Cyclotron dee design rules

The magnetic field is uniform at 0.493 T, to within one percent, out to a radius of 6.19 cm... The RF electrode radius is 7.14 cm containing the full uniform region.

King, A Preliminary Design for a Small Permanent Magnet Cyclotron — Houghton College thesis (2002) — p. 22-23

Editorial note, tabletop extrapolation: Suggests planning the reference machine's usable beam radius around ~80% of the 8-in pole (~3.2 in) unless shims extend the flat region - with the machine's own field map as the arbiter (dg-098, dg-638).

Cited in: Cyclotron Magnet Design

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.

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.

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.

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.]

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 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.

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 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.

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.

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').

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.

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.

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.

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.

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 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.

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.

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.

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).

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.

A peak DEE voltage of 10kV was chosen. First the ion source was not included as to see the distortion in the field lines due to the DEE-Dummy DEE asymmetry. The distortion is satisfactorily low with a dummy DEE of 3/8-inch thickness.

Koeth, Rutgers 12 Inch Cyclotron Ion Source Studies: Part I (2006) — p. 2

Editorial note, tabletop extrapolation: Supports the single-dee/dummy-dee topology at the reference machine's scale: a ~10 mm grounded bar is a proven starting geometry that frees chamber space - re-run the electrostatic model for a new machine's own dee, gap and pole geometry.

the beam width was found to be limited by the internal aperture of the D's out to about one-third of the final radius and then to narrow in a nearly linear fashion out to the exit slit.

Livingston & Blewett, Particle Accelerators (1962) — p. 163-167

Editorial note, tabletop extrapolation: Give the first third of radius generous vertical aperture - that is where the envelope filled the dee aperture on MIT's machine - and let the outer region run tighter, which also helps RF economy. Confirm on the actual machine (witness strips, dg-695) rather than assuming the same profile.

Graphite is coming into wide use for cones, arc bodies, and also for D feelers or accelerating electrodes; it operates at high temperatures with a minimum of sputtering or evaporation. ... Extensions on the D faces opposite the source, called 'feelers' or 'auspullers,' have been used to improve beam intensity; they decrease the physical spacings and increase the electric field at the source. They also change the dimensions and focal properties of this first electric lens.

Livingston & Blewett, Particle Accelerators (1962) — p. 166-178

Editorial note, tabletop extrapolation: Graphite source parts run hot without spraying metal; a feeler on the dee edge is a cheap first-turn-capture upgrade with historical standing - though even the source notes quantitative evidence on its focusing effect was thin, so tune it empirically.

There is no vertical magnetic focusing at the center of the magnet. By a fortunate coincidence, electrostatic focusing by the accelerating fields is effective for low-energy ions.

Humphries, Principles of Charged Particle Acceleration (1986) — p. 524, 526

Editorial note, tabletop extrapolation: Explains why source-to-dee geometry (chimney position, puller gap, aperture height) dominates beam capture on small machines: at the center magnetic vertical focusing vanishes and only builds as n grows off zero with radius, so the electric gap lens is what the first turn or two get. Central-region electrode design is where capture is won on the documented machines.

most uncontaminated cathode sites did not break down at 95MV/m (figure 4.8). Excluding the two sites for which tests were halted prematurely (as explained in the caption of figure 4.8), 40 of 52 contaminated sites broke down, while only 1 of 16 uncontaminated sites broke down at or below the maximum field

Werner, Probing and Modeling Voltage Breakdown in Vacuum — Cornell dissertation (2004) — p. 78

Editorial note, tabletop extrapolation: A big lever on the reference machine's dee-voltage ceiling: gloves, solvent cleaning, and dust-free assembly of dee and stem are cheap holdoff - one major control among several, not a guarantee.

breakdown occurs between 5 and 200 MV/m ... In general, smaller gaps can withstand higher fields. ... Note that cathodes can reach fields higher than 100 MV/m, but, observing the maximum voltage, only with a gap smaller than 150 microns

Werner, Probing and Modeling Voltage Breakdown in Vacuum — Cornell dissertation (2004) — p. 78, 95

Editorial note, tabletop extrapolation: At 13 kV across the reference machine's ~6 mm gap the mean field is ~2 MV/m, comfortably low - but mean field is only the first check. Local enhancement at edges and asperities, particles, insulator surfaces and gas pressure can still start an arc, so treat sparking there as a diagnostic checklist, not an impossibility.

In the 'early processing' regime, breakdown is overwhelmingly likely to increase the breakdown field of a cathode site.

