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

Tabletop: Matches the reference machine's 8 in poles: plan for a usable beam radius of ~3.2 in unless shims extend the flat region.

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

Tabletop: This is the closest historical analogue to a next machine's target: same pole diameter as the reference machine, ~3x their field and ~10x their dee voltage buy ~10x the energy.

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.

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

Tabletop: 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 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

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

Tabletop: Concrete LC numbers for a next machine's tank at the same scale; the swappable-primary approach lets you retune coupling without rebuilding the tank.

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. 1

Tabletop: 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

Tabletop: This is the sizing equation for the reference machine's LDMOS upgrade: doubling dee voltage costs 4x power, so going from 1.3 kV to 5-13 kV needs a 15-100x power increase unless L/C or Rs improves.

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

Tabletop: When predicting a next machine's dee voltage, don't use the coil resistance alone; the stainless chamber and stem return path dominates losses, so use copper return paths where possible and expect ~1 ohm scale Rs.

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

Tabletop: For a next machine, shrinking dee-to-liner capacitance (larger dee-to-lid spacing) and using a bigger low-loss coil buys dee voltage for free before spending on amplifier watts.

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. 8

Tabletop: Scales the reference machine's plan: with a similar tank, a 500 W LDMOS amp should land near 10 kVp-p - comfortably in their 5-13 kV target - and 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.

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

Tabletop: At 1.3 kV the builder has enormous margin; for a next machine at several kV, ~50 kV/in of clearance in vacuum with rounded edges is a comfortable design gradient.

it has been found necessary to have these tubes spaced as closely as 2 to 3 in. to prevent local heating and warping of the D's under power.

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

Tabletop: At tens of watts the builder needs no water, but the warping lesson stands: dee thermal drift detunes the resonator, so keep dee structures stiff and thermally anchored.

Such a variable capacitance can be provided by a movable plate on the side wall of the chamber facing one edge of the D ... a range of motion sufficient to tune over about 1 per cent in frequency.

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

Tabletop: 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

Tabletop: The reference machine already does this; it remains the right choice for a next machine unless push-pull two-dee RF is needed for higher energy gain per turn.

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

Tabletop: A directly copyable dee geometry for an 8-10 inch pole; note the dees must be water cooled once RF power reaches ~kW.

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

Tabletop: This is the reference machine's exact topology, validated on a comparable machine; the deformable-inductor trim is a simple tuning mechanism for 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

Tabletop: Exactly the reference machine's architecture; the dummy-dee edge is a proven low-cost next-machine upgrade for a cleaner accelerating gap.

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

Tabletop: Confirms the single-dee choice for a next machine unless dee voltage 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

Tabletop: Benchmarks the reference machine's setup (1.3 kV from 5-50 W is right on this curve) and warns that the autotuner path plateaus in the low-kV range.

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

Tabletop: 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

Tabletop: Anchors the power budget: even a well-built 12-inch tank needs kW-class RF for ~10 kV dee voltage, so the reference machine's 500 W LDMOS should target ~4-8 kV peak.

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

Tabletop: Explains why the reference machine's next big win may be Dee voltage, not magnet shaping: at ~160 keV with a low Dee voltage the turn count is what kills the beam.

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

Tabletop: For a fill-gas machine like the reference machine's, dee volts are the strongest single knob on beam current; prioritize RF voltage over almost everything else.

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

Tabletop: Tells the builder that Dee voltage is a tank-Q problem, not a brute-force power problem: a modest amplifier plus a good resonator beats a big amplifier into a lossy one.

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

Tabletop: Directly applicable test discipline for a next machine's dee-voltage conditioning: rate the machine at the level it holds quietly for minutes, not the level it touches.

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

Tabletop: Directly applicable if a next machine's RF start-up stutters or the dee glows at low voltage: insulate the dee for DC and add a few-hundred-volt negative bias through an RF choke.

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

Tabletop: Scales directly: the reference machine's 1.3 kV needs well under a millimeter electrically, so their clearances are set by beam aperture and tolerance, but a 20-50 kV dee on a next machine should keep several millimeters to grounded surfaces.

