a pick-up, including the dee-voltage calibration chain on this machine. Other feedback routes exist (directional-coupler signals, other probe types); a motor-driven vacuum variable capacitor is an amateur-accessible tuner implementation.

Pick-Up calibration has been performed using the Shunt impedance method, HV-HF Probe measurement. X-Ray Measurement via Bremsstrahlung radiation (done for HVDC) is currently in progress. Further testing of closed loop electronics, cooling system implementation, high power amplifier and modifications in the matching network are being currently being done.

IUAC, Annual Report 2024–25, Chapter 3 — Research Support Facilities (table-top cyclotron RF system) — p. 18

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: names three routes to the perennial small-cyclotron problem of knowing the actual dee voltage — circuit calculation from shunt impedance, a high-voltage RF probe, and bremsstrahlung X-rays. Cross-checking more than one is what separates a calibrated number from a nominal one (the reference machine's own dee voltage is exactly such an uncalibrated nominal). For RF fields the X-ray route needs care beyond reading an endpoint — electron trajectories, RF phase and detector response all enter — which may be why the source lists it as in progress rather than done.

Presently, the practical amount of RF power that can be safely used for prolonged operation is about 500 watts. Operating with power levels on the order of 1kW have been tried, but only for very brief periods (30 seconds). […] The first betatron image (left sinusoidal pattern) is of 500 watts and the second (right sinusoidal pattern) was with 600 watts of RF power. The RF power of 500 watts corresponded to approximately 10 kVp-p and 600 watts corresponded to approximately 11 kVp-p.

Koeth, Hanebuth, Hoffman & Schneider, Rutgers 12-Inch Cyclotron Ion Source Studies: Part II (2007) — p. 3

Editorial note, tabletop extrapolation: A scale-matched RF data point: about 500 W forward power buys ~10 kVp-p on this 12-inch dee in this resonator, stated by the authors as their prolonged-operation practice; 1 kW was ATTEMPTED for ~30-second periods (~11 kVp-p at 600 W per the same figure). The source does not say what sets the limit — heating, breakdown, matching components — so read the numbers as one resonator's operating envelope, not as permission for pulsed operation at double power.

A series of images were taken at differing RF input power levels. The ion beam's radius was calculated by using a calibration of the images pixels against the 0.25 inch diameter of the chimney. The initial energy of the ions (protons in this case) was determined from the calculated radius, magnetic field and the mass; and was then plotted as a function of input power. Twice the energy data was plotted against previously quoted peak-to-peak DEE voltages.[6] There is strong agreement with the older data; a slight increase in DEE voltage for a given power is seen – this is attributed to improvement in the Q from reworking the RF matching box.

Koeth, Hanebuth, Hoffman & Schneider, Rutgers 12-Inch Cyclotron Ion Source Studies: Part II (2007) — p. 5

Editorial note, tabletop extrapolation: An independent, non-electrical dee-voltage calibration for any machine with a viewport — valuable precisely because divider and probe measurements are the usual error source at this scale. The physics of the factor of two, stated correctly: the imaged initial arc follows the FIRST gap crossing, so its radius measures the energy qV_peak; doubling converts V_peak to the peak-to-peak voltage the older rectifier data quoted. Identify which turn you are imaging and know the local field before applying it. Fig. 13 shows the resulting curve out to ~1400 W forward power against a theoretical curve with Rs = 0.8 Ohms.

This result is not understood, as only integer odd harmonic numbers support magnetic resonance acceleration. At an even harmonic, when acceleration occurs at a gap crossing, deceleration must occur at the subsequent crossing, yielding zero net accelerator per revolution. In the region between an even and odd harmonic, there is a balance of acceleration and phase slippage which the ions encounter. Operating a cyclotron near, but not on, an odd harmonic, can still lead to a successful resonantly accelerated beam, provided that the integrated phase slippage over all revolutions is less than 180 before hitting the target or extraction point. The greater the DEE voltage, the fewer the number of ion revolutions are needed to achieve the desired energy, thus the tolerance of phase slippage per turn increases with DEE voltage.

Koeth, Ponter, Hoffman, Schneider & Krutzler, Rutgers 12-Inch Cyclotron Electrostatic Deflector (2010, rev. 2011) — p. 6

Editorial note, tabletop extrapolation: Directly relevant to low-dee-voltage machines, in mirror image: many hundreds of turns means very little tolerable slip per turn, which is an operational argument for dee voltage beyond simple turn-count. State the physics as the source's gap phasing gives it: odd harmonics are the resonant condition for this conventional geometry, and near-harmonic operation can survive if the bunch stays inside the accelerating phase window — the 180-degree integrated-slip figure is an approximate span, conditional on where in phase the ions start and which way they slip. The reported 2.22 and 4.25 harmonic numbers are stated by the authors as "not understood" — an open anomaly, not a result. ("accelerator per revolution" is the source's typo for "acceleration".)

While the constructed radial sector pole tips were not intended to support acceleration, with sufficient DEE voltage protons were successfully accelerated. The incurred phase slippage at normal operating conditions - namely a DEE voltage of 8 kV-peak - was indeed too severe to successfully bring ions to the full radius. However, a DEE voltage of 20 kV peak accepted ions over 20° of the RF cycle and accelerated … them to the periphery. This suggested that our first attempt is not too far from a practical design.

Koeth, Hine, Hoffman, Krutzler, Ponter, Rosenberg, Ruisard & Schneider, Comparison of Azimuthally Varying with Constant Gradient Magnetic Fields with the Rutgers 12-Inch Cyclotron (2011) — p. 9

Editorial note, tabletop extrapolation: Quantifies what a non-isochronous field costs in dee voltage, on this field and RF model: at the machine's normal 8 kV-peak the slippage was fatal; 20 kV-peak accepted a 20° RF window and carried protons to the periphery — a factor of 2.5, for this map. Recalculate the acceptance-versus-voltage curve for your own field, harmonic and RF waveform; the transferable shape is that voltage buys phase margin against a mismatched field (dg-1786 is the measured version of the same lesson). Simulation results, not measured beam.

SPIRAL AVF DESIGN Finally, we present the optimized design for a set of spiral pole tips that are intended to guide beam. The result was a four sector Archimedean spiral sweeping 270 degrees, and will herein be referred to as AKG270. With the exception of the weak focusing central region, these pole tips aimed to satisfy the isochronous condition, in order to minimize the phase slippage, and reduce the minimum DEE voltage while preserving axial stability throughout the accelerating region.

Koeth, Hine, Hoffman, Krutzler, Ponter, Rosenberg, Ruisard & Schneider, Comparison of Azimuthally Varying with Constant Gradient Magnetic Fields with the Rutgers 12-Inch Cyclotron (2011) — p. 10

Editorial note, tabletop extrapolation: The design pattern worth copying is the HYBRID: weak focusing kept in the centre where flutter cannot help, spiral-AVF outboard where isochronism pays — that is what minimized phase slippage and dee voltage while preserving axial stability here. The 270-degree four-sector Archimedean sweep is this magnet's optimized answer (the authors credit their machine shop for cutting it); another machine re-runs the optimization on its own field map and takes whatever sweep its tunes demand.

Protons were flown with RF in SIMION with the AKG270 magnetic field. The trajectory of a single proton is shown in Figure 21. The driving frequency and amplitude were iteratively tuned to locate the minimum peak DEE voltage necessary to successfully accelerate the proton to the target. This lowest practical voltage found in the simulation was 6 kVpeak at a frequency of 15.534 MHz.

Koeth, Hine, Hoffman, Krutzler, Ponter, Rosenberg, Ruisard & Schneider, Comparison of Azimuthally Varying with Constant Gradient Magnetic Fields with the Rutgers 12-Inch Cyclotron (2011) — p. 11

Editorial note, tabletop extrapolation: Quantifies the payoff of designing for isochronism, within one simulation campaign: 6 kV-peak at 15.534 MHz sufficed in the AKG270 spiral field, versus the 20 kV-peak the non-isochronous radial-sector field needed and the machine's normal 8 kV (both from the same study's radial-sector section, dg-1716). If shunt impedance and loading were unchanged, cavity loss ∝ V² would differ by ~11× between 6 and 20 kV — a conditional estimate, computed here. The frequency checks: 15.534 MHz ↔ ~1.02 T for protons at the fundamental (computed). Field shaping as a lever on the RF budget is the transferable idea; single-particle simulation, not measured beam.

Figure 30. Average Bz as a function of radius for the AKG270 pole tips in the median plane.

Koeth, Hine, Hoffman, Krutzler, Ponter, Rosenberg, Ruisard & Schneider, Comparison of Azimuthally Varying with Constant Gradient Magnetic Fields with the Rutgers 12-Inch Cyclotron (2011) — p. 11

Editorial note, tabletop extrapolation: What a hybrid weak-focusing-plus-near-isochronous profile looks like in practice on a 12-inch pole, directly comparable with the same paper's weak-focusing profile (dg-1724): much flatter across the middle of the ion region. The design intent and its payoff — minimized slippage, the 6 kV-peak minimum dee voltage — are carried on their own cards (dg-1717, dg-1722). A flat average field approximates isochronism only in the nonrelativistic limit; a higher-energy design shapes ⟨B⟩ to track γ instead. Digitized values approximate.

The project slated for Spring 2012 will develop a beam phase measurement probe. This experiment measures the beam arrival time with respect to the RF cycle. Measuring variations in the beam’s arrival time along a radial line is a method of characterizing the field’s isochronism. At the time of this writing, the authors are exploring an FFT based method to derive the radial and axial tune values from the SIMION simulations. Such a method would be quicker in the evaluation of the magnetic field configurations, reserving the tedium of trace space plot generation for only the most promising candidates.

Koeth, Hine, Hoffman, Krutzler, Ponter, Rosenberg, Ruisard & Schneider, Comparison of Azimuthally Varying with Constant Gradient Magnetic Fields with the Rutgers 12-Inch Cyclotron (2011) — p. 12

Editorial note, tabletop extrapolation: Both items are stated as the authors' intent at the time of writing, not results, and should be read as such. The beam-phase-probe method is nevertheless a described technique a tabletop builder can adopt: radial variation in arrival phase is a direct, measurable isochronism error. The FFT tune-extraction point is a workflow recommendation for anyone running an orbit tracker — screen candidate fields by tune, then spend trace-space effort only on survivors.

The faces of the 9-inch pole tips were parallel within 0.0001 inches – no effort of shaping the field for focusing was expended. Ions were produced with a crude filament near the top lid of the cyclotron chamber, and the entire chamber was filled with hydrogen gas. Even with a maximum RF power of just 50 watts, thus a DEE Vp-p of 3300V, beam currents on the order of 10nAmps of 0.60 MeV protons were reproducibly achieved with the 9-inch magnet.

Koeth, Hanebuth, Schneider & Hoffman, Observation of Betatron Motion in the Rutgers 12-Inch Cyclotron (2006) — p. 1

Editorial note, tabletop extrapolation: A directly comparable data point for the 8-12 inch class: a flat-pole, gas-filled-chamber, filament-source machine at 3300 V dee reproducibly delivered ~10 nA at 0.60 MeV — a demonstrated outcome showing a crude first configuration can produce measurable beam, not a yield to expect. The 0.0001-inch figure is the reported PARALLELISM of the opposed pole faces (each face's own flatness is not stated), and is what a university shop achieved.

It was calculated that the required RF power for the first revolutions of ions to clear the chimney (with the cyclotron operation at 14.900MHz) was 165 watts as plotted in figure 7. [4,7] Confirmation of the ions source model came from establishing beam with 300 watts of RF power and slowing decreasing RF power. Beam intensity decreased with decreasing RF power, but at 170 watts the beam current abruptly dropped to zero.

Koeth, Hanebuth, Schneider & Hoffman, Observation of Betatron Motion in the Rutgers 12-Inch Cyclotron (2006) — p. 4

Editorial note, tabletop extrapolation: A rare validated model-vs-measurement pair at this scale: predicted 165 W first-turn chimney-clearance threshold, measured abrupt cutoff at 170 W. Diagnostic reading: beam that fades then DROPS to zero as RF power falls, near a modeled clearance threshold, is consistent with the first turn striking the source structure — check dee voltage, RF stability, source output and tuning before assigning the cause, since phase-acceptance loss and resonator instability can also end beam abruptly.

This caps thickness was greater than the turn-to-turn spacing of the ion revolutions at a radius greater than 2.1 inches when operating at 14.900MHz with a DEE voltage of 7,500 Vp-p. Such a thick tip would prevent the ions from hitting the sensitive portion of the ion collector, rather the ions would just return to chassis ground. A new, simpler, Faraday cup was installed. It simply consists of an unshielded aluminum block. RF suppression was still a concern, so externally a notch filter, with -100dB of rejection at 14.900MHz, was installed in the Faraday cup line that connects to the electrometer. An RF choke was also installed in this line, just before the electrometer connection.

Koeth, Hanebuth, Schneider & Hoffman, Observation of Betatron Motion in the Rutgers 12-Inch Cyclotron (2006) — p. 4

Editorial note, tabletop extrapolation: A specific, easily repeated mistake: a grounded shield that projects into the incoming beam path intercepts ions before the collector once its effective radial thickness exceeds the local turn spacing — compute Δr(r) (dg-1740) before designing any probe tip. This machine's solution moved RF rejection out of the vacuum entirely (bare aluminum block collector; -100 dB notch filter plus RF choke in the electrometer line); suitably thin or recessed in-vacuum guarding remains an option the memo simply did not need.

The operational sequence was as follows: pump the cyclotron chamber below 1E-5 Torr, shut off ion gauge, turn on the magnet with approximately 20 amps of excitation current, turn on filament bias supply (-200V), then slowly ramp filament heater supply until thermionic emission on order of 10mA is reached, slowly admit hydrogen gas until an increase in emission current was noted. Final optimal filament heater current is noted at 20.6 Amps (for 0.015 inch diameter 1% Th-W wire) and final optimal leak dial setting of 104 was recored. RF was turned on at a low level and tuned to resonance (found to be 14.8640 MHz), the RF drive was increase to 300 watts – corresponding to 7,500 Vp-p on the DEE. … To satisfy the “cyclotron resonance condition” the magnet current was slowly swept up while monitoring the electrometer needle for deflection.

Koeth, Hanebuth, Schneider & Hoffman, Observation of Betatron Motion in the Rutgers 12-Inch Cyclotron (2006) — p. 5

Editorial note, tabletop extrapolation: A complete, numbered startup sequence at exactly the target machine class, including the filament wire spec (0.015 inch 1% thoriated tungsten) and its 20.6 A heating current, and the order of operations: vacuum, gauge off, magnet, bias, heater, gas, RF to resonance, then sweep the magnet current up while watching the electrometer. The numbers are this machine's optimum, not universal setpoints; the ORDER is the transferable part.