Werner, Probing and Modeling Voltage Breakdown in Vacuum — Cornell dissertation (2004) — p. 91-92

Editorial note, tabletop extrapolation: Ramp the next machine's dee voltage slowly and accept the limited, current-limited micro-discharges that come with first processing - that conditioning is what raises the ceiling. Deliberately provoking arcs as 'cleaning' is a different matter: arcs can damage electrodes and insulators, and current limiting does not control the stored-energy delivery into the fault (dg-285). Let conditioning happen; do not manufacture it.

slipping a 1/4 in. pyrex tube completely over the 3/16 in. copper dee support rod from the dee edge to at least 2 inches beyond the seal

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 7

Editorial note, tabletop extrapolation: The cited machine's construction: a continuous Pyrex sleeve over the dee support rod, extending well past the seal for creepage. For a new machine, design stem insulation from peak RF voltage, surface-flashover behavior and the sleeve-to-stem annulus (sealed or vented?) rather than copying the geometry - and note glass sleeves bring their own charging and thermal-stress habits under RF.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

Aluminum=290 kV/inch ... We settled on a minimum radius of R=.1875 inches ... Emax=170 kV/inch

Ponter, Beam Energy Measurements with a New HV Deflection System and Ion Source Upgrades on the Rutgers 12-Inch Cyclotron (2010) — p. 8

Editorial note, tabletop extrapolation: The method transfers to 5-13 kV dees: radius all dee and stem edges and check the enhanced field with the formula. The 290 kV/in is one team's design number, not a material constant - vacuum holdoff moves with gap, finish, contamination and conditioning - so copy their margin practice (peak field well under the adopted figure), not their number.

a discharge from the dee to the chamber wall damaged the glass insulation and 'dee' electrode ... Four machinable ceramic strips, each roughly 2.53 cm long, 0.77 cm wide and 0.18 cm thick, hold the two dees together at the appropriate separation gap of 0.635 cm.

Haas, Characterizing the Performance of the Houghton College Cyclotron — Houghton College thesis (2009) — p. 2, 52

Editorial note, tabletop extrapolation: Machinable ceramic (Macor-class) spacers are the pattern to copy for the reference machine's dee-to-dummy-dee gap; ceramics still flash over and track, so verify surface-field and creepage margins for the actual gap and voltage rather than treating the material as spark-proof.

This design strategy made it impossible to fix a single component of the apparatus, such as the insulation, without replacing the entire piece.

Haas, Characterizing the Performance of the Houghton College Cyclotron — Houghton College thesis (2009) — p. 47

Editorial note, tabletop extrapolation: A next machine should assume sparks and insulator damage happen across a machine's life: modular fastening where practical turns rebuilds into part swaps - the source's glued chamber is the cautionary case. Where glue or solder is structurally necessary, design the bonded assembly itself as the replaceable unit.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

To vent the screw holes, a small hole was drilled in the side of each screw hole using a No. 55 drill bit. The screw holes need to be vented so that they do not trap air or water and slowly outgas when the dee is placed in the vacuum chamber.

Haas, Characterizing the Performance of the Houghton College Cyclotron — Houghton College thesis (2009) — p. 52

Editorial note, tabletop extrapolation: Directly applicable to any screwed-together dee: unvented blind holes are virtual leaks that slow pumpdown and add residual gas load - size and place vents for conductance and cleaning access.

Cited in: The Vacuum Budget of a Cyclotron

the RF voltage on the dee is typically between 1 and 2 kV, far greater than the 1-3 V DC placed across the filament. Thus, the filament and wires must be adequately insulated from the dee ... Insulation was supplied by a 2.33 cm by 2.71 cm machinable ceramic rectangle approximately 0.18 cm thick. ... Two barrel connectors, each 1.28 cm long and 0.32 cm in diameter, were glued to the ceramic insulator using Hysol Loctite 1C vacuum epoxy

Haas, Characterizing the Performance of the Houghton College Cyclotron — Houghton College thesis (2009) — p. 54

Editorial note, tabletop extrapolation: Matches the reference machine's ~1.3 kV operating point today. At the planned 5-13 kV, do not just scale the creepage proportionally: reassess peak field and vacuum surface flashover for the actual geometry and check the feedthrough's rating.

Ceramic spacers hold the Dee and Dummy Dee apart with a gap of 0.635 cm. The entire Dee electrode assembly is supported by three KF-16 electrical feedthroughs through ports at 120 degrees from each other. ... A circular ring of 6061 T6 aluminium, 1.27 cm thick, 0.6 cm wide, and 15.6 cm outside diameter, formed the walls for both the Dee and Dummy Dee. Two 5052 aluminium sheets, 0.13 cm thick, were fastened to the top and bottom of the ring with vented screws.

Yuly, The Houghton College Cyclotron: a Tool for Educating Undergraduates — Cyclotrons 2013, WE1PB01 (2013) — p. 2

Editorial note, tabletop extrapolation: Direct fabrication prior art at exactly tabletop scale; the single-Dee-plus-dummy topology needs live RF on only one electrode - the design rationale for fewer HV feedthroughs - and the vented screws are the kind of vacuum detail worth copying wholesale.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

some 90% of the initial supply of ions are lost to the dee surfaces. The loss may be reduced by increasing the dee voltage, thus reducing the number of turns an ion makes

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 18

Editorial note, tabletop extrapolation: Directly applicable: at 1.3 kV the reference machine's protons make many turns, and the quoted machine cut its central losses with more dee volts. A strong transmission lever - alongside central-region geometry (dg-348), which shapes what the first turns even see; measure which binds before spending (dg-303).

The sides of the second set of dees are 1/8 in. copper with five loops of 7/8 in. copper tubing flattened and furnace brazed ... Both designs have proved satisfactory but the latter is much easier and less expensive.

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 50

Editorial note, tabletop extrapolation: At 1.3 kV and tens of RF watts the builder probably needs no water - but decide from computed or measured dissipation and temperature, not from voltage. If a next machine's dee runs kilowatt-class RF, brazed-on flattened tubing is the historically cheap construction; substituting soft solder needs its own validation (joint temperature, strength, vacuum compatibility).