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

Tabletop: Directly applicable when the builder trims a next machine's dee for probe or source clearance: keep the dee close to 180 degrees or account for the sin(theta/2) energy-gain penalty.

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

Tabletop: 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

Tabletop: Directly applicable: multipactor lives exactly in the few-hundred-volt, MHz regime of a starting tabletop dee; plan the DC-bias insulation into a next machine's dee stem from day one.

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

Tabletop: For dees, stems, and tank coils at 9 MHz: bare electrical-grade copper plus thin lacquer beats commercial silver or nickel plate.

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

Tabletop: Polishing dee edges and stems serves double duty at 5-13 kV: lower RF resistance and higher voltage-breakdown threshold.

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

Tabletop: Supports the single-dee/dummy-dee topology at the reference machine's scale; a ~10 mm grounded bar is field-equivalent enough to a second dee and frees chamber space.

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

Tabletop: Give the first third of radius generous vertical aperture (that is where ions are lost); the outer region can be tight, which also helps RF economy.

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.

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

Tabletop: Graphite source parts keep metal sputter off insulators and chamber walls; a feeler (puller) on the dee edge is the single cheapest first-turn-capture upgrade.

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

Tabletop: Explains why source-to-dee geometry (chimney position, puller gap, aperture height) dominates beam capture on small machines: the magnet cannot help until several turns out.

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

Tabletop: The single biggest lever on the reference machine's dee-voltage ceiling: gloves, solvent cleaning, and dust-free assembly of dee and stem buy more holdoff than any material upgrade.

breakdown occurs between 5 and 200 MV/m ... In general, smaller gaps can withstand higher fields.

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

Tabletop: At 13 kV across the reference machine's ~6 mm gap the mean field is only ~2 MV/m - if it sparks there, the cause is edges, insulators, particles or gas pressure, never the vacuum gap itself.

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

Tabletop: After assembling the next machine, the builder should ramp dee voltage slowly and let a limited number of current-limited sparks condition the surfaces before declaring a voltage ceiling.

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

Tabletop: Directly applicable at 1.3 kV and above: give the stem a continuous insulating sleeve with generous creepage past the grounded feedthrough.

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

Tabletop: The edge-radius rule the builder needs when pushing dee voltage to 5-13 kV: radius all dee and stem edges so the enhanced edge field stays under ~half the material's breakdown value.

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

Tabletop: Machinable ceramic (Macor-class) spacers are the spark-tolerant choice for holding the reference machine's dee-to-dummy-dee gap, replacing glass or plastic.

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

Tabletop: A next machine should assume sparks WILL damage insulators eventually; screw-together modularity turns a total rebuild into a one-part swap.

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

Tabletop: Directly applicable to any screwed-together dee on a next machine: unvented blind holes are virtual leaks that cap the achievable base pressure.

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

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

Tabletop: Matches the reference machine's ~1.3 kV operating point today; at their planned 5-13 kV the same geometry needs proportionally more ceramic creepage distance.

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.

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

Tabletop: Direct fabrication template; the single-Dee-plus-dummy topology halves the RF feedthrough problem versus two live Dees.

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

Tabletop: Directly applicable: at 1.3 kV the reference machine's protons make many turns; the single biggest transmission lever for a next machine is more dee volts, not more source current.

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

Tabletop: At 1.3 kV the builder needs no water; if a next machine's dee runs kilowatt-class RF, soldered-on flattened tubing along the dee lip is the proven cheap construction.

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

Tabletop: Perforation transfers directly (pressure inside an unvented dee can be much worse than gauge pressure); graphite armor matters only if a next machine reaches activation-capable energies.

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

Tabletop: 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

Tabletop: Sets the scaling for a next machine: roughly, final energy in a classical machine tracks dee voltage; the reference machine's few-kV dee at ~160 keV is consistent, and ~1 MeV needs proportionally more volts per turn or a flatter field.

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

Tabletop: At the reference machine's few-MHz, few-kV/cm gap fields this gives huge margin, but it is the correct sizing formula if a next machine pushes dee voltage up to tens of kV across small central-region gaps.