The accelerating voltage is adjusted to find a balance between two characteristics of the beam image: if the voltage is not large enough the radial turn to turn separation is too small and one cannot distinguish between two consecutive turns in the beam image, if the voltage is too large then the length of the turn by turn signal is reduced.

Hernalsteens, Ponter, Beaudoin, Koeth, Ruisard & Miller, Betatron Tune Characterization of the Rutgers 12-Inch Cyclotron for Different Magnetic Poles Configurations (2016) — p. 2

Editorial note, tabletop extrapolation: Practical operating guidance for anyone doing turn-resolved imaging on a small machine: dee voltage is the knob that trades turn separation against the number of turns in the field of view. Consistent with the turn-spacing relation Δr ≈ m·ΔE/(q²B²r) for energy gain ΔE per turn (equivalently m·ΔV/(qB²r) with ΔV the effective accelerating voltage) from the same program's 2006 betatron-motion note.

Primarily dedicated to proton acceleration, the cyclotron's Radio Frequency (RF) systems was retuned to 7.15 MHz to satisfy the magnetic resonance acceleration condition for deuterons having a q/m of half that of the single a.m.u. proton. A new, externally coiled, tank circuit inductor was wound to bring the DEE's 78 pF capacitance into resonance. The coupling loop was adjusted to present the RF power amplifier with a pure 50-ohm load.

Koeth, Neutron Production with a 12-Inch Cyclotron (2017) — p. 1

Editorial note, tabletop extrapolation: Species matters and it can change the RF plant, not just a dial: at fixed field, deuterons run at about half the proton frequency, and the resonator plus matching network must reach it — on this machine that meant winding a physically new tank inductor, because the existing tank could not tune an octave down. The 78 pF dee capacitance is this 12-inch machine's measured value; use it as a sanity anchor, not a design number.

A programmable Tektronix AFG3101 100 MHz arbitrary function generator supplied the RF drive and timing trigger output. The intermediate RF stage utilized a solid state ENI-350L which in turn drove the final power amplifier, an Ameritron AL-82 linear capable of 1500 Watts continuous. Lack of active DEE cooling limited the RF power to about 1000 watts average. When not in CW mode, pulsed RF operation was used to simultaneously achieve the highest DEE voltage possible while not exceeding the thermal tolerances. The RF auto tuner was only employed during CW operation, as provisions have not been installed for pulsed operation.

Koeth, Neutron Production with a 12-Inch Cyclotron (2017) — p. 1

Editorial note, tabletop extrapolation: A demonstrated tabletop RF plant, end to end: arbitrary function generator (drive + timing), solid-state intermediate stage, and an amateur-radio HF linear (AL-82 class, 1500 W continuous) into the matched tank. In THIS installation the uncooled dee — not the amplifier — set the ~1000 W average ceiling, and pulsing bought peak dee voltage inside that thermal budget (the auto-tuner only worked CW). Another machine repeats the analysis: matching range, tank losses, feedthrough heating and duty rating decide where its own ceiling sits.

The target, located at the end of a radial probe, is electrically isolated and connected to a BNC vacuum feed through. A short coaxial cable connected the target's signal to the input of oscilloscope's vertical amplifier. With 1MΩ input impedance, a 1µA beam current creates a 1V deflection. The rise time, as well as decay time noted in the beam current (lower) trace of figure 1 is an artifact of the RC response of the measurement circuitry, which utilized a low pass filter to suppress RF pickup from the DEE. The actual ion source current profile is prompt.

Koeth, Neutron Production with a 12-Inch Cyclotron (2017) — p. 2

Editorial note, tabletop extrapolation: A dead-simple current diagnostic for a pulsed machine: isolated target, BNC feedthrough, 1 MΩ scope input — 1 µA reads as 1 V. Three qualifications before trusting the number: it is COLLECTED current (secondary-electron emission makes it differ from incident beam unless suppressed or calibrated), the pulse must be long against the circuit RC for the trace to reach V = IR, and — the source's own warning — the visible rise and decay edges belong to the RF-suppression filter, not the beam.

The 12-inch cyclotron was tuned up for D+ ions, with the RF system tuned to 7.150MHz, for an average magnetic field set to 0.96T (by setting the top coil to 29.007Amps and bottom coil to 29.121 amps) with the AKG270 spiral poletips.[1] The ion source used the largest rectangular aperture chimney (hence lowest pressure differential), the Mass Flow Controller was set to 0.230 scc/m for an operating pressure of 3E-6 Torr, the ion source was run with a 10mA arc discharge current – all of these parameters balanced for optimal operating point.

Koeth, Gilde & Moroch, Measurement of Neutron Diffusion Time from Fast Pulsed Systems (draft, 2020) — p. 1

Editorial note, tabletop extrapolation: The most fully specified deuteron operating point in this collection — but treat it as recorded settings, not a validated matched pair: 7.150 MHz and 0.96 T are not mutually consistent with f = qB/2πm_d (7.150 MHz corresponds to ≈0.94 T; 0.96 T to ≈7.32 MHz, about 2% apart), and the draft does not say which number was measured against what. Reconcile against a field map or frequency counter before using the pair as a tune recipe. The slightly different top and bottom coil currents are reported settings; the draft does not state their purpose. Draft report.

The typical 12-inch cyclotron configuration to produce D-D neutrons through beam-on-target operation uses a long-pulsed mode with a duty factor of about 10% for RF thermal considerations given the passive cooling of the RF matching box components. However, the heretofore "pulsed mode" operation typically used beam-on durations of order 150ms - a lifetime as far as nuclear processes go.

Koeth, Gilde & Moroch, Measurement of Neutron Diffusion Time from Fast Pulsed Systems (draft, 2020) — p. 1

Editorial note, tabletop extrapolation: In the Rutgers system the duty-factor limit lived in a specific place — passive cooling of the matching-box components, not the dee and not the amplifier — at about 10% duty and ~150 ms beam-on. The transferable step is identifying which component limits a given machine's duty factor by loss estimate and temperature measurement, not the 10% figure itself. Draft report.

the cyclotron was pushed into its shortest pulsed mode operation yet, with only 230 RF cycles at 7.15 MHz (an RF drive pulse of 30 us duration), which resulted in the generation of a 10us beam-on-target pulse after the 20us ring up time. With such a short pulse duration, the pulse repetition rate could safely be increased up to 200pps (200Hz). Figure 2 shows the RF pulse structures on an oscilloscope with a time base of 10us/div: the upper trace is driving RF pulse, lower trace is actual DEE voltage, note the ring-up-time is due to the high Q of the tank circuit.

Koeth, Gilde & Moroch, Measurement of Neutron Diffusion Time from Fast Pulsed Systems (draft, 2020) — p. 2

Editorial note, tabletop extrapolation: Quantifies the price of a high-Q resonant dee for pulsed work on a tabletop machine: two thirds of a 30 microsecond drive pulse is spent ringing up, leaving 10 microseconds of usable flat top. A builder planning fast pulsed operation must budget the ring-up time explicitly. 230 cycles at 7.15 MHz is 32 microseconds, consistent with the stated 30 us. Draft report. (The quoted passage opens on the last line of p.1.)

As predicted via simulation, phase slippage at standard DEE voltage (8 kV) was so severe that ions were not delivered to the deflector.

Ruisard, Hine, Koeth & Rosenberg, The Rutgers Cyclotron: Placing Student's Careers on Target — WE1PB02, Proceedings of Cyclotrons2013 (2013) — p. 2

Editorial note, tabletop extrapolation: PDF p.2 = printed p.292. A cautionary data point for anyone tempted by straight radial-sector AVF tips: on this machine the phase slippage was fatal at 8 kV on the dee — and, holding the same field-frequency mismatch and final radius, a machine with LESS energy gain per turn takes more turns and accumulates more slip, so a low-voltage build should expect this failure mode to bite harder, not softer. Check isochronism in the tracker before cutting sectored steel (the spiral redesign that followed is dg-1745's story).

Additional SIMION studies identified 6 kV peak voltage and 15.534 MHz frequency as the optimal working point for proton transport.

Ruisard, Hine, Koeth & Rosenberg, The Rutgers Cyclotron: Placing Student's Careers on Target — WE1PB02, Proceedings of Cyclotrons2013 (2013) — p. 4

Editorial note, tabletop extrapolation: PDF p.4 = printed p.294. Shows a tabletop-scale RF operating point being chosen from tracking rather than by trial: a dee-voltage/frequency pair reported to the nearest kilohertz (15.534 MHz) with its 6 kV partner. The transferable practice: the tracker picks the working point before the machine is fired, and the optimum is jointly a voltage AND a frequency. The pair itself belongs to this field map — re-derive yours from your own model.

Over a decade of experimentation has been focused on transverse beam measurements without any knowledge of the longitudinal behavior. This is because the large residual electric field of the radio frequency (RF) accelerating potential makes standard electronic beam phase and bunch length measurements impossible. RF filtering permits average beam current measurements, but removes any time structure within an RF cycle.

Gonski, Burcher, Lazarov, Krutzler, Koeth & Beaudoin, A Novel Optical Method for Measuring Beam Phase and Width in the Rutgers 12-Inch Cyclotron — WE1PB04, Proceedings of Cyclotrons2013 (2013) — p. 1

Editorial note, tabletop extrapolation: PDF p.1 = printed p.299. Why a small machine cannot simply put a pickup in the chamber and read phase: at these radii a probe sits inside the dee's residual field, and the fix that recovers a current reading (RF filtering) is exactly the one that erases the RF-cycle time structure. Whether a carefully shielded electronic pickup could do better on some machine is untested here — this program's answer was to go optical.

We have developed an optical based measurement that is insensitive to DEE voltage using a fast (3 ns) phosphor screen viewed by a gated camera to create “time sliced” images which longitudinally profile the beam. The phosphor plate is located on the end of a radial positioner that can sweep the entire chamber radius and hence any ion revolution. … This optical method mitigates measurement difficulties due to interfering RF fields near the accelerating gaps, and enables measurements to be made arbitrarily close to the ion source.

Gonski, Burcher, Lazarov, Krutzler, Koeth & Beaudoin, A Novel Optical Method for Measuring Beam Phase and Width in the Rutgers 12-Inch Cyclotron — WE1PB04, Proceedings of Cyclotrons2013 (2013) — p. 1

Editorial note, tabletop extrapolation: PDF p.1 = printed p.299 (conclusion on p.3/printed p.301). The central transferable idea: convert a longitudinal measurement that residual RF spoils into an optical one — the paper's own claims are that it mitigates the RF-field interference near the gaps and reaches anywhere the radial probe does, including the central region. A radial positioner already exists on most small machines as a beam probe; the added cost is the fast phosphor and the gated camera, the camera being the expensive item.

Operation at 7.8 MHz was a compromise between maximum achievable proton energy and extending the RF period so as to maximize the time resolution

Gonski, Burcher, Lazarov, Krutzler, Koeth & Beaudoin, A Novel Optical Method for Measuring Beam Phase and Width in the Rutgers 12-Inch Cyclotron — WE1PB04, Proceedings of Cyclotrons2013 (2013) — p. 2

Editorial note, tabletop extrapolation: PDF p.2 = printed p.300. A tabletop machine running at a few MHz is accidentally well suited to this measurement: at lower cyclotron frequency a fixed gate width spans fewer RF degrees (Δφ = 360·f·Δt), so the same 3 ns camera gate buys finer phase resolution. Direct computation gives 3 ns of a 128.2 ns period = 8.42 degrees; the paper's 9 degrees is its rounding of that.

The cyclotron RF was operated in pulsed mode at a frequency of 20Hz to permit instantaneous high power (thus high DEE voltage)

Gonski, Burcher, Lazarov, Krutzler, Koeth & Beaudoin, A Novel Optical Method for Measuring Beam Phase and Width in the Rutgers 12-Inch Cyclotron — WE1PB04, Proceedings of Cyclotrons2013 (2013) — p. 2

Editorial note, tabletop extrapolation: PDF p.2 = printed p.300. The most portable RF trick in this collection for an amateur whose dee voltage is limited by amplifier and tank heating rather than by breakdown: pulse the RF and gate the measurement late in the pulse. Estimate the amplitude ring-up as τ ≈ Q_L/(πf) and put the gate several time constants in; choose repetition rate and duty from measured voltage and thermal limits — the 20 Hz here is what Rutgers' hardware wanted, not a design number.

we observe a tendency for bunch length to decrease with a rising magnetic field.

Gonski, Burcher, Lazarov, Krutzler, Koeth & Beaudoin, A Novel Optical Method for Measuring Beam Phase and Width in the Rutgers 12-Inch Cyclotron — WE1PB04, Proceedings of Cyclotrons2013 (2013) — p. 3

Editorial note, tabletop extrapolation: PDF p.3 = printed p.301 (Table 1; the 91 mm probe radius and ~100 keV termination energy are on PDF p.2). Rare published bunch-length numbers for a tabletop machine at almost exactly the 100 keV end of the target class: a beam tens of RF degrees long, with the measured means falling as field rises — the source states this as a tendency. The tabulated ±0.03 T is comparable to the spacing between the three field values; if that uncertainty were independent per row the settings would barely be distinguishable, so either it is largely common-mode (calibration) or ±0.003 T was intended — an unverified hypothesis, reported here as such with the printed value preserved.

We find that operating below the nominal magnetic field increased the turn-to-turn phase slippage.

Gonski, Burcher, Lazarov, Krutzler, Koeth & Beaudoin, A Novel Optical Method for Measuring Beam Phase and Width in the Rutgers 12-Inch Cyclotron — WE1PB04, Proceedings of Cyclotrons2013 (2013) — p. 2

Editorial note, tabletop extrapolation: PDF p.2 = printed p.300 (the linear fit is Fig. 5, PDF p.3 / printed p.301). Practical tuning guidance: on this machine, field trim and RF phase budget were one knob, with an approximately linear response over the measured 0.498–0.566 T and a definite sign — below nominal costs phase. On another machine, run the same local field scan (or a trajectory model) to get the slope and sign; the linearity is an observation over this range, not a law.

This error is acceptable, as long as the overall integrated phase slippage is less than 90°.