The peripheral walls of the dees are perforated to permit high pumping speed. Graphite plates are attached to the inside of the dees ... to protect the copper from the stray proton beam.

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 50, 7

Editorial note, tabletop extrapolation: Perforation transfers directly - pressure inside an unvented dee can sit far above gauge pressure (the dee interior is a conductance-choked volume). Graphite armor earns its place wherever stray beam dwells, at ANY energy: heating, sputtering and erosion first (dg-426's material lesson), with activation reduction joining the list at higher energies.

Cited in: The Vacuum Budget of a Cyclotron

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.

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.

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.

The chimney is centered at (0.000,0.000) and the puller is centered at (0.021,0.000). The minimum gap between the chimney and the puller is 2.9 mm while the gap at the source opening is 3.0 mm, meaning that the beam does not see the peak electric field. [K100 geometry]

Forringer, Phase Space Characterization of an Internal Ion Source for Cyclotrons — MSU dissertation (2004) — p. 78, 85

Editorial note, tabletop extrapolation: Gap sets extraction field at fixed voltage, so at a few kV on the dee the chimney-puller gap must shrink below these machines' values to recover useful gradient - but there is no constant-kV-per-mm law to size it by (dg-419): pick a gap, then verify holdoff on the bench with the actual electrodes, finish and RF. The K100's deliberate 0.5 mm center offset - trading peak field at the beam for extraction optics - is the transferable design idea.

The inclusion of a chimney placed on top of the existing design will permit the thermionic electrons to travel to the median plane, thereby generating ions in the entire column. A small aperture, 1/16 of an inch in diameter, opening towards the DEE permits ions to be drawn into the accelerating field.

Koeth, Rutgers 12 Inch Cyclotron Ion Source Studies: Part I (2006) — p. 2-3

Editorial note, tabletop extrapolation: The half-step option: chimney-over-filament keeps the reference machine's existing filament supply and adds gas confinement plus a defined 1.6 mm emission aperture. Injection matching to the first orbit remains its own design question (aperture position, puller, phase - dg-348), not an automatic property; a PIG chimney gets the same geometry benefits and deletes the filament, at the price of a new arc supply (dg-383).

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.

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.

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.

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.

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.

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).

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.

It must be kept in mind for systems having low accelerating voltages similar to the 184-inch cyclotron, that the ions will rapidly increase the amplitude of their vertical oscillations at the point where n = 0.2.

Sewell, Henrich & Vale, Some Operating Phenomena Associated with the 184-inch Cyclotron — MDDC-1092 (1947) — p. 4

Editorial note, tabletop extrapolation: The reference machine's few-kV dee means many turns near any resonance radius - the slow-crossing regime the quote warns about. Keep n below 0.2 over the whole usable radius (the mapped check, dg-138), and give the dee aperture real margin over the expected radial oscillation amplitude.

Cited in: Beam Dynamics: An Interactive Laboratory

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.

Pole tip dia. 31 in. Beam radius, max 12.6 in. Field gap, center 5.5 in. ... Dee dia. 29 in. Dee aperture 3 1/4 in.

Howard, Cyclotrons and High-Energy Accelerators, 1958 — ORNL-2644 (1958) — p. 26

Editorial note, tabletop extrapolation: Sanity template for a next machine on 8-inch poles: ratios of this class suggest a 1-1.4 in gap, a 0.5-0.8 in dee aperture, and energy planned at a 3.2-3.6 in beam radius rather than the pole edge - starting proportions to check against the machine's own field map and stability analysis, not expected dimensions.

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.

Electric focusing with carbon grids on the dees successful on first four revolutions

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

Editorial note, tabletop extrapolation: First-turn loss at low dee voltage is a classic tabletop failure mode, and the ANU carbon-grid result makes grid focusing worth testing - model the electric fields first, note a slit plate is not the same as a transparent grid, and check interception, RF loading, heating and outgassing at low current before adopting it.

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 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.

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.

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.

an increase in bias potential on the dees increases the beam accelerated to maximum radius by a factor of as much as 30% when the cyclotron is operated without an accelerating slit (rf) mounted on the dee.

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

Editorial note, tabletop extrapolation: Worth a cheap experiment on the reference machine - with a proper RF-rated bias-injection network (choke/filter, insulation, supply protection), never a bare DC supply on a live dee. ORNL's stated reading is that bias pulls badly-phased ions deeper into the gap field; with a slit installed they saw no bias effect. The source does not rank the two approaches - test both on the actual 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).

the ion source position is limited to a maximum radius of 2.5 inches. This forces operation at comparatively low dee voltages (20-30 kv) in order to center the orbits.

Jungerman, Kibbe & Peek, Central Region Studies for Incorporating an Axial Ion Source in the Davis 76-in. Cyclotron — UCD-CNL-49 (1966) — p. 5

Editorial note, tabletop extrapolation: The design logic transfers directly to a next machine's central-region layout: pick dee voltage and source-puller radius TOGETHER from the first-orbit geometry. It also cuts the other way for the reference machine's 5-13 kV upgrade: raising dee voltage moves the optimum source position outward — re-scan source position after the RF upgrade.

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

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 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.