For internal sources, the anode is usually grounded and 30-100 kV of rf voltage is used for extraction with a feeler or puller extending from the dee.

Clark, Ion Sources for Cyclotrons — Cyclotrons '81, Caen (1981) — p. 3

Tabletop: The reference machine extracts with its few-kV dee — 10x less voltage than any literature machine. Compensate with a small source-puller gap (1.5-2.5 mm, cf. Siemens 2.3 mm, K100 2.9 mm) since extracted current scales ~V^1.5/d^2, and expect proportionally lower beam than published uA figures.

The minimum gap between the chimney and the puller is 2.9 mm [K100 geometry]

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

Tabletop: Gap scales with voltage to hold gradient — at a few kV dee the builder can close the chimney-puller gap to ~1.5-2 mm to recover extraction field, still an easy gradient (<2 kV/mm) against vacuum breakdown limits.

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

Tabletop: The half-step option — chimney-over-filament keeps the reference machine's existing filament supply and adds gas confinement + defined emission aperture. Worth knowing it exists, but a PIG chimney gets the same geometry benefits and deletes the filament.

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

Tabletop: Directly applicable - a DC-isolated dee mount costs little at design time and gives the multipactor-suppression knob the Berkeley reports show is essential.

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

Tabletop: Oscillator/transmission-line practice, transferable - lossy coupled loads and mode traps work identically on a fixed-frequency dee resonator driven by an LDMOS chain.

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.

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

Tabletop: Directly applicable scaling - at 13 kV the same conservative ~17 kV/inch rule wants ~3/4" dee-to-liner clearance; tighter gaps must lean on the 0.080"/50 kV bench data with derating.

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

Tabletop: Directly applicable - a bench quarter-wave resonator lets the builder soak-test a next machine's dee-stem insulators at full 5-13 kV RF with only tens of watts of drive.

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

Tabletop: Directly applicable breakdown data for setting a next machine's dee-to-liner and puller gaps at 5-13 kV - and a warning that discharge-roughened surfaces lose ~40% of bench hold-off.

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

Tabletop: Directly applicable if the next machine's dee or stem is water-cooled while DC-biased - length of insulating hose plus DI water sets the leakage current.

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

Tabletop: Transferable method - a next machine's resonator can be prototyped at reduced scale with a VNA, remembering effective dee capacitance is not the static capacitance (500 vs 1000 pF on the 184-inch).

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

Tabletop: Directly applicable - the complete 1948 recipe for the RF discharges that plague small chambers at kV-level dee voltages; perforated shields keep pumping speed.

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

Tabletop: Directly applicable - the entire next machine's dee sits in 0.59 T, so if bias is used to kill discharges, start negative; positive bias risks a permanent Penning discharge.

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

Tabletop: 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.

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

Tabletop: Directly applicable benchmark near the reference machine's 9 MHz - scaled by its much smaller dee capacitance and Q, it frames how many LDMOS kW the 5-13 kV goal really needs.

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.

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

Tabletop: 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 - plan a DC bias supply on the dee from day one.

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

Tabletop: Conditionally applicable - a bipolar, current-limited bias supply on the next machine's dee lets the builder try both polarities safely and keep whichever helps beam.

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

Tabletop: The reference machine's few-kV dee means thousands of turns - the explicit worst case named here; keep dee aperture at least twice the expected radial oscillation amplitude and keep n < 0.2 over the whole usable radius.

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

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

Tabletop: Proof that low dee voltage works at small radius: the 16-inch ISSP machine is the existence proof for a next machine's sub-MeV goal with a ~10 kV-class dee, provided the field profile keeps the many 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

Tabletop: Sanity template for a next machine on 8-in poles: expect ~1.0-1.4 in gap, ~0.5-0.8 in dee aperture, and plan energy at a 3.2-3.6 in beam radius, not at the pole edge.

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

Tabletop: The cheapest extraction upgrade known: mechanical slits in the center region plus tight dee-amplitude regulation; for a next machine's turn-separation budget, orbit-center definition on turns 1-3 matters more than deflector finesse.