Gonski, Burcher, Lazarov, Krutzler, Koeth & Beaudoin, A Novel Optical Method for Measuring Beam Phase and Width in the Rutgers 12-Inch Cyclotron — WE1PB04, Proceedings of Cyclotrons2013 (2013) — p. 1

Editorial note, tabletop extrapolation: PDF p.1 = printed p.299. The governing constraint for any non-isochronous tabletop machine, under the source's convention: keep the integrated phase slippage inside the source's 90-degree budget, remembering the whole phase TRAJECTORY matters — a net-zero final slip does not save a beam that left the accelerating window mid-flight. Low dee voltage hurts twice (more turns against the same budget), and the deliberate start-above-nominal-field trick is best read as centering the phase excursion, not as a free correction.

The cyclotron has a single 5-inch radius DEE with a 0.9 inch vertical aperture and a matching dummy DEE. The Radio Frequency (RF) supply is tuneable from 2 to 30 MHz with power adjustable up to 1.5 kW; it can be operated in continuous or pulsed mode and is capable of achieving a peak DEE voltage of 10 kV.

Koeth, Beam Physics Demonstrations with the Rutgers 12-Inch Cyclotron — WEPPT025, Proceedings of Cyclotrons2013 (2013) — p. 1

Editorial note, tabletop extrapolation: PDF p.1 = printed p.369. The RF benchmark for the tabletop class as one machine's data point: 1.5 kW of tunable drive and a 10 kV peak dee voltage on a 5-inch dee — noting the two maxima need not be simultaneous, and what a kilowatt buys on another machine depends on its loaded Q, coupling and shunt impedance, which an upgrade should measure rather than scale. The 0.9-inch dee aperture is likewise this machine's choice, not a permitted fraction of any gap.

For reasons that will be discussed later the operating frequency is 13.56+0.03 MHz. Using the cyclotron frequency relationship: f = qB/2(pi)m a magnetic field of 0.889 Tesla was determined to be the operating field value. This was a welcome operating value, as the magnet need only be run at 70 percent of its maximum values, reducing the chance of coil failure by pressing the tolerances.

Koeth, The Construction and Operation of a Nine Inch Cyclotron (undated scan; the machine ran 1995–1999) — p. 1

Editorial note, tabletop extrapolation: A builder who inherits a fixed RF frequency (13.56 MHz here — a standard ISM frequency with cheap surplus hardware) can invert the design order and let the magnet operating point follow. Computed: 0.889 T is 74.1% of the 1.2 T ceiling — the author's "70 percent" is his rounding — and he treated the margin as a reliability choice for his coils; what margin buys on another magnet is a thermal/insulation/cooling question to check, not a free good. The quote's "+" before 0.03 MHz is a plus-or-minus sign the scan renders as a plus with an underline.

The DEE is supported by a 0.500 inch copper rod that is mounted to a CF2.75 flange. This whole assembly is then suspended from the chamber by a ceramic brake terminated with CF2.75 flanges at either end. This provides a substantial vacuum tight high voltage feed-though. The copper stem protrudes the vacuum flange by several inches allowing direct connection to the high voltage terminal in the RF matching cabinet, which is mounted just outside of the magnet coils.

Koeth, The Construction and Operation of a Nine Inch Cyclotron (undated scan; the machine ran 1995–1999) — p. 2

Editorial note, tabletop extrapolation: The mechanically simplest dee feed-through arrangement in the amateur literature - the same copper rod is structural support, RF conductor and vacuum feed-through, with a commercially available ceramic break doing the insulating. Keeping the matching cabinet immediately outside the coils keeps the high-impedance high-voltage run short. Note the appendix drawing (PDF p.16) dimensions this copper stem as 0.375 inch with a 0.75 inch brass collar, which disagrees with the 0.500 inch in the text. The source spells "break" as "brake" and "feed-through" as "feed-though".

MOPA - Master Oscillator Power Amplifier ideology was decided upon as it is known to be the most stable as well as the simplest to invoke. The MOPA system oscillates at the driving frequency with great stability, even under glow discharge conditions. However, because the cyclotron tank circuit possess a high Q, very careful tuning becomes necessary when ensuring maximum power delivery. Other oscillator systems were considered, such as an SEO - Self Excited Oscillator, where active feed back from a pickup loop in the chamber allows for the natural frequency of the tank circuit to be sought out and oscillate automatically. Another advantage of SEO systems is their characteristic to have a very high efficiency. However, self excited systems are very complicated and require utmost care from an experienced radio engineer to prevent unwanted modes of oscillations, known as parasitic oscillations.

Koeth, The Construction and Operation of a Nine Inch Cyclotron (undated scan; the machine ran 1995–1999) — p. 3

Editorial note, tabletop extrapolation: This is the clearest amateur-scale statement of the MOPA-vs-SEO trade for a cyclotron RF system, and it comes down in favour of MOPA for a first machine. The "known to be the most stable" and "very complicated" framings are the author's claims, presented as such. The key operational point for a tabletop builder is that MOPA holds frequency through a glow discharge, at the cost of needing careful manual tuning into a high-Q tank.

An HP8165 digital programmable RF signal source was used to drive an ENI350L 100 watt solid state amplifier. This method was much more convenient as fine tuning was easily achieved at the signal source rather than by manually tuning the tank circuit. The smallest adjustment capable of the HP8165 is 10kHz, which proved to be sufficiently sensitive. The output of the ENI350L amplifier was then passed through a Bird wattmeter (model 4410) and on to the RF cabinet.

Koeth, The Construction and Operation of a Nine Inch Cyclotron (undated scan; the machine ran 1995–1999) — p. 3

Editorial note, tabletop extrapolation: Calibration data from one resonator, plus one broadly good idea. The data: 100 W of solid-state drive bought ~1700 V peak dee here (16 W forward on the beam run of record), and 10 kHz source steps proved finer than the ~90 kHz loaded bandwidth — comfortable for THIS tank. The idea: fine-tune at the SIGNAL SOURCE, not the tank — it removes mechanical tuning from the operator's inner loop. Size your own amplifier from your dee capacitance, loaded Q, coupling and target voltage, with headroom for mismatch and discharge transients.

It utilizes the lumped capacitance of the DEE, which is approximately 70pF, to create a tank circuit out of the chamber itself. Using the resonance equation for an inductor in parallel with a capacitor: fr=1/2(pi)sqrt(LC) L, the inductance, was chosen to bring the fr to resonance at 13.56 MHz. Initially, coarse tuning was to create an 8 turn coil of length 5 inches, with a cross sectional area of 2.14 inches^2, out of 1/4-inch copper refrigeration tubing.

Koeth, The Construction and Operation of a Nine Inch Cyclotron (undated scan; the machine ran 1995–1999) — p. 3

Editorial note, tabletop extrapolation: The topology is the copyable part: use the dee-to-lid capacitance itself (~70 pF here) as the tank C, add an air-core tubing inductor, and couple through a coaxial few-turn primary with movable taps to find 50 Ω — no quarter-wave stem, no vacuum variable. Two numbers to reconcile on your bench: resonance at 13.56 MHz with 70 pF wants ≈2.0 µH (computed from the source's own equation), while Wheeler's formula on the printed coil geometry (8 turns, 5 in long, 2.14 in² area) yields only ≈0.8 µH — leads, strays and the actual in-situ capacitance evidently make up the difference, which is precisely why you measure fr in place and provide fine tuning rather than copying dimensions. (The 3-turn coaxial primary, adjustable taps and 50-ohm loading are printed on p.4.)

Cooling became a necessity when the RF power began to heat the secondary coil such that thermal expansion changed the tank fr. General Electric Dielectrol transformer oil is pumped through the 1/4 inch tubing of the secondary. The oil was then passed through a small heat exchanger that is cooled by flowing water. The oil is then returned to the pump reservoir of approximately two gallons volume. No effort was made to measure the cooling rate of the oil.

Koeth, The Construction and Operation of a Nine Inch Cyclotron (undated scan; the machine ran 1995–1999) — p. 4

Editorial note, tabletop extrapolation: A concrete failure mode plus fix at tabletop RF power levels (tens of watts to ~100 W into a high-Q tank): the tank drifts off tune as it warms, and the fix is to circulate a dielectric coolant inside the hollow tubing that already forms the inductor. Using transformer oil rather than water keeps the coolant non-conductive at the high-voltage end. The author notes no calorimetry was done, so no efficiency number can be taken from this.

For this cyclotron the non-loaded Q was about 1600. The measured Q of the tank circuit is somewhat less due to loading, denoted as QL. Looking at the voltage developed on a capacitve pickup very loosely coupled to the DEE, a sweeping RF signal was injected into the transmatch. ... fr was found to be 13.60 MHz. Because the response is measured in voltage rather than power, delta-f is measured at 70.7% of the maximum height, which was found to be 90kHz. Thus the QL of the tank circuit was measured to be 150, a very reasonable QL for a tank circuit of this type.

Koeth, The Construction and Operation of a Nine Inch Cyclotron (undated scan; the machine ran 1995–1999) — p. 4

Editorial note, tabletop extrapolation: A complete bench procedure: sweep RF into the transmatch, watch a very loosely coupled capacitive pickup, and take Δf at 70.7% of maximum height — the detail people get wrong, since a VOLTAGE response uses 1/√2 of peak, not half height. This resonator measured QL = 150 (13.60 MHz / 90 kHz = 151, consistent) against an unloaded ~1600; your own chamber-as-tank number depends on conductor losses, coupling and loading, and is a twenty-minute measurement by this method. (Spelling "capacitve" as printed; source cross-reference misprint: p.4 says the Q sweep is 'shown in Fig.3' — the sweep is Fig. 4; Fig. 3 is the RF block diagram.)

The high voltage capacitor, denoted as C1, was charged to the peak RF voltage through the rectifier and bled off by the high impedance resistor network. A DMM with a high input impedance was placed across R2 to measure the developed voltage. The ratio of R2 to R1 is 1:9.1E+5, thus the peak DEE voltage is: V(D-peak) = 9.1E+5 x V(r2)

Koeth, The Construction and Operation of a Nine Inch Cyclotron (undated scan; the machine ran 1995–1999) — p. 4

Editorial note, tabletop extrapolation: A workable absolute dee-voltage measurement built from a rectifier, a capacitor, two resistors and a DMM — which is to say, a HOMEMADE high-voltage RF probe, and it deserves probe-grade engineering: voltage-rated component strings, enclosure, a verified discharge path, remote reading. Its accuracy hangs on diode drop, leakage and the resistors' voltage coefficient, and the signal is small — at 1700 V peak the R2 reading is about 1.9 mV (computed), so calibrate the chain and estimate its uncertainty before quoting dee volts from it. The resistor values are read from Fig. 5 (R1 = 750 MΩ, R2 = 820 Ω); 750E6/820 = 914,600, consistent with the printed 9.1E+5.

As expected, the peak DEE voltage rises as the square root of the applied RF power, Fig.6, and the peak induced voltage is linearly proportional to the peak DEE voltage, Fig.7.

Koeth, The Construction and Operation of a Nine Inch Cyclotron (undated scan; the machine ran 1995–1999) — p. 4

Editorial note, tabletop extrapolation: The method transfers, the number does not: measure YOUR dee voltage against forward power and expect approximate √P scaling while coupling and loaded Q stay fixed — this resonator's curve ran ~500 V near 4 W to ~1700 V at 60 W (points read from the rendered Fig. 6, 0-2000 V / 0-80 W axes; they bracket, not define, one exact coefficient). The practice worth copying outright: calibrate the cheap capacitive pickup against the rectifier divider once (Fig. 7's linearity), then use the pickup as the day-to-day reference. (The quoted sentence is the last line of p.4 and continues on p.5.)

the magnet poles must be attracting one another under the tremendous force, thereby squeezing the lids on the vacuum chamber. The inward movement of the lids would decrease the distance between the DEE and the lids creating an increase in chamber capacitance, thereby bringing down fr. The distance of movement was calculated from the change in frequency. Just using the approximation for a parallel plate capacitor the distance the gap decreased was on the order of 7 nanometers. The attractive force between the two poles was also estimated, at 1 Tesla the attractive force is approximately 16,000 N which the equivalent of placing a 3,500 pound mass on the top yoke. … Under such forces it is reasonable to imagine deflection on the order of 70 Angstroms.

Koeth, The Construction and Operation of a Nine Inch Cyclotron (undated scan; the machine ran 1995–1999) — p. 5

Editorial note, tabletop extrapolation: The most surprising transferable failure mode in the document, appearing when the chamber is shimmed snugly between the poles: Fig. 8 shows the tank fr flat at ~13.559 MHz from 0.17-0.67 T then falling to ~13.551 MHz near 1.0-1.07 T — an ~8 kHz walk, comparable to this RF source's 10 kHz tuning step. Expect the tank to move during a magnet ramp and either retune per field point or decouple the lids from the pole faces. The 16,000 N checks against B²A/2μ₀ for a 9-inch pole at 1 T (computed, ≈16,300 N); the attribution of the shift to lid motion is the author's interpretation, consistent between his frequency-derived 7 nm and force-based plausibility argument.

It is worth noting that even under maximum ion current conditions of 50 nanoamps no beam loading was noticed.

Koeth, The Construction and Operation of a Nine Inch Cyclotron (undated scan; the machine ran 1995–1999) — p. 5

Editorial note, tabletop extrapolation: A useful separation-of-concerns datum: at 50 nA this machine saw no detectable beam loading, so RF tuning and beam tuning decoupled cleanly — expect the same at nanoamp-class currents, as a practical matter rather than a law (loading scales with current and energy gain, and a sensitive enough RF measurement might resolve it). The corollary stands: at these currents beam loading is useless as a diagnostic; a collector is the instrument.

The measured ion peak at 0.885 Tesla tightly corresponded with the theoretical value to 0.6%. ... However an unexpected peak at 0.449 Tesla developed. ... After an investigation into the matter, it was determined that indeed singly charged protons were being accelerated. ... the RF frequencies required for acceleration of the ions at the low magnetic fields, developed from excitation of higher frequency modes of oscillation in the tank circuit. ... If the applied frequency were double that of the fundamental, on it's second crossing of the gap the ion would receive a de-acceleration, thus gaining zero net acceleration. However, if the RF frequency were triple that of the fundamental it is seen that the electric field direction is again in sync with ion's travel. This effect holds true for any odd multiple of the fundamental cyclotron frequency.