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).

several leaks in very inaccessible locations have delayed final assembly. In order to repair the leaks in the internal water-cooling tubes it was necessary to cut windows through the sides of the dees. The windows were then closed by Heliarc welding.

Howard (ed.), Electronuclear Research Division Semiannual, period ending 20 September 1954 — ORNL-1795 (1954) — p. 19

Editorial note, tabletop extrapolation: If a next machine's dees carry water: treat internal cooling leakage as a credible failure and route tubing so joints and runs can be reached (or provide removable covers) where RF and vacuum allow; pressure-test the dee as a unit BEFORE it meets the liner; and note the historical recovery mode - cut a window, fix, reweld - is documented practice worth keeping in the back pocket.

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.

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.

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.

This paper presents in summary formulas for the computation of electric fields and potentials of an idealized cyclotron dee geometry.

Beal, Computation of Electric Field and Potential of an Idealized Dee Geometry — MSUCP-12 (1961) — p. 6

Editorial note, tabletop extrapolation: TRACKER SEED (flagged): this is directly implementable as the gap-field model in the tiny and the next machine's Python trackers — roughly ten lines plus a Newton solve — replacing or validating FEMM electrostatic maps. Identify 2h with the dee aperture, 2k with the dee-to-dummy-dee gap, 2V0 with the full dee-to-dummy-dee voltage (a grounded dummy dee is the same solution shifted by a constant, V0 = V_dee/2).

Therefore, equations 2 and 4 coupled with equations 3 and 5 can be used to determine the electric field and potential at a point X, Y of the dee region.

Beal, Computation of Electric Field and Potential of an Idealized Dee Geometry — MSUCP-12 (1961) — p. 5

Editorial note, tabletop extrapolation: E_y(x,y) is what a tracker needs for the Rose/Wilson electric gap-focusing term - available analytically at any point, no field map required. Whether that term dominates first-turn axial stability on a sub-kV machine is for the axial-stability calculation to say; implement, verify against finite differences, and let the tracking decide.

The iteration process suggested by Murray and Ratner for calculation of X1 converges slowly for small values of a, and does not converge at all for large a. An iteration process, described below, suggested by M.M. Gordon was used and was found to work well for all cases. ... This iteration is Newtonian in character such that if a given X1 has an error of order e, then X1 given by equation 9 will have an error at order e squared. ... X1 ~ X/(1+a) for X1 small ... X1 ~ X - a for X1 large.

Beal, Computation of Electric Field and Potential of an Idealized Dee Geometry — MSUCP-12 (1961) — p. 7

Editorial note, tabletop extrapolation: Copy the iteration and its initial-guess branch into the tracker's field routine; iterate to a set tolerance - quadratic convergence is local, so the branch guess is what makes it robust - cheap enough to call per integration step, or use once to build a spline.

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).

Table 1 gives values of electric field and potential for a wide range of dee gap arrangements. [tables span PDF pages 11-19]

Beal, Computation of Electric Field and Potential of an Idealized Dee Geometry — MSUCP-12 (1961) — p. 11

Editorial note, tabletop extrapolation: Unit-test targets for the tracker's gap-field routine AND an independent check on FEMM electrostatic runs: model the same idealized geometry once and agree within a DOCUMENTED convergence tolerance - set by a mesh/domain convergence study against the table's demonstrated accuracy - before trusting FEMM on the real electrode shapes; the table's five printed digits are formatting, not a five-digit acceptance criterion — a five-figure match to the printed table would mean an implementation reproducing the paper's rounding errors (see the rule's dated erratum).

A fixed point computer program written by D.A. Johnson for use on MISTIC was used to calculate the above equations for Ex and Vx at the point (X,0) with alpha<4. [defs: alpha = 1/A ; A = a^2/(1-a^2) ; (pi/2)(k/h) = cosh^-1(1/a) + (1-a^2)^1/2 / a^2]

Beal, Computation of Electric Field and Potential of an Idealized Dee Geometry — MSUCP-12 (1961) — p. PDF 8 (printed p. 5), Sec. IV Results, for the alpha<4 statement; alpha's definition on PDF 7 (printed p. 4), and the k/h relation on PDF 5 (printed p. 2)

Editorial note, tabletop extrapolation: For use on a next machine, the real deviations to check against FEMM are finite dee thickness, the rounded tip, and the curved gap line near the source at small radius - run the comparison over the actual geometry rather than assuming the analytic solution's quality at any radius; near center the ion-source chimney dominates the field regardless.

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.

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.

foils must be flat since ripples increase the effective source thickness and thereby degrade the performance.

International Nuclear Target Development Society Workshop — ANL/PHY-84-2, Argonne National Laboratory (1983) — p. 224

Editorial note, tabletop extrapolation: The cleanest statement in this collection that foil flatness is physics, not cosmetics - applicable to any internal foil in proportion to how its incidence geometry turns ripple into path-length spread; and the Chalk River system stands as an existence proof that in-vacuum consumable-changers can share space with a live dee structure (details per the re-read).

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 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

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.]

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.

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 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.