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

Tabletop: First-turn loss at low dee voltage is a classic tabletop failure mode; a fine grid (or slit plate) on the dummy-dee aperture is a proven 1950s fix that costs an afternoon to try.

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

Tabletop: 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

Tabletop: 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

Tabletop: Confirmed independently on the machine side in ucrl-3187 p.5,11 (dees could not be servoed individually until neutralized). A single-dee next machine dodges this entirely - which is itself the design lesson - but it governs any future two-dee or dee+dummy-dee variant with separate tuners.

thermal effects detuned the machine sufficiently so that ion lock prevented the rf from being restored

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

Tabletop: The reference machine already shows warm-up drift; the transferable practice is a permanent low-level sweep capability (VNA or dip meter on a pickup loop) so resonance can be found cold without RF power, plus logging tune position vs temperature - cheap now, standard then.

In the weak vertical field component of the accelerating voltage in the 184-inch cyclotron the beam loss was impressively fast.

Stubbins, Radiofrequency System for Extracting Particles from a Cyclotron — UCRL-8578 (1958) — p. 5

Tabletop: A real design caution at any scale - dee misalignment or asymmetric liners give exactly the z-proportional E_z this resonance needs. Keep a next machine's dee/dummy-dee vertically symmetric and check whether nu_z resonates with any strong rf harmonic 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

Tabletop: Directly transferable acceptance test for the reference machine's LDMOS upgrade — run the dees 25% above the planned operating voltage for hours before calling the RF done; a margin that survives only seconds is not margin.

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

Tabletop: Worth a cheap experiment on the reference machine (a DC bias supply on the dee), but the ORNL conclusion is that geometric phase selection (a slit) beats electrostatic tricks — put the effort into the puller/slit geometry first.

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

Tabletop: Transferable at proportional scale (tens of volts on the reference machine's ~1 kV dees, a few hundred on the LDMOS upgrade) — multipactor/ion loading during RF ramp-up is a classic small-machine failure mode and a bias supply is the classical cure.

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

Tabletop: The 400-500 kV is MW-era and does not transfer; the material practice does — if the reference machine's 5-13 kV upgrade sparks at the dee gap, graphite edge pieces are the period-proven remedy and are trivially machinable.

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

Tabletop: 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

Tabletop: Dees are pumping dead-ends by construction - drilling the dee back and any stem shrouds (small holes, below RF-significant size) is free conductance exactly where the ion source dumps its gas.

The fairly low efficiency, 27 per cent, indicates that it would be desirable to go to six type-880 tubes in the final model, especially since power-supply capacity is available for the additional tubes.

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

Tabletop: 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

Tabletop: Both suppression tools are amateur-accessible - a strap that shorts the parasitic mode's voltage pattern without disturbing the wanted mode, and a loop selectively coupling the parasite into a lossy load; relevant 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

Tabletop: For the reference machine's LDMOS upgrade toward 5-13 kV dees, walk the whole rf path in air - feedthroughs, stem gaps, coupling hardware - because atmospheric-side spark gaps, not vacuum gaps, set the first ceiling.

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

Tabletop: 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

Tabletop: 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 every millimeter given to voltage clearance is field (B ~ 1/gap) taken from energy. Decide dee voltage and gap in the same trade study.

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.

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

Tabletop: If a next machine's dees carry water, route tubing so every brazed or welded joint can be reached, pressure-test the dee as a unit BEFORE it meets the liner, and treat a cut-window-and-reweld as a planned repair mode (it worked) - the recovery technique is as instructive as the failure.

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

Tabletop: The mechanical execution of the 1663 insulate-for-bias rule - for a next machine, one stiff cantilevered dee-stem mount outside the field region, isolated by insulators, is simpler than distributed insulated supports and keeps the bias feed and rf geometry clean.

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

Tabletop: Same margin philosophy as the 63-inch 75-vs-60-kV acceptance hold (ornl-1339) - for the reference machine's LDMOS upgrade, compute the threshold dee voltage for the intended turn count and buy amplifier/resonator headroom for ~2x it, not 1.1x.