Koeth, The Construction and Operation of a Nine Inch Cyclotron (undated scan; the machine ran 1995–1999) — p. 8

Editorial note, tabletop extrapolation: The most instructive diagnostic story in the document, with one open number. A builder ramping the magnet while watching a collector WILL see spurious low-field peaks and will suspect contaminant species; this source traced its extra peak to the RF tank ringing on harmonic modes, protons confirmed. Unresolved, computed here: 0.449 T is almost exactly half of 0.885 T — at fixed drive frequency that is an even multiple of the ion's fundamental, which the source's own two-crossing argument says gives zero net acceleration; a third-harmonic peak would sit near 0.295 T. So the qualitative lesson (check the RF spectrum and recompute candidate resonances via B = 2πmf/(qh) before blaming ion species) stands, while this particular peak's mechanism needs a nonideal ingredient the source does not supply. The author's reported consequences — harmonic operation sharpens the field peak; suppressing tank harmonics improves efficiency — were stated intent, not achieved results. Ellipses mark omitted intervening text.

Sufficient data has been taken with this feasibility-study cyclotron to warrant progression to a twelve inch magnet. It is reasonable to expect one million volt protons with a magnetic field of 1.2 Tesla, and an fr of 18 MHz. Such a magnet system is currently being obtained. ... The use of a solid state amplifier is precluded once power requirements exceed 500 Watts. ... Finally, after the twelve inch system has proved operable, a tangential accessory vacuum port will be added with the intention to extract the proton beam.

Koeth, The Construction and Operation of a Nine Inch Cyclotron (undated scan; the machine ran 1995–1999) — p. 8

Editorial note, tabletop extrapolation: Design intent, not achievement — every number is a plan as of September 1999. What transfers is the staging philosophy: prove the concept on a small borrowed magnet (~184 keV, 9 inches) before committing to the larger machine. The "solid state precluded above 500 W" line is the author's 1999 equipment landscape, not a law — modern LDMOS amplifiers run solid-state into the kilowatts (the same lineage's later 1.5 kW AL-82 tube chain and pulsed operation, dg-1756/dg-1804, show the options both ways). The 1 µA figure on the same page is what "could have been achieved" with more source work — expectation, not measurement. Ellipses mark omitted text. (The first two quoted sentences begin on p.8.)

The three-sector cyclotron operating at the 6 harmonic mode of acceleration allows to have an effective magnetic system due to wide sectors providing higher mean field and narrow valleys sufficient for placing resonators corresponding to 6th harmonic of acceleration

Karamyshev, A New Design of PET Cyclotron — IPAC2022, paper THPOMS016, JACoW (2022) — p. 1

Editorial note, tabletop extrapolation: Relevant only to a sector-focused (AVF) tabletop design; a classical uniform-field machine at h = 1 has no valleys to house resonators. For a small AVF study it shows that sector count and harmonic number are chosen together, since the valleys set the room available for dees.

90 degrees azimuthal width, and valleys are about 30 degrees. In such case the 6th harmonic mode is optimal for acceleration and the resonance frequency must be 145 MHz for magnetic field equal to 1.55 T.

Karamyshev, A New Design of PET Cyclotron — IPAC2022, paper THPOMS016, JACoW (2022) — p. 1

Editorial note, tabletop extrapolation: The arithmetic transfers directly: f_RF = h · qB/(2π m γ) ≈ h × 15.2 MHz/T for protons/H-, so 1.55 T at h = 6 gives ~142–145 MHz. At ~0.6 T a tabletop machine at h = 1 sits near 9 MHz; raising h is the lever that moves the RF into a chosen band without changing the field.

RF frequency is placed in 144-146 MHz range, which is dedicated for amateur use. This ensures that there should be no issues with legal use of the frequency.

Karamyshev, A New Design of PET Cyclotron — IPAC2022, paper THPOMS016, JACoW (2022) — p. 1

Editorial note, tabletop extrapolation: A tabletop design can treat the RF frequency as a spectrum-allocation input as well as a physics output: field and harmonic number together decide which band the oscillator falls in. Whether an amateur allocation actually permits running an accelerator's RF is a licensing question the paper asserts but does not analyse.

Such configuration is beneficial for both magnet and RF design, as the magnet, while having necessary average magnet field is being very efficient (has small number of A*turns), high frequency RF system is very compact.

Karamyshev, A New Design of PET Cyclotron — IPAC2022, paper THPOMS016, JACoW (2022) — p. 1

Editorial note, tabletop extrapolation: The underlying trade is general: higher RF frequency shrinks resonator size (quarter-wave length scales as 1/f). For a tabletop machine with ~9 MHz RF, resonator size is dominated by lumped dee capacitance rather than line length, so the compactness gain the paper describes applies mainly to designs operating at high harmonic.

All 3 cavities will be powered independently with a coupling loop. It is not possible to have galvanic connection in the center region.

Karamyshev, A New Design of PET Cyclotron — IPAC2022, paper THPOMS016, JACoW (2022) — p. 3

Editorial note, tabletop extrapolation: Where a common galvanic connection between dees is impractical, independently fed, phase-controlled coupling loops are one transferable solution; a single-dee or two-dee tabletop machine with one resonator avoids the issue.

The active tuning system must be designed to bring the cavities on the frequency initially to compensate detuning for temperature variations due to RF heating and can be realized by capacitance tuner from radial direction.

Karamyshev, A New Design of PET Cyclotron — IPAC2022, paper THPOMS016, JACoW (2022) — p. 3

Editorial note, tabletop extrapolation: Thermal detuning follows the power actually dissipated in the resonator walls and where it lands, not the drive power alone; it is smaller at the dee voltages tabletop machines run but not zero, and a high-Q resonator still drifts as dee and stem warm. Estimate the wall loss and the resulting frequency shift against the resonator's bandwidth; a trimmer capacitor or a frequency-following drive serves the same function as the paper's radial tuner.

high frequency of RF system can potentially lead to poor capture of particles in the first accelerating gap. But this problem can be solved if in the first accelerating gap particles will arrive with some energy

Karamyshev, A New Design of PET Cyclotron — IPAC2022, paper THPOMS016, JACoW (2022) — p. 3

Editorial note, tabletop extrapolation: Transit phase across a gap is roughly Δφ ≈ 2π·f·g/v, so the comparison depends on gap width and the ion's speed at the gap as well as on frequency: at ~9 MHz (protons, h = 1, ~0.6 T) the effect is weaker than at 145 MHz for the same gap and entry energy, and it grows with a higher harmonic, a wider first gap, or a lower injection velocity.

Particles start from the PIG source, which is placed under 7500 V and accelerate to the “Cup” (red part on Fig. 6) and arrive to the first gap with 7.5 keV energy. Also, the advantage of such central region is that one ion source placed in the middle can deliver beam in each gap simultaneously, due to the symmetry of such central region.

Karamyshev, A New Design of PET Cyclotron — IPAC2022, paper THPOMS016, JACoW (2022) — p. 3

Editorial note, tabletop extrapolation: A DC pre-acceleration stage between an internal source and the first RF gap is a transferable central-region idea: it raises the energy entering the first gap independently of the dee voltage, which can help a low-dee-voltage tabletop machine with first-turn clearance.

The hill gap is 4 cm and the valley gap is 64 cm, same as the distance between the upper and lower return yokes.

Pandit, Sing Babu, Goswami, Sarma et al., Magnetic Field Calculations of a 10 MeV High Current Compact Cyclotron — APAC 2007, paper WEPMA005, JACoW (2007) — p. 1

Editorial note, tabletop extrapolation: The 4 cm hill and 64 cm valley gaps are the reference geometry behind this machine's flutter, not a ratio to scale: a tabletop AVF study takes flutter and tunes from its own computed median-plane field and chooses hill and valley gaps from those results.

It was found that these tubes will produce X-rays when operated with a forward or reverse potential. Under reverse potential, measured outputs were observed to drop by a factor of 50 to 100.

Properzio, Woodcock & Heidersdorf, X-Ray Emission from Cold-Cathode Gas Discharge Tubes Used for Educational Purposes — BRH/DEP 70-1, Bureau of Radiological Health, US Public Health Service (1970) — p. 18

Editorial note, tabletop extrapolation: In an RF-driven machine opposing surfaces can serve as electron targets during different phases, and a dc bias, asymmetric electron production, geometry or shielding can make the two half-cycles very unequal; the BRH's 50–100-fold dc polarity factor is not to be used quantitatively for an RF machine. Which surface dominates follows from the phase-dependent electron current and energy, the target material, geometry and shielding — or from measurement.

The significant fact is that placement of the survey instrument in the rf shield only slightly changes the response when compared to that of an unshielded instrument.

Properzio, Woodcock & Heidersdorf, X-Ray Emission from Cold-Cathode Gas Discharge Tubes Used for Educational Purposes — BRH/DEP 70-1, Bureau of Radiological Health, US Public Health Service (1970) — p. 46

Editorial note, tabletop extrapolation: An RF-driven accelerator presents the same interference problem to survey instruments near the resonator. A seam-continuous conductive-fabric bag is a low-cost candidate fix that the BRH found barely changed the meter's X-ray response; its RF attenuation at a resonator frequency of a few to tens of MHz was not measured (the cited fabric data cover 350–1000 MHz). Validate the shielded meter with a check source or a calibrated field, and cross-check readings at the energized machine with a passive dosimeter or an RF-immune detector — an RF-on, beam-off reading may be genuine X-rays from dark current, field emission or multipactor and must not be discounted as interference.

Constant potentials may require 15 to 25 percent larger thicknesses of lead and 5 to 15 percent larger thicknesses of concrete than those given here for pulsating potentials.

NCRP Report No. 26, Medical X-Ray Protection Up to Three Million Volts — NBS Handbook 76, National Bureau of Standards (1961) — p. 47

Editorial note, tabletop extrapolation: The factor is the handbook's for 250-300 kVp and is not stated for lower voltages; using it at tens of kV is an extrapolation. A d-c electrode or a well-filtered supply produces more photons near the endpoint than a pulsating one at the same peak voltage, so an electrode held at steady d-c (extractor, deflector, rectifier stack) is the constant-potential case; an RF dee, near peak for only part of each cycle, plausibly sits closer to the pulsating case (an interpretation, not the source's).

The effective potential is twice the potential applied to the x-ray tube, and the radiation is very penetrating.

ANSI N43.2-1971, Radiation Safety for X-Ray Diffraction and Fluorescence Analysis Equipment — NBS Handbook 111, National Bureau of Standards (1972) — p. 19

Editorial note, tabletop extrapolation: Any vacuum-tube rectifier, high-voltage valve or vacuum switch in an accelerator's power train can be an X-ray source in its own right, and its endpoint can exceed the electrode voltage. A possible analogue in a two-dee RF machine (an interpretation, not the source's) is electrons crossing between dees driven in antiphase, which could gain up to the dee-to-dee potential (twice the dee-to-ground amplitude); survey the power supplies as well as the chamber.

multipacting relies only on secondary electron emission from the electrodes. Thus, it is not dependent on the type of gas in which the breakdown takes place.

Woo, Final Report on RF Voltage Breakdown in Coaxial Transmission Lines — JPL Technical Report 32-1500, Jet Propulsion Laboratory, prepared under NASA contract NAS 7-100 (1970) — p. 10

Editorial note, tabletop extrapolation: Within Woo's collisionless, field-free two-surface model the gas species drops out and fd is the scaling parameter, so results from other machines scale by fd for a fixed impedance rather than by voltage alone. Whether a given gap actually multipacts still depends on the RF voltage band and phase, geometry, the electrodes' secondary-emission yield and surface condition, the pressure-dependent collision probability near the mean-free-path limit, and any magnetic or dc field — a gap inside a cyclotron magnet needs its own check (dg-1986, dg-1988).

Note that multipacting will not occur for values of fd lower than 70 MHz-cm; this represents the cutoff situation. […] The boundary AB represents the threshold conditions for multipacting. However, boundary AB shifts to higher voltages with the occurrence of multipacting and the consequent outgassing of the electrodes (Fig. 2). […] Thus, the threshold values for multipacting should be used when designing breakdown-free lines.

Woo, Final Report on RF Voltage Breakdown in Coaxial Transmission Lines — JPL Technical Report 32-1500, Jet Propulsion Laboratory, prepared under NASA contract NAS 7-100 (1970) — p. 13

Editorial note, tabletop extrapolation: Referee arithmetic: the 70 MHz-cm cutoff is a gap below ~7.8 cm at 9 MHz or ~2.6 cm at 27 MHz. These are field-free coaxial and parallel-plate results; Woo notes that scaling relations with a magnetic field were derived but not experimentally verified, and that dc or magnetic fields can give one-sided modes, so a gap inside a cyclotron magnet needs its own check.

although a dc bias can be used to prevent multipacting it would have to be fairly high. In many cases, therefore, this method would be undesirable.

Woo, Final Report on RF Voltage Breakdown in Coaxial Transmission Lines — JPL Technical Report 32-1500, Jet Propulsion Laboratory, prepared under NASA contract NAS 7-100 (1970) — p. 13

Editorial note, tabletop extrapolation: Supplies a measured bias map behind the qualitative dee-bias rules, for one coaxial configuration: there the bias needed to clear the band was about −100 V or +150 V against RF levels of ~80–370 V rms, and a small positive bias (~ +25 V) lowered the onset to ~80 V rms (figure readings). For dees the transferable point is qualitative — a bias well below the RF amplitude may not clear the band and can move or enlarge it; the bias needed is geometry-specific and found by analysis or measurement.

The mean free path limit represents the condition that the electron mean free path is equal to d. The mean free path limit, therefore, separates the ionization and multipacting breakdown regions.

Woo, Final Report on RF Voltage Breakdown in Coaxial Transmission Lines — JPL Technical Report 32-1500, Jet Propulsion Laboratory, prepared under NASA contract NAS 7-100 (1970) — p. 17

Editorial note, tabletop extrapolation: Referee arithmetic from Fig. 7 (p.19): the air mean-free-path line follows p x d ~ 0.025 torr-cm, so at 1 Pa (7.5 x 10^-3 torr) a gap below ~3 cm is on the collisionless side and at 0.1 Pa almost any bench gap is — a collision-regime estimate only. fd below 70 MHz-cm excludes Woo's field-free two-surface mode (a 3 cm gap at 9 MHz is fd ~ 27); fd above it merely permits multipacting, which also needs a resonant voltage band and sufficient secondary yield, and a cyclotron's magnetic field changes the trajectories and allows other modes. A different fill gas shifts the line with its electron mean free path; the report places multipacting generally below 10^-2 torr (p.9).

This is equivalent to saying that each minimum occurs at a pressure given in microns (1 micron = 10^-3 torr) equal to the frequency given in MHz.