Da der Innendurchmesser des Dees 140 mm beträgt, hat ρ den Wert 70 mm und ist damit um 5 mm kleiner als der Polradius [tr.: dee ID 140 mm, rho 70 mm, 5 mm less than pole radius]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 37

Editorial note, tabletop extrapolation: Treat the 5 mm as this machine's geometric margin, not a rule: COLUMBUS runs a very LARGE gap-to-diameter ratio (75/150 = 0.5), so its field is far from flat at the edge anyway and the machine needs no extraction. For a 20 cm pole with a 2-3 cm gap the ratio is much smaller and the flat region proportionally wider - but the usable radius still comes from a measured or FEMM field map plus orbit-excursion and clearance checks, not from a fixed edge offset.

Die Endenergie der Ionen ist so etwas wie die Höhe einer Leiter und die Beschleunigungsspannung ist dann der Abstand der einzelnen Sprossen [tr.: final energy is the ladder height, voltage the rung spacing]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 41-42

Editorial note, tabletop extrapolation: Recomputed for 1000 V protons at 185 mT: r1 = 24.7 mm, matching the book. A 150 keV machine at 1 kV needs 150 ideal crossings; at 5 kV only 30 - relaxing vacuum and field-error tolerance roughly in proportion. The idealization to keep visible: real voltage also moves capture, turn separation and whether the top rung is reachable at all (dg-1376's ceiling-vs-attainability).

Protonen ab U0 ≥ 200 V und H2+-Ionen ab U0 ≥ 400 V – bereits beim ersten Umlauf – hinreichend weit von der Ionenquelle entfernt [tr.: clear of the source from 200 V / 400 V on the first turn]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 42-43

Editorial note, tabletop extrapolation: The scaling is the useful transfer: at 0.6 T and a 15 mm clearance radius the same ideal estimate gives ~3.9 kV for protons - so a sub-kV dee on a higher-field machine would NOT clear a 15-mm-class source housing under these assumptions; trace the actual source and gap geometry (launch phase, initial position, 3-D fields) before trusting the ideal number either way.

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

Mit Spannungen kleiner als 2–3 kV sind wir auf der sicheren Seite [tr.: with voltages below 2-3 kV we are on the safe side]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 41

Editorial note, tabletop extrapolation: Electron energies equal to the dee voltage produce bremsstrahlung with end-point energy of the same value; at 3 keV any metal wall stops it, at 15-30 keV it does not, and stray electron currents in a multipacting dee are not bounded by the beam current. Flashover can also occur below 3 kV with bad geometry, pressure or contamination. Check, do not assume: evaluate the actual electrode potentials, survey with a suitable low-energy detector at operating power, and treat viewports and thin windows as the weak points.

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.

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.

Bei der Dimensionierung des Dummy-Dees stellt sich natürlich die Frage nach der Tiefe und der Größe des Beschleunigungsspalts gap. Aus Plausibilitätsgründen wurde jeweils ein Maß von 20 mm gewählt. [tr.: in dimensioning the dummy dee the question arises of its depth and the size of the accelerating gap; on plausibility grounds 20 mm was chosen for each]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 46

Editorial note, tabletop extrapolation: A wide gap simplifies the source mount (the chimney sits inside it) at the cost of transit-time factor; choose the gap from the transit calculation - T = sin(x)/x with x = omega*g/(2v) over the actual injection and orbit velocities - rather than adopting either 20 mm or any other fixed number.

Für 16 Beschleunigungen wären 2,76 m Weglänge erforderlich, die mit 3 m knapp erreicht werden [tr.: 16 accelerations need 2.76 m of path, barely reached with 3 m]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 54-55

Editorial note, tabletop extrapolation: Recomputed: r1 = 17.5 mm, sum sqrt(i) for i=1..16 = 44.47, giving 2.45 m of arcs plus 16*0.02 = 0.32 m of gap = 2.76 m. Caution: the bitmap Table 6.2 lists 2.44 m and 1.27 m, i.e. arcs only without the k*gap term; use the text figure.

Zu diesem Zweck wurden an dem Dee zwei Extraktions- bzw. Pullerelektroden angebracht. Nun bleibt noch die eingangs gestellte Frage zu klären, warum kein zweiter Ionenstrahl während der positiven Halbwelle entsteht. Ein Grund dafür ist die Tatsache, dass die Ionen nur aus dem Schlitz extrahiert werden können, der dem Dee gegenüberliegt. Ein weiterer Grund ist das Potenzial des Kamins, das das gleiche ist wie das des Dummy-Dees, nämlich Masse. Somit könnten auch während der positiven Halbwelle der Beschleunigungsspannung keine Ionen in das Dummy-Dee extrahiert werden. [tr.: two extraction/puller electrodes were fitted to the dee; the question why no second ion beam forms during the positive half-wave is answered by two reasons - ions can only leave through the slit facing the dee, and the chimney sits at the same potential as the dummy dee, namely ground, so no ions can be extracted into the dummy dee during the positive half-wave]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 65-66

Editorial note, tabletop extrapolation: Grounding the chimney with a one-sided slit answers the reverse-beam question students raise - by construction on this machine. If the source is biased instead, the slit-to-puller spacing, the bias polarity and the counter-beam question all reopen: analyze, don't assume.

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.

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).

A system of two brass dees with differing radii allowed for ion extraction. ... For a collector, a small copper sheet was set into the path of ions leaving the larger dee, which drew electrons to itself when the ion beam was incident.