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

Tabletop: 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

Tabletop: The reference machine's lore confirmed at lab scale — final RF tuning of a next machine's cavity must be done with dummy dee, source structure, and probes installed, or budget a multi-percent retune.

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

Tabletop: The recovery plan if a next machine's fixed-frequency cavity misses 9-ish MHz after assembly; note both fixes tax drive power, so aim the design low in frequency and trim up with the cheaper capacitive side when possible.

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

Tabletop: On a small machine the dee-stem-to-chamber-wall clearance is the same critical region — it sets both the resonant frequency and where I^2R heating concentrates; machine it to drawing, do not shim it by eye.

The oscillator must be stable enough to sustain an arc drawn from the dee face (simulating discharges in that region).

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

Tabletop: The arc test transfers verbatim to the planned LDMOS amplifier — prove the driver (and its protection) rides through a real drawn arc at the dee before trusting it in vacuum, where sparking during conditioning is guaranteed.

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

Tabletop: Same differential technique as Koeth's Rutgers dee-capacitance note already in this collection — an LCR meter plus one disassembly step yields every lumped C in a next machine's tank model, feeding the resonance and Q predictions.

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

Tabletop: 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

Tabletop: E_y(x,y) is exactly what a tracker needs for the Rose/Wilson electric gap-focusing term that dominates axial stability on the first turns of a sub-kV machine like the reference machine — available here analytically at any (x,y), no field map required.

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.

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

Tabletop: Copy the iteration and its initial-guess branch verbatim into the tracker's field routine; a handful of iterations reaches machine precision, 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

Tabletop: Sets the real ceiling on gap-field strength for any dee redesign — with a 1-inch aperture (h = 0.5 in) and 5 kV dee-to-dummy (V0 = 2.5 kV), peak field cannot exceed ~2 kV/cm no matter how tight the gap; widening the aperture for beam height costs peak field one-for-one.

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

Tabletop: Transit-time factors and gap-crossing phase errors for the tiny machine and a next machine must be computed on this extended profile — at low first-turn velocities the particle spends a large RF phase interval inside a field region ~2h long, which a delta-kick model at the gap centerline gets wrong.

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

Tabletop: Kills the tempting back-of-envelope E = V_dee/gap for both breakdown margin and energy-gain 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 the tables.

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

Tabletop: Unit-test targets for the tracker's gap-field routine AND an independent check on FEMM electrostatic runs — model the same idealized geometry in FEMM once and match these 5-digit values before trusting FEMM on the real next-machine electrode shapes.

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 a<4.

Beal, Computation of Electric Field and Potential of an Idealized Dee Geometry — MSUCP-12 (1961) — p. 8

Tabletop: For use on a next machine, the real deviations to check against FEMM are finite dee thickness, the rounded/blunted tip, and the curved gap line near the source at small radius — expect the analytic solution to be excellent at mid-radius and approximate near center where the ion-source chimney dominates the field anyway.

The basic variation of line Zo along the resonator tends to minimize the capacitor Cmax/Cmin ratio needed.

Rainwater et al., The Columbia University Nevis Synchrocyclotron Major Modification — NEVIS-189 / R-774 / CU-295 (1971) — p. 9

Tabletop: FM machinery itself does not transfer, but the impedance-profile trick applies to any tunable tank, and to any RF cavity that needs a swept or trimmed frequency range.

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

Tabletop: Directly relevant at a next machine's planned 5-13 kV dees where multipactor bands are widest; corroborates the glow corner's multipactor-mechanism rules with a 1971 operating-lab remedy and a concrete bias magnitude to scale from.

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

Tabletop: An existence proof that in-vacuum consumable-changers can share space with a live dee structure, and the cleanest statement in this collection that foil flatness is an orbit-quality parameter, not cosmetics — relevant to any internal-foil or internal-target scheme.

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

Tabletop: DIRECT — this sentence names the exact configuration of the 8" machine (simple dee system as the tank circuit) and matches its documented multi-year pattern of RF amplifiers failing to bring the dee to voltage. Multipactor loading in the ~100 V band is a named, testable candidate cause for that history, distinct from amplifier inadequacy.