Woo, Final Report on RF Voltage Breakdown in Coaxial Transmission Lines — JPL Technical Report 32-1500, Jet Propulsion Laboratory, prepared under NASA contract NAS 7-100 (1970) — p. 20

Editorial note, tabletop extrapolation: Referee arithmetic: the diffusion-controlled minimum would fall near 9 microns (~1.2 Pa) at 9 MHz and near 27 microns (~3.6 Pa) at 27 MHz, so a 0.1-1 Pa fill sits at or below it, on the side where ignition gets harder as pressure falls. The rule holds for fd > 100 MHz-cm (a gap above ~11 cm at 9 MHz); bench gaps at 9 MHz are fd < 100, where Woo's oscillation-amplitude limit raises breakdown further. Air data in coaxial lines.

When fd is less than 145 MHz-cm, the ionization breakdown power level is higher than the multipacting power level whereas the reverse is true when fd is greater than 145 MHz-cm.

Woo, Final Report on RF Voltage Breakdown in Coaxial Transmission Lines — JPL Technical Report 32-1500, Jet Propulsion Laboratory, prepared under NASA contract NAS 7-100 (1970) — p. 24

Editorial note, tabletop extrapolation: Measured minima for Woo's 50-ohm air-filled coaxial specimens: of order 50–75 V across gaps of fd 100–400 MHz-cm at the pressure minimum. Not a floor for other geometries or gases — the breakdown level moves with gas, geometry, field enhancement, frequency, electrode condition, magnetic field and impedance — but a reminder that a low-voltage RF electrode in gas near its pressure minimum can ignite at tens of volts: check the operating pressure against the minimum for the actual gap and gas.

The carbon dioxide and argon gases had a purity level of 99.99%. […] As can be seen, breakdown in carbon dioxide is 12-18% lower than that of air while breakdown in argon is 45-60% lower.

Woo, Final Report on RF Voltage Breakdown in Coaxial Transmission Lines — JPL Technical Report 32-1500, Jet Propulsion Laboratory, prepared under NASA contract NAS 7-100 (1970) — p. 30

Editorial note, tabletop extrapolation: Air-based breakdown charts overstate the margin for an argon fill: in Woo's lines argon broke down at roughly half the air power (a 45–60 % reduction in power is a smaller reduction in voltage). Neon was not measured in this report, so its breakdown level must be measured in the actual fill or taken from another source rather than read from air charts.

Thus, both types of surface treatment will not eliminate multipacting in coaxial transmission lines.

Woo, Final Report on RF Voltage Breakdown in Coaxial Transmission Lines — JPL Technical Report 32-1500, Jet Propulsion Laboratory, prepared under NASA contract NAS 7-100 (1970) — p. 38

Editorial note, tabletop extrapolation: Reported as Woo's judgement for air-exposed coaxial lines: a low-yield coating on a component that is vented to air between runs may not keep its secondary yield below unity. Which lever is more reliable for a dee — geometry, bias or conditioning — is not established by this source, and a dc bias brings its own electrical hazards.

we find a turning point (point "B" in figure 4(a)) beyond which we experience a sudden increase of the breakdown voltage

Korolov & Donkó, Breakdown in hydrogen and deuterium gases in static and radio-frequency fields — Physics of Plasmas (2015), doi:10.1063/1.4929858; arXiv:1512.08726 — p. 4

Editorial note, tabletop extrapolation: In this 13.56 MHz, 1 cm hydrogen experiment the low-pL branch is multi-valued: ignition at fixed pressure under rising voltage and at fixed voltage under rising pressure can occur at different points. In comparable systems characterise ignition with both sweeps rather than assuming a unique threshold.

at lower frequency the electron oscillation amplitude is higher at otherwise same conditions, therefore the bending point "B" moves to higher pL at lower f

Korolov & Donkó, Breakdown in hydrogen and deuterium gases in static and radio-frequency fields — Physics of Plasmas (2015), doi:10.1063/1.4929858; arXiv:1512.08726 — p. 5

Editorial note, tabletop extrapolation: Referee inference, limited: Korolov & Donkó tie the shape of the RF curve to the electron oscillation amplitude relative to the gap, which depends on the RF field, frequency, collision rate and geometry — and, in a cyclotron's 0.5–1 T field, on the strong magnetization of electrons at MHz frequencies, which the unmagnetized 1 cm bench case does not include. The surface-governed regime therefore cannot be assumed for a magnetized dee gap: calculate the electron motion for the actual field, frequency, gas and gap, or test ignition in the magnetized gap. The paper's data are for hydrogen at L = 1 cm and pL of roughly 1–30 Torr cm.

a factor of 1.8 is found (71 V vs. 125 V) between the minimum breakdown voltage values.

Korolov & Donkó, Breakdown in hydrogen and deuterium gases in static and radio-frequency fields — Physics of Plasmas (2015), doi:10.1063/1.4929858; arXiv:1512.08726 — p. 5

Editorial note, tabletop extrapolation: Two careful measurements of the same nominal system differed by a factor of about 1.8, which the authors attribute to systematic error or impurities in the other data set — the reason to characterise ignition in the actual cell, not a general uncertainty cap. The authors conditioned their stainless electrodes with ~8 mA dc discharges of both polarities for about 10 minutes (p. 2) — their preparation, with its own electrical and surface-modification hazards, not a universal prescription. The yield is quoted as 0.008 in the text and the Fig. 4(a) legend; the Fig. 4(b) legend prints 0.08.

The power added efficiency of 75% was measured without using the circulator.

Smirnov, Ivanov, Krasnov, Polikhov, Rezanov & Sharkov (Siemens Research Center, Moscow), 72 MHz Solid-State Amplifier Power Test — IPAC2014, paper WEPME008, JACoW (2014) — p. 2

Editorial note, tabletop extrapolation: The topology (identical 48–50 V class-AB LDMOS modules, 50 Ohm in and out, summed in a combiner) transfers to a tabletop dee drive, where one or two modules may suffice and a combiner may be unnecessary. The module's efficiency, gain, power and band are calibration context only: dissipation for a tabletop stage comes from the chosen device's datasheet or its measured drain efficiency at the intended frequency, bias, output network and power. The ~75 % (one module, matched load, no circulator), 50 % (whole system, wall plug), 2 kW per module and 51 dB gain are this generator's numbers.

As for now, the maximum output power of 2500 W can be handled during short pulses. The CW regime is limited because of the following reasons. The output impedance of the transistor amplifier is ~1 Ohm, which has to be matched to a 50 Ohm output. Currently, we use a single-stage planar transformer which results in too high current that leads to the local overheating (115 °C) as shown in Fig. 3. This problem will be solved in the next version of RFPA by using prematching circuit between transistor output and planar transformer. In order to reduce the risk of RFPA damage, for further tests the output RF power has been limited to 1800 W at 5 ms pulses with 20% duty cycle.

Smirnov, Ivanov, Krasnov, Polikhov, Rezanov & Sharkov (Siemens Research Center, Moscow), 72 MHz Solid-State Amplifier Power Test — IPAC2014, paper WEPME008, JACoW (2014) — p. 2

Editorial note, tabletop extrapolation: The impedance-transformation problem scales with power: at 100 W-1 kW from a 50 V LDMOS device the ideal drain load line is about 1-12 Ohm (V_dd^2/2P, see formula), so the output transformer carries large currents and is a thermal component to be IR-imaged or thermocoupled at full power, not only an RF one. The 115 C hot spot and the 1800 W/20 % derating are this module's history, not a general rating.

Two trombone phase shifters were connected between the RFPA and the cavity to represent different transmission line lengths to the cavity and to adjust the phase difference between forward and reflected waves.

Smirnov, Ivanov, Krasnov, Polikhov, Rezanov & Sharkov (Siemens Research Center, Moscow), 72 MHz Solid-State Amplifier Power Test — IPAC2014, paper WEPME008, JACoW (2014) — p. 2

Editorial note, tabletop extrapolation: Directly transferable as a bench method for a tabletop drive: the electrical length of the cable between amplifier and dee decides what impedance the transistor sees off resonance. Sweep the reflection phase through a full 360 degrees (a line stretcher or a set of cable lengths) at low power, across the detuning and coupling states the dee will see, to map the candidate worst-case impedances; then test at power incrementally with protection in place — the low-power sweep maps, it does not prove high-power stability or ruggedness. The Q, frequency and test powers are those of this 72 MHz test resonator.

50 us pulses used at these measurements. Use of longer pulses makes no sense because the fill time of the cavity is nearly 10 us.

Smirnov, Ivanov, Krasnov, Polikhov, Rezanov & Sharkov (Siemens Research Center, Moscow), 72 MHz Solid-State Amplifier Power Test — IPAC2014, paper WEPME008, JACoW (2014) — p. 2

Editorial note, tabletop extrapolation: The relation transfers and favours low frequency: at fixed loaded Q the fill time grows as 1/f, so a 6-30 MHz dee has a longer settling time than a 72 MHz cavity of the same Q. A soft-start or pulsed test on a tabletop dee should use pulses several fill times long, computed from that dee's measured loaded Q and frequency.

These measurements showed that the RFPA experiences no problems when feeding the resonator (can handle full reflection), even if at certain phaselengths filling and decay times raised and the reflected power level increased. Nevertheless, these issues will not negatively affect the generator during CW cyclotron operation, taking into account matched conditions with cavity beam loading.

Smirnov, Ivanov, Krasnov, Polikhov, Rezanov & Sharkov (Siemens Research Center, Moscow), 72 MHz Solid-State Amplifier Power Test — IPAC2014, paper WEPME008, JACoW (2014) — p. 3

Editorial note, tabletop extrapolation: Evidence from one module, 50 µs pulses, one 72 MHz test resonator and the phases tried: a rugged LDMOS stage rode the start-up transient of a high-Q resonator without an isolator. The authors' CW judgment rests on matched conditions with beam loading; the test does not establish CW survival under sustained full mismatch (start-up, beam loss, detuning, arcs, tuner faults), and a lower-frequency cavity's longer fill time lengthens the exposure. At tabletop frequencies, where ferrite circulators are bulky or unavailable, omitting one requires the device's rated mismatch ruggedness plus protected high-power testing under no-beam, detuned and fault conditions.

The necessity of using the circulators is due to low and unequal isolations (from 14 dB to 16 dB) between power combiner inputs

Smirnov, Ivanov, Krasnov, Polikhov, Rezanov & Sharkov (Siemens Research Center, Moscow), 72 MHz Solid-State Amplifier Power Test — IPAC2014, paper WEPME008, JACoW (2014) — p. 3

Editorial note, tabletop extrapolation: Applies only if a tabletop drive combines two or more modules: inter-port isolation is one of the factors (with module gain balance and phasing) that decide whether paralleled amplifiers stay stable. A single-module drive does not face this issue; a multi-module drive calls for a combiner with adequate input isolation (the source gives no design; isolating hybrid or Wilkinson-type combiners with a balance load are the usual general RF answer, not this paper's). The 14–16 dB isolation and 0.5 % dissipation are this combiner's; the ~15 % penalty is what the source attributes to running the system with the circulators the poor isolation required.

The control system has function of resonance frequency tracking of the cyclotron during operation and adjusts simultaneously the operation frequency of the generator.

Smirnov, Ivanov, Krasnov, Polikhov, Rezanov & Sharkov (Siemens Research Center, Moscow), 72 MHz Solid-State Amplifier Power Test — IPAC2014, paper WEPME008, JACoW (2014) — p. 1

Editorial note, tabletop extrapolation: The telemetry transfers to a tabletop drive: drain voltage/current, drive level and forward/reflected power per stage are cheap to measure and are the inputs any protection loop needs. The frequency tracking does not transfer as stated: in a fixed-field cyclotron the RF frequency is set by field and harmonic for beam synchronism, so the dee is held on resonance by a mechanical or electrical tuner while the RF stays at the beam-synchronous frequency — letting the generator chase cavity drift would slip the beam phase.

The matching is between the real part of the tetrode 4CW100000E cathode impedance, Zc and Z0 (50Ω). We may use the simple Γ-matching network, because Zc<<Z0.

Caruso, Caruso, Longhitano, Spartà, Sura & Primadei, Hybrid Configuration, Solid State–Tube, Revamps an Obsolete Tube Amplifier for the INFN K-800 Superconducting Cyclotron — Cyclotrons 2016, paper WEB02, JACoW (2016) — p. 3

Editorial note, tabletop extrapolation: The source's Gamma network — a shunt variable capacitor across a series path of the second variable capacitor, the inductor and the load, i.e. a two-arm L-section with three physical reactances — is the standard way to bring a 50 Ohm solid-state stage onto a low-impedance load and applies to a tabletop drive; vacuum or air variables keep it tunable. The 10–1000 pF range and the 15–50 MHz band belong to this kW-class tube-driving stage; a tabletop network must be designed for its own load impedance.

All the frequency range is perfect matched at 50Ω, an example of this result, at 43,61 MHz is shown in Fig. 9.

Caruso, Caruso, Longhitano, Spartà, Sura & Primadei, Hybrid Configuration, Solid State–Tube, Revamps an Obsolete Tube Amplifier for the INFN K-800 Superconducting Cyclotron — Cyclotrons 2016, paper WEB02, JACoW (2016) — p. 3

Editorial note, tabletop extrapolation: Transfers as a planning fact for this network at this tuning: the VSWR stayed below ~1.5 only within roughly +/-190–200 kHz of the tuned point (figure reading), so a tabletop drive that changes frequency (field changes, different species) needs tunable elements or a re-tune procedure; other settings and networks have their own bandwidth, set by loaded Q and the matching design.

Mismatch up to 2.0:1 was tested too (30%);

Caruso, Caruso, Longhitano, Spartà, Sura & Primadei, Hybrid Configuration, Solid State–Tube, Revamps an Obsolete Tube Amplifier for the INFN K-800 Superconducting Cyclotron — Cyclotrons 2016, paper WEB02, JACoW (2016) — p. 3

Editorial note, tabletop extrapolation: Useful only as a conversion warning: when a source quotes a mismatch percentage, check whether it means voltage or power before using it to size a reflected-power trip on a tabletop LDMOS drive. The 2:1 test applies to this kW-class amplifier, not to any other device's ruggedness.

The system works very well with a lot of final 1st stage configuration (tetrode, mosfet, bjt, new LDMOS etc) of the SSA drivers,

Caruso, Caruso, Longhitano, Spartà, Sura & Primadei, Hybrid Configuration, Solid State–Tube, Revamps an Obsolete Tube Amplifier for the INFN K-800 Superconducting Cyclotron — Cyclotrons 2016, paper WEB02, JACoW (2016) — p. 3

Editorial note, tabletop extrapolation: The design principle transfers to a tabletop drive: a standardized 50 Ohm interface plus an adequately ranged tunable match may ease substituting amplifiers (commercial, homebuilt, upgraded), subject to verifying frequency, power, impedance, stability and the resonator coupler's rating and tuning range. The kW figures belong to this tube final stage.