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 16

Editorial note, tabletop extrapolation: An asymmetric dee pair is a construction-level extraction trick published almost nowhere else - the radius step letting outward-spiraling ions escape the smaller electrode's envelope is the natural geometric reading (our reconstruction; the survey states the arrangement and the collector, not the mechanism), and no deflector is mentioned for this machine.

The dees were held in place with bent glass rods, which also raised both dees off the bottom plate.

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 16

Editorial note, tabletop extrapolation: Flame-bent glass rod is cheap, vacuum-compatible standoff stock with a real precedent (and the same survey shows glass slides used similarly) - as HISTORICAL construction: for a new build, treat surface flashover, creepage geometry, cleaning, and flame-bending residual stress as the qualification items; bulk dielectric strength is the one property that was never the problem.

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.

Two dees were constructed of copper and were mounted with blocks of insulating dielectric material such that they could be moved independently of each other. ... The dees were operated at 3,750 V, using a manually adjustable resonating circuit.

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 18

Editorial note, tabletop extrapolation: Independently adjustable dee mounts let gap and centering be tuned after assembly rather than machined perfectly the first time - the transferable idea. Treat 3.75 kV as reported without a stated convention (peak vs RMS, dee-to-ground vs gap not specified in the survey), i.e. a datum with an asterisk, not calibration.

the electrode was 1 cm thick, and the ion beam produced was less than one mm wide

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 26

Editorial note, tabletop extrapolation: Passive fringe-field focusing compressed a working machine's beam to millimetre scale - encouraging, but don't divide the two numbers: the 1 cm is the electrode's THICKNESS, not necessarily the clear aperture, and the survey doesn't give the beam-width direction. Whether a centimetre-class dee aperture bottlenecks a new machine is an envelope/acceptance calculation, not this datum.

The open face of the dee was squared using a milling machine, to give the final dimensions of 14.3 mm thick

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 40

Editorial note, tabletop extrapolation: Soldered thin-sheet construction plus one milling pass on the gap face gives a straight accelerating edge without hogging a cavity from solid - the transferable fabrication move. The single-screw-plus-lock-washer mount is the historical retention only: for a new build add a positive anti-rotation feature (key, second fastener) and a qualified RF contact, since a lock washer neither prevents rotation reliably nor makes a stable RF joint.

The dummy dee is made from two 0.9 mm thick by 5 mm wide strips of copper

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 40

Editorial note, tabletop extrapolation: Reducing the grounded electrode to a strip frame saves material, mass, and pumping-shadow volume while still defining the accelerating gap; the precedent indicates only the driven electrode needs an enclosed field-free interior.

held together by three insulating glass microscope slides, which were glued to the copper with Loctite 1C Hysol vacuum epoxy

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 41

Editorial note, tabletop extrapolation: The idea worth keeping is fixing the alignment-critical gap OUTSIDE the chamber, as one assembly. Glass slides are flat and cheap but not vacuum-qualified as supplied: clean and bake them, use a low-outgassing adhesive with a controlled bond line, check creepage across the glass between driven and grounded copper, and test the assembly at full RF voltage under vacuum before trusting it - insulator surfaces spanning electrodes are where flashover lives.

The filament was mounted on the dummy dee, and was powered by wires that entered and exited through two diametrically placed feed-throughs. ... The filament was kept isolated from ground so it could be negatively biased to increase the energy of the emitted electrons.

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 17

Editorial note, tabletop extrapolation: Using the dummy dee as the source's mechanical platform puts the emitter at the gap with no extra standoff hardware - the documented arrangement; whether the two-feedthrough run keeps the loop taut against Lorentz forces is our engineering reading, so anchor the leads deliberately either way (dg-1463's lesson).

[a] chamber with a diameter of 200 mm and a height of 75 mm. ... Diameter of the Dees 140 mm (5.5 in) Flux density 185 mT (H+) | 370 mT (H2+) ... Dee Voltage 0.5 - 3.0 kV Final Energy ~ 4,1 keV (H+) | 7,5 keV (H2+)

Wolf & Prechtl, COLUMBUS — A Small Cyclotron for School and Teaching Purposes — THPO001, Proceedings of Cyclotrons2022 (2022) — p. 2

Editorial note, tabletop extrapolation: A long-serving teaching machine running protons at half its field capability eases magnet, RF and matching demands at the cost of energy. The quoted energies imply a ~48-50 mm detection radius (nonrelativistic equilibrium-orbit calculation at the stated fields - a derived number, not a printed one); treat the table as the published 2022 configuration without assuming every entry is a measured operating value.

carried out on the Iowa State University undergraduate cyclotron which operates under the following conditions: Magnetic field strength, B0 — 17,000 gauss; Diameter of dees — 22.5 cm; Peak dee-to-dee voltage, 2V0 — 10 kv; Dee height, 2k — 2.4 cm; Dee gap — 1.4 cm

Mueller, Proton Orbit Calculations for the Iowa State University Cyclotron — Proceedings of the Iowa Academy of Science 68(1), 492–501 (1961) — p. 3

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: a fully documented parameter set for a very-high-field undergraduate build — 1.7 T on a small pole is what buys MeV-class energy in 11 cm with only 10 kV of RF. The rigidity relation sets the energy-radius product (a uniform 1.7 T at 11 cm would give somewhat more than the reported 1.5 MeV; the real radial profile droops); the RF voltage sets gain per turn and phase acceptance, not the final energy. It anchors the high-field corner of the small-machine design space.

the electric field is considered as concentrated in a region of zero width at the center of the dee gap. The dee-to-dee voltage is defined as V; therefore, a proton will receive a boost of energy, ∆E = eV, when it crosses the dee gap. It is assumed that the momentum is altered only in the direction perpendicular to the dee gap and parallel to the median plane ... During this instantaneous acceleration r, and z are not altered ... If an orbital radius were to exceed that of an initial deceleration, the proton energy would increase since velocity and radius are proportional; however, this contradicts the loss of energy in deceleration. Hence, it is assumed that once a proton suffers an electric deceleration it will never reach a greater energy.