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

Tabletop: The decision menu for any machine that stalls in the multipactor band: bias, drive-through, or (this report's contribution) 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 few-hundred-volt DC offset on the dee — pick by which fights the existing hardware least.

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

Tabletop: Transferable decision pattern: on a machine whose dee stem is grounded through the tank structure, retrofitting DC bias means rebuilding the stem insulation, while a shock starter touches nothing but a spare port. Choose the quench that is additive.

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

Tabletop: The cheapest cure in this collection for a stalled self-excited start: one loop, one capacitor, one spark gap, one HV supply — all amateur-stock parts. The key insight is that the kick need only clear the top of the loading band, not deliver operating power; everything above a few hundred volts is the oscillator's own job.

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

Tabletop: A free diagnostic: ring the dee (impulse or drive-and-release), scope the pickup envelope, and look for a kink. A visible steep-decay segment localizes the multipactor band on YOUR machine and tells you whether nominal operating voltage sits inside it — the critical question for any dee running near a few hundred volts.

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 (c. 1950) — p. 58

Tabletop: The construction vocabulary (EHC copper skin, silver-soldered cooling, silver-plated RF joints, high-pressure sliding contacts) is exactly what a 5-13 kV LDMOS-driven dee upgrade needs; split-for-repair is cheap foresight at any scale. Same contact-pressure concern as the nyo-9683/ornl-2648 sliding-contact rules.

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 (c. 1950) — p. 75

Tabletop: 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/(2R_shunt)), then buy the amplifier with a 2-3x factor for the terms the lumped model misses. The Koeth Rutgers dee-voltage note is the same math on an 8-12 inch machine.

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 (c. 1950) — p. 76

Tabletop: For a one-dee-plus-dummy machine the mode problem collapses, but the principle stands for any driven system — verify which resonance the amplifier is locking to (a network analyzer sweep distinguishes the modes), because the wrong one accelerates nothing. Also this collection's second explicit SELF-EXCITED architecture choice (see ucrl-9435 rule on the self-excited-vs-MOPA tension).

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 (c. 1950) — p. 75

Tabletop: The corpus's driven-start cure (mddc-1045 tickler; nyo-9359's catalog) as a 1951 DESIGN feature rather than a retrofit — including the elegant half-frequency/doubler isolation trick so the starter needs no 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 ~100-V multipactor band without foldback/protection tripping.

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

Tabletop: DIRECT — the ~100-150 V band is exactly where a small machine's dee voltage must pass on every start. Completes this collection's cure set with the DC SWEEP variant: mddc-1045 (bias + tickler), nyo-9359 (impulse), ucrl-64 (volume reduction + bias), aecu-1951 (booster drive-through). Same author lineage as ucrl-3153/3187.

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

Tabletop: DIRECT for the 5-13 kV dee upgrade: plan a conditioning campaign (auto-recycle protection makes it unattended) rather than interpreting early sparking as failure. A tabletop resonator stores millijoules, so conditioning is gentle — the count, not the violence, does the work. Corroborates the ornl-2648/nyo-9683 conditioning rules and quantifies them.

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

Tabletop: The four-line budget is the right form at any scale — a tabletop version is watts of copper loss, ~zero stray-ion, uW of beam, and a misc line that is mostly coupling/radiation. The named "stray-ion loss at the center" term is a reminder that source gas load steals RF power — one more reason the reference machine's beam and RF problems interlock.

If the circuit is made too fast, it takes too long to bake the resonators in. If it is made too slow, the spark damage to the dee and linear surfaces will be excessive.

Smith, The RCA 6949 as a Self-Excited Cyclotron Oscillator — UCRL-9435, Lawrence Radiation Laboratory (1960) — p. 7

Tabletop: A protection spec you cannot derive from electronics alone — the dwell time is chosen so each spark finishes cleaning the spot that caused it. For a tabletop supply: let a dee spark burn ~1 ms before the drop-and-retry, but trip amplifier-device faults as fast as the electronics allow. Two speeds, two purposes.