The drivers are class A, wideband, 50 dB gain and a maximum out power of 200 W.

Caruso, Caruso, Longhitano, Spartà, Sura & Primadei, Hybrid Configuration, Solid State–Tube, Revamps an Obsolete Tube Amplifier for the INFN K-800 Superconducting Cyclotron — Cyclotrons 2016, paper WEB02, JACoW (2016) — p. 1

Editorial note, tabletop extrapolation: Two transferable points: a ~200 W wideband class-A amplifier of the kind used here as a mere driver is the same power class as an entire tabletop dee drive — and since a class-A stage's efficiency ceiling is 50 % for an ideal tuned load (dg-2021's source), its DC input and heat load are taken from its datasheet rather than inferred; and running power devices well below their maximum rating is the stated reason this facility's tubes lasted longer. The 75/30 kW figures are this tetrode stage's.

The interest of the market in our frequency/power range is moving from vacuum tube to solid state devices. […] the end of production of the tetrode, RS1054E, in a few months. The strong decrease in demand on the worldwide market for this specific tetrode, was the reason Thales stopped production altogether. We were only given the opportunity to buy the last three tetrodes at the very unreasonable price of about 60 k€! […] Thales sent us notification a very short time before ending production. […] In the end, the solid state solution greatly reduces the cost of the revamp and the maintenance operations.

Caruso, Caruso, Longhitano, Spartà, Sura & Primadei, Hybrid Configuration, Solid State–Tube, Revamps an Obsolete Tube Amplifier for the INFN K-800 Superconducting Cyclotron — Cyclotrons 2016, paper WEB02, JACoW (2016) — p. 2

Editorial note, tabletop extrapolation: For a tabletop drive the same direction is relevant, and the supply situation for the chosen devices should be checked at design time rather than assumed. The cost conclusions are this facility's, not a general costing.

Each module is equipped with four high power LDMOS transistors which are driven at about 60% of their maximum power capability.

Röcken et al. (Varian Medical Systems Particle Therapy), Progress at Varian's Superconducting Cyclotrons: A Base for the ProBeam Platform — Cyclotrons 2013, paper MOPPT012, JACoW (2013) — p. 2

Editorial note, tabletop extrapolation: The ~60 % derating is a design choice reported for this system, and it is the transferable idea: specify a 6-30 MHz tabletop LDMOS stage so that normal operation sits well below the device's maximum output, (the paper gives no reason for the 60 %; headroom for mismatch, transients and device life is the usual motive). The module power, count and 72 MHz frequency are Varian's.

Especially at frequencies below 100 MHz reflection protection by circulators becomes difficult and no standard components are commercially available.

Röcken et al. (Varian Medical Systems Particle Therapy), Progress at Varian's Superconducting Cyclotrons: A Base for the ProBeam Platform — Cyclotrons 2013, paper MOPPT012, JACoW (2013) — p. 2

Editorial note, tabletop extrapolation: Bears on a 6-30 MHz drive of 100 W-1 kW: a ferrite circulator at these frequencies is large and, per this source (writing about its 72 MHz, ~120 kW system), not a standard commercial component below 100 MHz, so device ruggedness (rated mismatch tolerance), fast reflected-power trips and drive foldback carry the protection burden. Whether a suitable HF isolator exists at a given power must be checked, not assumed.

Compared to tetrode amplifiers as used previously, we could increase the reflected power protection threshold from 5% to 10% of the maximum forward power.

Röcken et al. (Varian Medical Systems Particle Therapy), Progress at Varian's Superconducting Cyclotrons: A Base for the ProBeam Platform — Cyclotrons 2013, paper MOPPT012, JACoW (2013) — p. 2

Editorial note, tabletop extrapolation: The transferable lesson is the trade itself: a trip threshold set too low stops conditioning at every multipactor or spark event, so the threshold is set from the specific amplifier's demonstrated reflection tolerance. Because the source's percentages refer to maximum forward power, the equivalent VSWR rises at reduced drive (formula); arc transients also need time-domain, device-specific limits, not a steady-state VSWR alone. The 5 % and 10 % values are Varian's.

Prior to beam commissioning the RF resonator has to be conditioned. Within approx. 100 h of pulse and cw RF operation, the RF power is stepwise increased to its operational value of nearly 120 kW.

Röcken et al. (Varian Medical Systems Particle Therapy), Progress at Varian's Superconducting Cyclotrons: A Base for the ProBeam Platform — Cyclotrons 2013, paper MOPPT012, JACoW (2013) — p. 1

Editorial note, tabletop extrapolation: Staged conditioning — initially pulsed at low duty, then CW, stepping power up — is a candidate method for a tabletop dee raised to high voltage for the first time; whether it is needed, and its sequence and duration, follow from that dee's vacuum, arc and reflected-power behaviour. The 100 h and 120 kW are this superconducting cyclotron's figures.

The signals from the RF pickup loops, including spare signals, are digitized by AD converters and further processed on a FPGA board. Beside the basic feedback functionality also high level functions for pulse processing and machine protection are integrated. The flexibility in re-programming of the FPGA allowed fast optimization of machine protection procedures and implementation of new operational features in order to improve the overall RF system stability.

Röcken et al. (Varian Medical Systems Particle Therapy), Progress at Varian's Superconducting Cyclotrons: A Base for the ProBeam Platform — Cyclotrons 2013, paper MOPPT012, JACoW (2013) — p. 2

Editorial note, tabletop extrapolation: The architecture, not Varian's hardware, is what applies to a tabletop drive: direct digitisation of a dee pickup is within reach of low-cost FPGA or SDR boards (an engineering observation, not the paper's), and putting reflected-power and pickup-collapse trips in the same re-programmable logic as the amplitude loop lets protection be tuned during conditioning — with independent fail-safe interlocks kept in place.

This technique was used for the adjustment of the coupling factor during the assembly of the input coupler by rotation (with a target of 1 for minimum reflected power with negligible beam current).

Gavela et al. (CIEMAT), Fabrication and Tests of a RF Cavity for a Novel Compact Superconducting Cyclotron for Radioisotope Production — IPAC2017, paper THPVA062, JACoW (2017) — p. 2

Editorial note, tabletop extrapolation: Directly transferable: a rotatable loop (or adjustable tap) measured with a low-cost VNA sets beta ~1 before any power is applied — the no-beam, single-dominant-port target. Whether beam loading is negligible is decided by comparing beam power with the measured cavity wall loss, not by beam current alone; with on-resonance beam loading the optimum input coupling is approximately beta = 1 + P_beam/P_wall.

After that, measurements of resonant frequency, Q factor, coupling factor, and tuners regulation range were done. […] Table 1: Low Power Measurements Under Vacuum — Minimum frequency (plungers up) 60.150 MHz; Maximum frequency (plungers down) 60.375 MHz; QL 2,333; Q0 4,763; Coupling factor 1.042; Rshunt 303 kΩ; Expected forward power at 60 kV 5.93 kW; Expected pickup power at 60 kV 32.0 dBm

Gavela et al. (CIEMAT), Fabrication and Tests of a RF Cavity for a Novel Compact Superconducting Cyclotron for Radioisotope Production — IPAC2017, paper THPVA062, JACoW (2017) — p. 2

Editorial note, tabletop extrapolation: The measurement set (tuner frequency range, Q_L, Q0, beta) is the minimum characterisation a tabletop dee resonator should get from a VNA before a solid-state amplifier is connected; Q_L sets the loaded 3 dB bandwidth (f/Q_L) that frames acceptable detuning and the control requirements. The values themselves belong to this 60 MHz quarter-wave cavity.

bining the VNA measurements with the Rshunt/Q figure obtained from the finite element 3D model. Table 1 summarizes these results. […] Table 1: Low Power Measurements Under Vacuum — Minimum frequency (plungers up) 60.150 MHz; Maximum frequency (plungers down) 60.375 MHz; QL 2,333; Q0 4,763; Coupling factor 1.042; Rshunt 303 kΩ; Expected forward power at 60 kV 5.93 kW; Expected pickup power at 60 kV 32.0 dBm

Gavela et al. (CIEMAT), Fabrication and Tests of a RF Cavity for a Novel Compact Superconducting Cyclotron for Radioisotope Production — IPAC2017, paper THPVA062, JACoW (2017) — p. 3

Editorial note, tabletop extrapolation: Applicable to a tabletop dee: R/Q depends on geometry and comes from a full-wave eigenmode model (or a validated lumped derivation) of the dee, Q from the VNA; their product gives Rshunt = (R/Q)·Q0 under the source's voltage conventions and so the voltage-to-wall-loss scale. The pickup scale needs the measured pickup coupling or a calibrated S21 as well — it does not follow from R/Q alone. Cross-check the calibration by an independent method such as an X-ray endpoint (dg-2052 ff.), noting that electrons need not sample the full gap voltage and that the measurement deliberately produces X-rays requiring radiation controls.

The factors that are not included in the simulations (contacts, surface impurities, roughness, etc.) usually account for a 20-30% decrease in Q0,

Gavela et al. (CIEMAT), Fabrication and Tests of a RF Cavity for a Novel Compact Superconducting Cyclotron for Radioisotope Production — IPAC2017, paper THPVA062, JACoW (2017) — p. 3

Editorial note, tabletop extrapolation: A conditional sensitivity example: if Q comes out 25 % below the design assumption, fixed-voltage wall power rises by 1/0.75 = 1.33 (arithmetic). The authors' 20–30 % is their experience with their construction, not a bound for a home-built dee whose bolted joints and sliding contacts may cost more; measure the unloaded Q (coupling-corrected) and verify losses at representative power.

The cavity showed better behaviour (less multipacting activity, lower arcs rate and reduced conditioning time) when this magnetic field was present,

Gavela et al. (CIEMAT), Fabrication and Tests of a RF Cavity for a Novel Compact Superconducting Cyclotron for Radioisotope Production — IPAC2017, paper THPVA062, JACoW (2017) — p. 3

Editorial note, tabletop extrapolation: Relevant to a tabletop dee, which operates inside the main magnet: multipactor conditions depend on the magnetic field, so conditioning on the bench without field may neither reproduce nor clear the in-magnet behaviour. The direction of the effect is this cavity's observation; another geometry and field must be tested in place.

A fast interlock system governed by the reverse power signal detected the arcs and stopped immediately the RF power.

Gavela et al. (CIEMAT), Fabrication and Tests of a RF Cavity for a Novel Compact Superconducting Cyclotron for Radioisotope Production — IPAC2017, paper THPVA062, JACoW (2017) — p. 3

Editorial note, tabletop extrapolation: Transfers to a tabletop LDMOS dee drive as one input: an arc collapses the dee impedance and sends reflected power back, so a directional-coupler reverse-power comparator that removes drive is a useful arc detector. By itself it does not protect the transistor — reflected energy reaches the device before any trip acts, and survival depends on mismatch phase, the device's rated load-pull envelope, coupler directivity, threshold, total shutdown latency and stored energy. Validate threshold and latency against the device's mismatch safe-operating envelope and add isolation, a dump load, drive foldback or a rugged device where needed. The arc counts and voltages are this cavity's.

In class B, the amplifier only consumes power when it is driven by RF. This provides a much better efficiency, approaching 78.5% for an ideal transistor.

Jacob (ESRF), Radio Frequency Solid State Amplifiers — CAS–CERN Accelerator School: Power Converters, CERN-2015-003, pp. 197–216 (2015); arXiv:1607.01570 — p. 6

Editorial note, tabletop extrapolation: Transfers to a tabletop dee drive: push-pull class AB LDMOS is the standard compromise. A high-Q dee filters near its fundamental but cannot be assumed to suppress harmonics that land on other cavity or feed-line modes, so the output network and the modes deserve a survey. Class A wideband amplifiers (common as bench drivers) draw at least 2 W of DC per RF watt at full output (efficiency <= 50 %), against ~1.4 W for a 70 %-efficient class-AB stage.

the odd characteristic Ids(−Vgs) = −Ids(Vgs) minimizes the second harmonic H2 and higher even harmonics.

Jacob (ESRF), Radio Frequency Solid State Amplifiers — CAS–CERN Accelerator School: Power Converters, CERN-2015-003, pp. 197–216 (2015); arXiv:1607.01570 — p. 6

Editorial note, tabletop extrapolation: Explains why a push-pull LDMOS stage at 6-30 MHz can be expected to show a suppressed second harmonic relative to the odd ones; the third harmonic of a 9 MHz drive (27 MHz) may fall where a dee resonator or its feed line has other modes, so it deserves attention in output-filter design. The ESRF specification (same source, p16) nonetheless puts H3 lower than H2 for that system, so measured levels must come from the actual amplifier.

Each RF module is protected by a circulator with a 1200 W load against reverse power, and can therefore withstand operating with full reflection.

Jacob (ESRF), Radio Frequency Solid State Amplifiers — CAS–CERN Accelerator School: Power Converters, CERN-2015-003, pp. 197–216 (2015); arXiv:1607.01570 — p. 7

Editorial note, tabletop extrapolation: The protection logic transfers to 6-30 MHz (dump the reverse wave into a rated load so the transistor does not absorb it), but ferrite circulators grow with wavelength and, per the ProBeam report (Roecken et al. 2013), are hard to obtain below 100 MHz, so at tabletop frequencies more of the job falls to device ruggedness, drive foldback and fast trips. The 650 W/1200 W/68-70 % figures are this module's.

So, the power adds up correctly at the output of a combiner only by constructive interference, i.e. if and only if the signals at their inputs have the same amplitude and phase.

Jacob (ESRF), Radio Frequency Solid State Amplifiers — CAS–CERN Accelerator School: Power Converters, CERN-2015-003, pp. 197–216 (2015); arXiv:1607.01570 — p. 10

Editorial note, tabletop extrapolation: Relevant only when a tabletop drive sums two or more modules: phase-matched cables and equal module gain decide combining efficiency, and a non-directional combiner of the kind the source analyses has input-port coupling and no intrinsic isolation, so one failing module disturbs the others. Inspect the actual combiner's scattering matrix and isolation/load arrangement (hybrids obtain isolation through a terminated port) rather than judging by the presence of resistors. A single-module drive avoids combiner effects.