Moses, Proton Orbits in a Small Cyclotron — Proceedings of the Iowa Academy of Science 70(1), 403–414 (1963) — p. 7

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: the impulse-at-gap approximation is the standard trick that keeps a homebrew tracker fast — integrate smooth magnetic motion between gaps and apply discrete energy kicks; this study checked its implementation against one-step analytic predictions. First-deceleration is the study's termination convention, backed by its radius-energy argument — for another machine verify that argument holds (or track on to exclude later recovery), and benchmark the zero-width gap against a finite-gap/transit-time estimate where the gap is not small compared to the orbit.

To obtain Figure 6, a series of calculations was performed with r0i = 9cm, θ0 = 0, σz′ = Nπ/8 and δri varying from 0.1cm to 1.0cm. For each value of δri the maximum value of |z| was obtained. For example, if a proton entered the orbit with δri = 0.5cm, its axial amplitude should be less than 1/6.1 times the height of the dees if there is to be 100% certainty that the proton will not strike the dees.

Moses, Proton Orbits in a Small Cyclotron — Proceedings of the Iowa Academy of Science 70(1), 403–414 (1963) — p. 11

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: dee aperture is consumed multiplicatively by orbit-centering error — in this modeled geometry a half-centimeter centering error left about a sixth of the aperture usable through the resonance. The '100% certainty' is the model's own, within its tracked initial conditions and field approximation. Center the source and first turns well, or budget aperture for resonance-driven axial growth.

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.

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.

The new chimney's wall was thinned near the aperture to increase the amount of field that penetrates into the plasma column. To further take increase the local electric field, angled brass plates were mounted on the face of the DEE near the ion source aperture. The plates were named "pullers" for their obvious role in ion extraction. A simple PSF model showed that the field at the plasma sheath increased by a factor of 760. According to the Langmuir-Childs' (LC) law a 130 fold increase in the peak emitted ion source should result.[5] Already measurements show approximately two orders of magnitude increase, and significantly more is expected once better initial steering is accomplished (discussed later).

Koeth, Hanebuth, Hoffman & Schneider, Rutgers 12-Inch Cyclotron Ion Source Studies: Part II (2007) — p. 4

Editorial note, tabletop extrapolation: The highest-leverage source modification in this memo, entirely within tabletop means: angled brass pullers on the dee face plus a thinned chimney wall near the aperture. The prediction chain is the source's own — modeled sheath field ×760, a Langmuir-Child-based prediction of ×130 in peak emitted current, measured ≈×100 — and its internals are not fully spelled out: a naive I ∝ V^3/2 scaling of a ×760 equivalent-voltage gain would predict far more than ×130, so the source's figure evidently folds in the real extraction geometry. Carry the design move and the measured two-orders-of-magnitude result; re-derive any prediction for your own geometry with your own field model.

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.

Optimization of the puller placement and vertical gap needs further investigation. Livingston found that for a 0.0625 inch diameter aperture that pullers with a vertical ¼ inch gap residing ¼ inch away from the aperture yielded best results. [7] This parameter space for our cyclotron has not yet been explored. It is clear from figure 12 that the ions initial radius is very large, thus the pair of pullers plates could be replaced with by a single solid plate with just an aperture in it.

Koeth, Hanebuth, Hoffman & Schneider, Rutgers 12-Inch Cyclotron Ion Source Studies: Part II (2007) — p. 5

Editorial note, tabletop extrapolation: A historical calibration point rather than a recipe: Livingston, Holloway and Baker's 1939 optimum for a 1/16-inch capillary aperture was a 1/4-inch puller gap at 1/4-inch standoff — quoted approvingly here by authors who explicitly had NOT explored that space on their machine. Scan or model gap and standoff for your own extraction voltage, field and aperture. The memo's single-apertured-plate suggestion is an untested option for cases where trajectory calculation shows the first-turn radius clears the plate — verify, don't assume. (The quoted passage begins on p.5 — where the 0.0625 inch figure appears — and concludes on p.6.)

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.

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.

The natural question that should be asked: if the ion source aperture is in the median plane, why then the large vertical displacement? This can be attributed to the early ions sensitivity to any vertical component of the electrical field. Inspection of Fig 5 shows that the electric field from the ion source into the DEE diverges quickly. Thus a slight offset of the DEE with respect to the median plane will provide a significant vertical component. This can be mitigated by the installation of "pullers" on the DEE's aperture in the region of the ion source – a possible student project.