For full reflection |r| = 1, a non-powered RF module can therefore see reverse power as high as four times the nominal power of one module.

Jacob (ESRF), Radio Frequency Solid State Amplifiers — CAS–CERN Accelerator School: Power Converters, CERN-2015-003, pp. 197–216 (2015); arXiv:1607.01570 — p. 11

Editorial note, tabletop extrapolation: Applies to a multi-module tabletop drive built on a non-isolating combiner: rate each module's protective load or the device's reverse-power tolerance for the worst phase with a neighbour off, computed for the actual module count, not for the matched case. Irrelevant to a single-stage drive.

The SSAs were also tested successfully at full power with up to 30% power reflection at any phase. The SSAs had furthermore been designed with sufficient power reserve to benefit from the intrinsic redundancy of many combined RF amplifier modules, and full output power could easily be fed into a matched load with up to six missing RF modules! However, when testing the first SSA at full power with 30% reflection and some of the modules switched off, the output circuits and the loads of the unpowered RF modules were damaged, while the phase of the mismatch was varied. In fact, operating conditions as described in Eqs. (6–8) lead to an overloading of the circulator loads of the non-powered RF modules. As much as 1500–1700 W was measured depending on the location in the combiner, confirming experimentally the 1570 W predicted in Eq. (8). […] this interference could be made destructive by inserting 170 mm long delay lines at all of the outputs of all of the first combiner stages. […] the 800 W circulator loads were replaced with 1200 W loads

Jacob (ESRF), Radio Frequency Solid State Amplifiers — CAS–CERN Accelerator School: Power Converters, CERN-2015-003, pp. 197–216 (2015); arXiv:1607.01570 — p. 11

Editorial note, tabletop extrapolation: The method lesson transfers: a design that passed each condition separately (full power with 30 % reflection at any phase; full power with modules missing) failed in combination, so validate an amplifier-plus-load system at its worst-case combination — mismatch across all phases with a stage off — in staged, instrumented steps within component ratings. The 352 MHz delay-line length and load ratings are ESRF's.

It is worth noting that the efficiency drops fast when operating the amplifier at reduced power, and is only about 47% at 100 kW, i.e. at ⅔ of the nominal power.

Jacob (ESRF), Radio Frequency Solid State Amplifiers — CAS–CERN Accelerator School: Power Converters, CERN-2015-003, pp. 197–216 (2015); arXiv:1607.01570 — p. 14

Editorial note, tabletop extrapolation: Transfers as a question to measure for a tabletop class-AB LDMOS stage: back-off efficiency depends on bias, matching, supply and device, so take the selected pallet's efficiency map — a dee needing ~150 W from a 1 kW-capable pallet (an assumed example) may run far below peak efficiency and dissipate correspondingly more heat per RF watt; sizing the device or its supply voltage to the actual requirement helps. The percentages are this 352 MHz system's.

The P1 point, at which the gain compression reaches 1 dB, has been set above the nominal output power to limit distortion and safeguard the transistor against drain over-voltage. […] High peak drain voltage can damage the transistor. It is thus crucial to implement an overdrive protection interlock. […] Up to 1.3 dB transient gain increase has been measured in pulsed operation, which bears a risk of overdrive. The overdrive protection therefore needs to be adjusted carefully.

Jacob (ESRF), Radio Frequency Solid State Amplifiers — CAS–CERN Accelerator School: Power Converters, CERN-2015-003, pp. 197–216 (2015); arXiv:1607.01570 — p. 15

Editorial note, tabletop extrapolation: Transfers directly to LDMOS at 6-30 MHz: high peak drain voltage under overdrive or mismatch is a damage mechanism the source names, so the drive level should be limited in hardware (ALC clamp or input attenuator) and not only by the operator. The 1.3 dB transient gain is ESRF's measurement.

Sidebands < −68 dBc at 400 kHz (DC/DC converter switching, harmless).

Jacob (ESRF), Radio Frequency Solid State Amplifiers — CAS–CERN Accelerator School: Power Converters, CERN-2015-003, pp. 197–216 (2015); arXiv:1607.01570 — p. 16

Editorial note, tabletop extrapolation: Two points transfer to a tabletop drive: specify harmonic levels as dBc numbers and measure them; and converter ripple creates sidebands at offsets equal to the switching frequency which, after the resonator's filtering, can produce amplitude and/or phase modulation of the dee field — so measure both the amplifier spectrum and the dee-field response. Whether any level is acceptable depends on the resonator and local emission rules; the ESRF numbers are a specification example, not a requirement.

150 kW output power with ⅓, i.e. 50 kW, reflection at any phase, 80 kW output power with 100% reflection at any phase, 150 kW output power with 100% reflection at any phase for a duration of up to 20 µs. […] Note that for high power reflections, due to the limited isolation of the circulators of the RF modules, the residual reverse power reaching the transistor output circuit provokes a gain modulation. Also, the power combiner itself contributes to some gain modulation in the presence of high reflected power. As a result, the specified output power cannot be reached for some phase values of the mismatch, due to the overdrive limitation

Jacob (ESRF), Radio Frequency Solid State Amplifiers — CAS–CERN Accelerator School: Power Converters, CERN-2015-003, pp. 197–216 (2015); arXiv:1607.01570 — p. 16

Editorial note, tabletop extrapolation: The specification format transfers to a 100 W-1 kW tabletop drive: state output at a given reflected fraction for all phases, a reduced output at full reflection, and a short-duration full-reflection rating that covers dee arcs and start-up transients. The ESRF numbers are that system's.

the total transient reflection therefore peaks at more than 1.5 times the incoming pulse amplitude, corresponding to more than twice the input power;

Jacob (ESRF), Radio Frequency Solid State Amplifiers — CAS–CERN Accelerator School: Power Converters, CERN-2015-003, pp. 197–216 (2015); arXiv:1607.01570 — p. 17

Editorial note, tabletop extrapolation: Transfers to any tabletop dee driven by a soft-start, pulsed or interlock-tripped drive, at resonance and after the cavity has filled: switching the drive off is itself a reflected-power event — the emitted amplitude at switch-off is 2β/(1+β)·(1−e^(−t_p/T_f)), about 1 at β = 1 and above 1 for an over-coupled resonator once filled, smaller for a short pulse — so trips and foldback must not rely on reflected power falling when the drive is removed, and the device must tolerate the switch-off transient. Evaluate the actual coupling, detuning, pulse length and interlock response time; at β = 1 on resonance the steady reflection is zero, off resonance it is not.

The SSA is still protected by a second unfiltered fast interlock that triggers if the reflected power transient exceeds 150 kW.

Jacob (ESRF), Radio Frequency Solid State Amplifiers — CAS–CERN Accelerator School: Power Converters, CERN-2015-003, pp. 197–216 (2015); arXiv:1607.01570 — p. 18

Editorial note, tabletop extrapolation: The two-tier logic transfers to a tabletop LDMOS dee drive as one mitigation: a slow, averaged reflected-power trip tolerates the fill and switch-off transients of soft-start or pulsed conditioning, while a fast peak trip catches arcs. Thresholds and response times come from worst-case limits for the whole chain — the device's ratings under the specified bias, phase, pulse and thermal conditions, plus combiner, match, load and detector latency — across all mismatch phases, validated at reduced power before staged qualification, with direct arc detection where appropriate.

SSAs: transistors generally have a shorter product lifetime. However, there will always be comparable or even better transistors on the market. […] + SSAs do not need a high voltage power supply (50 V instead of 100 kV): + consequently there is no need for X-ray shielding; + 20 dB less phase noise. + High modularity/redundancy providing a high reliability in operation […] – More space required per kW for a SSA than for a klystron

Jacob (ESRF), Radio Frequency Solid State Amplifiers — CAS–CERN Accelerator School: Power Converters, CERN-2015-003, pp. 197–216 (2015); arXiv:1607.01570 — p. 18

Editorial note, tabletop extrapolation: For a tabletop drive the low supply voltage (about 50 V) is a major practical advantage over a tube stage, and it removes the tube-generated X-ray shielding question for the amplifier; shielding for the resonator (field-emission X-rays at high dee voltage, dg-1931/1936) and for the accelerated beam is assessed separately. The obsolescence point means a design should keep the transistor footprint and bias network replaceable. The cost, space and phase-noise comparisons are the author's judgment at 2014 prices for large systems.

As such, the system allows for operating frequency selection from 49 to 80 MHz and is compatible with single or double resonator configurations through the use of local oscillator synchronization and high-speed command exchange. An I/Q demodulation/modulation scheme is employed allowing for frequency and amplitude control. […] The FPGA is responsible for the high-speed signal processing such as the amplitude control loop, spark recovery, interlocks and safety. […] The Analog Devices Blackfin microcontroller handles the higher level interface with the motor drivers and Host PC. […] The operational frequency of the boards can be selected for a cyclotron between 49-80MHz by setting a few switches and restarting the LLRF. As this change does not require any hardware or software modifications it greatly increases the utility and modularity of the LLRF controllers.

Gold & Sabaiduc (Best Cyclotron Systems), Design of a Digital Low-Level RF System for Best Medical Cyclotrons — Cyclotrons 2013, paper TUPPT024, JACoW (2013) — p. 1

Editorial note, tabletop extrapolation: The fast/slow split transfers to a tabletop dee drive: spark response and amplitude regulation belong in programmable logic or a dedicated fast loop, while tuner motors and sequencing tolerate a microcontroller or host. Frequency selectability by switches is this 49–80 MHz design's; at a few MHz a direct-sampling digitiser can replace the IF mixing stage — an engineering option the paper does not address.

1. Pulse the RF power at 20% of full power until the cavity readback is above 15% of full power while tuning 2. Transition from pulsed RF to CW and enable the spark recovery and frequency tuning loop 3. Close the amplitude control loop 4. Ramp up the RF drive to full power […] All of the timing and threshold parameters are digitally adjustable which allows for rapid tuning of the procedure to ensure reliable start-up and operation.

Gold & Sabaiduc (Best Cyclotron Systems), Design of a Digital Low-Level RF System for Best Medical Cyclotrons — Cyclotrons 2013, paper TUPPT024, JACoW (2013) — p. 2

Editorial note, tabletop extrapolation: The paper states the aim as minimising the time from RF off to full power. As an engineering reading (not stated in the paper), a pulsed first step limits the average power into a resonator that is still off tune only to the extent its duty factor is below unity — the paper does not give the duty factor — and lets the tuner find resonance before CW is applied; reflected-power protection rests on measured mismatch and the amplifier's ratings, not on the pulsing. The 20 %/15 % numbers are the Best system's settings; for a different resonator they are starting values, which is why the source makes them adjustable.

Sparks are detected by monitoring for a rapid decline in the cavity voltage which happens on the order of 1µs. After detection the recovery procedure pauses the PI amplitude loop, turns off the RF drive for 2µs, applies an open loop drive to regain cavity voltage and then resumes the amplitude control. Properly regulated cavity voltage is restored within approximately 100µs for a typical case. During the cavity voltage recovery, the spark detection is again enabled to protect against the case where an additional spark occurs during the ramp.

Gold & Sabaiduc (Best Cyclotron Systems), Design of a Digital Low-Level RF System for Best Medical Cyclotrons — Cyclotrons 2013, paper TUPPT024, JACoW (2013) — p. 2

Editorial note, tabletop extrapolation: Pausing the integrator during the event is the key transferable step: a PI loop left running sees a collapsed read-back and winds up to full drive, which then lands on the arc. The microsecond timings are the 49–80 MHz Best resonators'; a resonator's own field-amplitude time constant scales as 2Q_L/omega, so a lower-frequency, lower-Q dee sets its own detection and refill times, to be measured on that dee.

The loop is implemented in the FPGA using a hardware description language, and also includes overshoot protection and integral anti-windup. An initial cutoff frequency of 20kHz is selected and can be fine tuned during the particular cyclotron commissioning.

Gold & Sabaiduc (Best Cyclotron Systems), Design of a Digital Low-Level RF System for Best Medical Cyclotrons — Cyclotrons 2013, paper TUPPT024, JACoW (2013) — p. 2

Editorial note, tabletop extrapolation: Anti-windup limits integrator accumulation during saturation (start-up, sparks, tuner moves) and an overshoot limiter bounds commanded-voltage excursions — control hygiene that transfers regardless of frequency, and that reduces the loop's own contribution to stressing a solid-state stage or a marginal dee gap. Independent, fail-safe arc, overvoltage, overcurrent and reflected-power interlocks are still required and validated on the actual RF plant. The 20 kHz figure is an initial setting for Best's resonators; the usable loop bandwidth on another dee is constrained by that resonator's own pole at its half-bandwidth f0/(2Q_L) (general resonator physics, not from the paper) and has to be set on the actual dee.

Automatic frequency control logic is contained in the microcontroller and has a response time of approximately 100Hz. The loop acts to maintain a constant phase offset between the forward drive and cavity voltage. Motor position feedback is given by a linear resistor and optical encoder. Frequency control is available in pulsed and CW mode.

Gold & Sabaiduc (Best Cyclotron Systems), Design of a Digital Low-Level RF System for Best Medical Cyclotrons — Cyclotrons 2013, paper TUPPT024, JACoW (2013) — p. 2

Editorial note, tabletop extrapolation: Forward-versus-pickup phase is the standard tuning error signal and is directly usable on a tabletop dee with a motor-driven trim capacitor, once calibrated for cable delay, coupling and beam loading; keeping the tuner loop much slower than the amplitude loop avoids the two fighting. The source's 'response time of approximately 100Hz' does not define its metric (bandwidth, update rate or something else), so it is not a design specification until the implementation or a measured loop response says otherwise.

This can produce either very short pulses for specific applications, or relatively long pulses with an adjustable duty factor to decrease the overall beam intensity during commissioning.

Gold & Sabaiduc (Best Cyclotron Systems), Design of a Digital Low-Level RF System for Best Medical Cyclotrons — Cyclotrons 2013, paper TUPPT024, JACoW (2013) — p. 2

Editorial note, tabletop extrapolation: Phase-lock is needed where resonators are independently driven and resonant; a shared amplifier feeding separate resonators does not by itself fix the gap-voltage phases (detuning, loading and unequal feed paths move them), while a single-dee machine has no second phase to lock. Programmed relative-phase gating for pulsing is distinct from a static phase offset, which changes acceleration and can raise internal beam loss — if phase is used as an intensity knob during commissioning, measure delivered beam and internal losses.

Fine tuning of the amplitude control loop is continuing to reach a stability target of 5 · 10−4 or better.

Gold & Sabaiduc (Best Cyclotron Systems), Design of a Digital Low-Level RF System for Best Medical Cyclotrons — Cyclotrons 2013, paper TUPPT024, JACoW (2013) — p. 3

Editorial note, tabletop extrapolation: 5 x 10^-4 is a stated goal for Best's resonators, not a demonstrated figure (Fig. 4 axes are unscaled), so it serves only as a reference point for what a commercial system aims at. An hours-long, initially supervised commissioning soak with spark recovery active is the transferable test for a dee drive; unattended operation comes only after independent protective trips (arc, vacuum, reflected power, thermal) and bounded restart logic have been validated.

For a synchronized operation of the modules, a distribution of the reference frequency and a 10 MHz clock signal had to be prepared using existing RF splitters.

Fanselow, Bundesmann, Denker et al. (Helmholtz-Zentrum Berlin), Operational Experience in the Treatment of Ocular Melanomas with a New Digital Low-Level RF Control System — Cyclotrons 2019, paper TUP007, JACoW (2019) — p. 1

Editorial note, tabletop extrapolation: A single shared reference and clock is what lets separate controllers (dee drive, buncher, any second dee) be synchronised; fixed relative phase after start-up additionally needs deterministic phase initialisation or a closed-loop phase measurement. For one dee and one controller it reduces to locking the controller to a stable reference. The HZB RF runs at 10–20 MHz with two 30 kW tube amplifiers (2 kW semiconductor drivers); the reference-distribution scheme is independent of amplifier power.

The RF systems were tuned with the old RF control to the standard therapy frequency of 19.3187 MHz to obtain a starting value of the resonance tuning for the LLRF.

Fanselow, Bundesmann, Denker et al. (Helmholtz-Zentrum Berlin), Operational Experience in the Treatment of Ocular Melanomas with a New Digital Low-Level RF Control System — Cyclotrons 2019, paper TUP007, JACoW (2019) — p. 2

Editorial note, tabletop extrapolation: Starting a tuner servo from a recorded, known-resonant tuner position keeps first closed-loop operation near resonance; verify resonance and matching at reduced power while watching reflected power and the protective trips before raising drive. The 115 kV amplitude is HZB's, far above a tabletop dee's few kilovolts — compare by the method, not the numbers.

Already during the adjustment of the accelerator the starting of the RF systems by the automatic resonance search of the LLRF was easier and faster than the manual resonance search of the old system. Thus, the cold start of the RF systems after the maintenance period can be carried out by all operators themselves without any problems and without the help of the RF group.

Fanselow, Bundesmann, Denker et al. (Helmholtz-Zentrum Berlin), Operational Experience in the Treatment of Ocular Melanomas with a New Digital Low-Level RF Control System — Cyclotrons 2019, paper TUP007, JACoW (2019) — p. 3

Editorial note, tabletop extrapolation: Automating the find-resonance step (a low-power sweep or tuner search, then lock) is an optional feature worth building into a small machine's first controller, since its resonance drifts with temperature between sessions; its sweep limits, reflected-power protection during the search and lock acquisition have to be validated.

Both systems now run more stable, with phase stability improving from 0.1° to 0.02° and amplitude stability from 0.5% to 0.7%.

Fanselow, Bundesmann, Denker et al. (Helmholtz-Zentrum Berlin), Operational Experience in the Treatment of Ocular Melanomas with a New Digital Low-Level RF Control System — Cyclotrons 2019, paper TUP007, JACoW (2019) — p. 3

Editorial note, tabletop extrapolation: These are HZB's numbers for its resonators and its definition of stability (not stated in the paper), useful as a reference for what a digital LLRF achieves at 10-20 MHz, not as a requirement for a different machine. The amplitude pair is reported as printed; whether it is a misprint or a change of measurement basis cannot be resolved from the paper.

the problem was identified as a suboptimal tuning of the RF power amplifiers output stage, resulting in the loop instability. To solve the problem, the integral coefficient of the phase modulator’s PID controller was first lowered. This allowed the power amplifier to be optimised at rated power. Thereafter the integral coefficient was returned to its nominal value and normal operation continued.

Fanselow, Bundesmann, Denker et al. (Helmholtz-Zentrum Berlin), Operational Experience in the Treatment of Ocular Melanomas with a New Digital Low-Level RF Control System — Cyclotrons 2019, paper TUP007, JACoW (2019) — p. 3

Editorial note, tabletop extrapolation: The lesson plausibly transfers across frequency and power: an LLRF loop's stability depends on the complex gain and phase response of the power stage it drives, so a re-tuned or mistuned amplifier output network can destabilise a loop that was stable before. When a loop goes unstable after a frequency change, check the amplifier's transfer response, loading and output-network tuning before re-tuning the controller.

The measuring circuits must be calibrated to determine the actual dee voltage. For calibration, a technique for measuring the spectrum of bremsstrahlung X-rays can be used.

Issatov, Kabytayeva et al. (FLNR JINR), Calibration of Measurement of Absolute Dee Voltage for U-400M Isochronous Cyclotron at FLNR JINR — RuPAC 2018, paper TUPSA31, JACoW (2018) — p. 1

Editorial note, tabletop extrapolation: As an engineering reading (the paper reports the frequency dependence without a mechanism), a capacitive pickup's ratio depends on its geometry and on the resonator's field distribution, which changes with tuning, loading and configuration. A fixed-frequency machine needs calibration under its actual operating configuration, re-validated after changes to tuning, loading, geometry, electronics or field pattern; a variable-frequency one needs a calibration curve across its range. The 130 kV scale is one to two orders of magnitude above a few-kV dee, which changes how easily the X-ray method can be applied (Miller & Kashy, 1975, report that their MSU set-up, relying on natural electron emission, measured the continuum only above about 30 kV, and show an 11.4 kV spectrum once filament electron sources were added).

The XR-100-CdTe is capable of detecting energies from a few keV to several hundreds of keV, with an efficiency that peaks from 10 to 100 keV [2].

Issatov, Kabytayeva et al. (FLNR JINR), Calibration of Measurement of Absolute Dee Voltage for U-400M Isochronous Cyclotron at FLNR JINR — RuPAC 2018, paper TUPSA31, JACoW (2018) — p. 1

Editorial note, tabletop extrapolation: A Peltier-cooled CdTe detector with a digital MCA (Si is an extrapolation from the cited CdTe) is a candidate to evaluate for this calibration at small scale, not a demonstrated solution: its 10–100 keV efficiency peak matches dee voltages of tens of kV, while for a dee at a few kV the photons are in the few-keV region where window and air-path transmission, dead layers, electron yield, solid angle, RF interference and background decide feasibility — an end-to-end efficiency and background estimate for the chosen detector, window and path is the first step.

An accurately determining of the maximum energy of X-ray spectrum was difficult because of background radiation from the induced activity of the internal elements of the cyclotron (Fig. 5).

Issatov, Kabytayeva et al. (FLNR JINR), Calibration of Measurement of Absolute Dee Voltage for U-400M Isochronous Cyclotron at FLNR JINR — RuPAC 2018, paper TUPSA31, JACoW (2018) — p. 2

Editorial note, tabletop extrapolation: Fitting a modelled endpoint shape rather than reading the last channel by eye reduces the endpoint's sensitivity to background; on a machine without beam-induced activation the background may instead be dominated by room radioactivity, as Miller & Kashy (1975) found at MSU. The FLUKA step is the U-400M authors' method; a simpler thick-target bremsstrahlung shape could serve the same purpose at low energy, which the paper does not test.

As shown on fig. 7 at the same voltage (55 kV) by pick-up electrodes and at different frequencies, the absolute dee voltages are different.

Issatov, Kabytayeva et al. (FLNR JINR), Calibration of Measurement of Absolute Dee Voltage for U-400M Isochronous Cyclotron at FLNR JINR — RuPAC 2018, paper TUPSA31, JACoW (2018) — p. 2

Editorial note, tabletop extrapolation: The factor itself is near 2 rather than 1 (Fig. 8: a 55 kV pick-up reading gives endpoints of roughly 90 keV at 17.5 MHz to 130 keV at 12.8 MHz, figure reading), and the paper does not say whether the endpoint is read as one dee-to-ground voltage or how the factor maps to dee volts, so the ratio is the U-400M calibration, not a conversion to reuse. For the U-400M pick-ups the frequency dependence is about 30 % over 12.8-17.5 MHz; the size of the effect on another resonator must be measured there. A fixed-frequency small cyclotron still has to calibrate its pickup once at its operating point, and again after any change that moves the frequency or the field pattern.

It can be seen from fig. 10 and 11 that at the dee voltage of 85 kV the beam loss on the internal elements of the cyclotron reaches 100%.

Issatov, Kabytayeva et al. (FLNR JINR), Calibration of Measurement of Absolute Dee Voltage for U-400M Isochronous Cyclotron at FLNR JINR — RuPAC 2018, paper TUPSA31, JACoW (2018) — p. 3

Editorial note, tabletop extrapolation: A central region is optimised for a specified dee-voltage range, and first-turn clearance of the source and puller and the capture fraction depend on the real, not the indicated, voltage; compute or measure that dependence for the machine's own geometry. The 85 kV and percentage figures belong to the U-400M central region.

In the X-ray technique described here the dee voltage is inferred from a measurement of the endpoint of the bremsstrahlung continuum, which corresponds to the peak dee voltage.

Miller & Kashy (Michigan State University Cyclotron Laboratory), Absolute Calibration of Dee Voltage by X-Ray Endpoint — Seventh International Conference on Cyclotrons and their Applications (Cyclotrons 1975), paper C-08, JACoW (1975) — p. 1

Editorial note, tabletop extrapolation: A small cyclotron without separated turns is exactly the case the authors single out; the method measures the peak voltage across the gap the electrons cross, independently of any pickup. Its practicality depends on the voltage scale (next rule).

The X-ray continuum could be measured only at voltages above about 30 kV, mainly because signals became undectable in the background from room radioactivity at lower voltages.

Miller & Kashy (Michigan State University Cyclotron Laboratory), Absolute Calibration of Dee Voltage by X-Ray Endpoint — Seventh International Conference on Cyclotrons and their Applications (Cyclotrons 1975), paper C-08, JACoW (1975) — p. 1

Editorial note, tabletop extrapolation: The ~30 kV figure is the MSU set-up's with natural electron emission, not a property of the method (the same paper shows an 11.4 kV spectrum with filament sources): it reflects photon yield from stray electrons versus room background at that detector and window. In physics terms the endpoint equals the peak dee voltage in keV, so a dee near 1 kV peak gives sub-keV photons that have 1/e lengths of a few micrometres in aluminium (NIST data, not the paper), which points toward an in-vacuum or windowless detector, while a 5-13 kV dee gives 5-13 keV photons that pass thin windows but lie below the ~30 kV MSU reached with natural electrons and near the 11.4 kV spectrum it showed with filaments, so a deliberate electron source and a thin, low-Z window would be the starting assumptions to test.

At voltages above about 40 kV it was necessary to use a filter in front of the detector to prevent the counting rate from becoming excessive.

Miller & Kashy (Michigan State University Cyclotron Laboratory), Absolute Calibration of Dee Voltage by X-Ray Endpoint — Seventh International Conference on Cyclotrons and their Applications (Cyclotrons 1975), paper C-08, JACoW (1975) — p. 1

Editorial note, tabletop extrapolation: A heated filament near the gap is an adjustable electron source that can make the X-ray yield controllable rather than dependent on stray emission — once its contribution is shown to dominate — and is the element a low-voltage dee would most need. Count rate and radiation output must then be measured while raising emission from a low setting: even at 5–13 kV a milliampere-scale electron current onto a target can saturate a nearby detector and is a radiation hazard in its own right, so check detector dead time, survey, and use source current, distance, collimation or attenuation as needed. The absorber wheel solved the high-rate problem at tens of kV.

The endpoint was determined by visual inspection of plots, as in Fig. 2, and comparison with a background spectrum measured with the rf turned off. Notice that good statistics are necessary in the background in order to determine the end point, since no use is made of the intense part of the spectrum in the analysis.

Miller & Kashy (Michigan State University Cyclotron Laboratory), Absolute Calibration of Dee Voltage by X-Ray Endpoint — Seventh International Conference on Cyclotrons and their Applications (Cyclotrons 1975), paper C-08, JACoW (1975) — p. 2

Editorial note, tabletop extrapolation: The RF-off background run is cheap and characterises the non-RF background against which a weak low-voltage endpoint is judged; it does not by itself validate the endpoint, since RF-correlated interference and other RF-on backgrounds need their own check. The 0.2 % transit-time correction is MSU's at 14–21 MHz with tens-of-kV gaps; for a different gap and voltage the electron transit time relative to the RF period has to be estimated before neglecting it.

There was no measurable dependence of the calibration on the mode (0° or 180°). The RMS deviation from the least squares line varied from 0.28 keV to 1.4 keV, with about 0.5 keV being typical.

Miller & Kashy (Michigan State University Cyclotron Laboratory), Absolute Calibration of Dee Voltage by X-Ray Endpoint — Seventh International Conference on Cyclotrons and their Applications (Cyclotrons 1975), paper C-08, JACoW (1975) — p. 2

Editorial note, tabletop extrapolation: Two independent papers (MSU 1975, and the U-400M 2018 result on dg-2050) found the dee-pickup calibration changing substantially with frequency. At a single operating frequency one calibration serves while the configuration is unchanged (loading, coupling, power level, electronics) and linearity has been shown; check for drift periodically and recalibrate after any change to frequency, loading, coupling or electronics.

We conclude that the absolute accuracy of the X-ray calibration technique described is better than 4% and is probably around 1% or 2% for voltages that are above 30 kV, corresponding to data in Table 1. By analyzing the fluctuations observed in the data we conclude that a single measurement of an endpoint is accurate to ±1 kV.

Miller & Kashy (Michigan State University Cyclotron Laboratory), Absolute Calibration of Dee Voltage by X-Ray Endpoint — Seventh International Conference on Cyclotrons and their Applications (Cyclotrons 1975), paper C-08, JACoW (1975) — p. 4

Editorial note, tabletop extrapolation: The accuracy statement is for the MSU apparatus above 30 kV. The ±1 kV single-endpoint uncertainty is an absolute figure: about 3 % at 30 kV, but roughly 10–20 % at 5–10 kV if it carried over unchanged, which a lower-voltage set-up would have to re-establish. Turn counting is a transferable cross-check for any machine with a turn-resolving probe — with its own dee angle in place of 69°, its harmonic, and injection-energy and phase corrections where they are not negligible, rather than MSU's constants.