Koeth, Hanebuth, Schneider & Hoffman, Observation of Betatron Motion in the Rutgers 12-Inch Cyclotron (2006) — p. 7

Editorial note, tabletop extrapolation: Why a median-plane source aperture still launches vertically displaced beam: in the central source-to-dee region the extraction field diverges strongly, so any dee offset from the median plane hands the earliest ions a vertical kick. No tolerance number is given — the source's stated remedy is pullers on the dee aperture near the source (offered as a possible student project, not a demonstrated fix); tightening dee-to-median-plane alignment is the natural corollary a builder draws, not the source's measured mitigation.

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 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.)

holds a 5-inch radius DEE and dummy DEE with a peak applied RF voltage of 10 kV and tunable frequency 2 - 30 MHz.

Ruisard, Hine, Koeth & Rosenberg, The Rutgers Cyclotron: Placing Student's Careers on Target — WE1PB02, Proceedings of Cyclotrons2013 (2013) — p. 1

Editorial note, tabletop extrapolation: PDF p.1 = printed p.291. A self-consistent parameter list for a machine at exactly this scale: 5-inch dee radius inside 12-inch poles, "10E-5 Torr" as printed — read as 1×10⁻⁵ Torr, the operating pressure the companion paper WEPPT025 states unambiguously — and a reported 10 kV peak applied dee voltage over a tunable 2–30 MHz range. The single-dee-plus-dummy-dee topology and the every-diagnostic-is-also-a-current-collector pattern are the parts worth copying; the numbers are reference-machine parameters, not targets.

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.

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".

The chamber's median plane is adjusted to be the same as the magnetic field's median plane. The Dummy DEE is mounted diametrically in the chamber making excellent electrical contact as it provides the aperture of the second accelerating electrode. The dummy DEE also provides a central mounting surface for the ion source.

Koeth, The Construction and Operation of a Nine Inch Cyclotron (undated scan; the machine ran 1995–1999) — p. 2

Editorial note, tabletop extrapolation: A topology that simplifies a small build: one driven dee (one HV feed-through) against a grounded dummy dee that doubles as a rigid, on-axis, at-ground mounting surface for the source — exactly where the source must sit. Whether one dee or two suits a given machine is an RF and symmetry decision, and some sources need bias or insulation rather than grounded mounting. The alignment rule worth copying outright: set the chamber median plane to the MAGNETIC median plane, not to the pole faces.

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.)

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.)

All dimentions are in inches Scale: 1/2 TOP VIEW

Koeth, The Construction and Operation of a Nine Inch Cyclotron (undated scan; the machine ran 1995–1999) — p. 12

Editorial note, tabletop extrapolation: A dimensioned drawing set — rare in the amateur literature — for one 11-inch-bore chamber: ports at 0/45/90/180/225/270 degrees, a 10.0-inch dee in the 11.0-inch bore (about 0.5 inch radial dee-to-wall clearance, computed), 13.0 inch flange-to-flange, 2.0 inch outside height, 0.25 inch lids. Use the angular map as a planning EXAMPLE — whether six azimuths serve a collector, flag, viewports and gauge without crowding depends on port diameters and the dee-stem geometry — and re-check mechanics, seals and RF clearances before cutting. (Dimensions read from the rendered sheets: top view PDF p.12, side view p.13, both printed rotated 90 degrees; "dimentions" as printed.)

CERAMIC STAND-OFF / DEE MIRRORED FACE / BRACKET / POWER FEED-THROUGH / VACUUM PORT / ASSC. PORT 2 … [p.16 sheet callouts:] CERAMIC STAND-OFF (0.5") / DEE SHOWN WITH TOP PLATE REMOVED / 10.0 / 0.375 / 0.75 / ACTUAL SIZE

Koeth, The Construction and Operation of a Nine Inch Cyclotron (undated scan; the machine ran 1995–1999) — p. 15

Editorial note, tabletop extrapolation: The documented geometry, as drawn: a 0.5-inch accelerating gap between the 1.00-inch dee and the mirrored dummy-dee face, dee on 0.5-inch ceramic stand-offs, inside the 1.50-inch chamber height with 0.25-inch dee-to-lid clearance. Reproduce it as historical reference geometry; whether the gap field is uniform enough and 0.25 inch stands your voltage are per-design questions for a field solve and a breakdown check. The dummy-dee sheet's "inside dimensions to mirror face dimentions of the DEE" note (PDF p.18, spelling as printed) is the fabrication shortcut: dimension the dummy by reference to the dee. (Drawing sheets are printed rotated 90 degrees; the p.15 assembly sheet labels the stand-off without a dimension — the 0.5" is on p.16.)

NOTE: DIMENSIONS A B & C ARE TO BE DETERMINED BY SHOP.

Koeth, The Construction and Operation of a Nine Inch Cyclotron (undated scan; the machine ran 1995–1999) — p. 14

Editorial note, tabletop extrapolation: Craft practice worth naming for amateur builders: fix on the drawing what beam geometry, RF, vacuum and fit require, and hand the rest to whoever is cutting metal — an over-specified fabricated dee is a simple part made expensive. The qualification is the rule: shop-determined details are safe to leave open only where they cannot move the physics (a 1/16-in brass box's edge radii and joint allowances, plausibly; anything touching gap, aperture or stem, never). (Numbers read from the rendered drawings, printed rotated 90 degrees.)