Cyclotron extraction design rules

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

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

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

for a final energy of T = 30 MeV, dT = 100 keV, and an extraction radius of 0.5 m, we find dr = 0.83 mm. This is a rather small number, e.g. when compared with a radial beam width of for instance 4 mm.

Botman & Hagedoorn, Extraction from Cyclotrons — CAS, CERN 96-02 (1996) — p. 6

Editorial note, tabletop extrapolation: Small machines fare better because dr/R scales as dT/T: a 350 keV next machine at 10-20 keV per turn carries a fractional turn separation 9-17x this 30 MeV machine's. Its beam width does not shrink in proportion, though - so the separation-vs-width comparison still needs the machine's own numbers (dg-495).

when a coherent oscillation amplitude x of 3 mm has been built up ... and acceleration takes place until vr = 0.8, the maximum turn separation due to precession is 3.8 mm.

Botman & Hagedoorn, Extraction from Cyclotrons — CAS, CERN 96-02 (1996) — p. 7

Editorial note, tabletop extrapolation: A deliberate few-mm coherent amplitude (source off-centering is one way to seed it), plus letting nu_r fall toward 0.8 in the fringe, can multiply turn spacing severalfold - IF the precession phase is arranged so the separation appears at the septum azimuth. It is a designed, tracked orbit-dynamics move, not a free effect.

Accelerating the beam far into the fringe field often means passing the vr = 2 vz coupling resonance. Energy can be exchanged from the radial to the vertical motion, blowing up the beam vertically and leading to beam loss. If the radial oscillation amplitude is not too large, and if the resonance is passed in only a few revolutions, vertical amplitude increase is avoided. In practice, a coherent radial oscillation amplitude of the same size as the incoherent amplitude, is a good criterion for efficient extraction. Another reason for requiring not too large radial oscillation is avoiding strong non linear effects.

Botman & Hagedoorn, Extraction from Cyclotrons — CAS, CERN 96-02 (1996) — p. 7

Editorial note, tabletop extrapolation: If a next machine's radial beam half-width is ~2-3 mm, start near a ~2-3 mm coherent amplitude and set the acceptable ceiling by tracking through the extraction field - the equality criterion is the source's practical starting point, not a hard limit.

one has to limit the radial amplitude, induced from the v = 1 resonance, to a few mm.

Heikkinen, Injection and Extraction for Cyclotrons — CAS, CERN 94-01 (1994) — p. 18

Editorial note, tabletop extrapolation: In a weak-focusing field the last turns sweep the field index upward toward these resonances: compute the actual tune curves from the measured field map, and keep energy gain per turn high through any crossing so that tracking predicts acceptable vertical growth - speed of crossing, not a fixed turn count, is the criterion.

Cited in: Beam Dynamics: An Interactive Laboratory

taking eps1 = 10-4, R = 1 m and vr - 1 = 0.01, one finds an orbit centre shift, i.e. a radial oscillation amplitude, of dx = 5 mm.

Botman & Hagedoorn, Extraction from Cyclotrons — CAS, CERN 96-02 (1996) — p. 9

Editorial note, tabletop extrapolation: Gauss-level azimuthal asymmetry matters at 0.59-0.89 T NEAR nu_r = 1: the (nu_r^2 - 1) denominator is what turns the quoted 0.6 G into 5 mm, and the sensitivity falls away from the resonance and shrinks with radius. It is both the knob (a deliberate shim or coil bump) and the hazard (uncontrolled bumps de-center the beam) - dg-562's tolerance computation is the same physics from the defensive side.

Cited in: Beam Dynamics: An Interactive Laboratory

For a typical conventional cyclotron (Bo ~ 1.7 T) a bump of 0.1 mT (1 G) introduces a radial gain of about 0.2 mm. To get a desired turn separation bigger bumps are needed (brute force). ... Since, for a given energy, the magnetic rigidity BR is constant, the radial gain per turn increases with a factor of R favouring larger machines.

Heikkinen, Injection and Extraction for Cyclotrons — CAS, CERN 94-01 (1994) — p. 14

Editorial note, tabletop extrapolation: Scaled to 0.6-0.9 T and r ~ 0.1 m the per-turn gain from 1 G is only ~0.04 mm, so mm-scale separation would take tens of gauss of first harmonic - precession is far cheaper than brute force.

n_eff is the effective duration of the resonance (typically around ten revolutions). ... Typically the extraction takes place near v = 0.8.

Heikkinen, Injection and Extraction for Cyclotrons — CAS, CERN 94-01 (1994) — p. 14

Editorial note, tabletop extrapolation: A smooth azimuthally symmetric weak-focusing machine approaches nu_r=1 from below and never crosses it, so create the amplitude by ion-source off-centering instead (a different mechanism than resonant buildup - verify what it delivers by tracking) and use the fringe region where nu_r has fallen toward the source's typical ~0.8 for precession, with the actual tune taken from the measured field map.

An angle kick of typically 50 to 100 mrad is provided. The inner electrode, septum, is at earth potential. At the entrance it has a thickness of a few tenths of a mm, increasing to several mm at the exit.

Botman & Hagedoorn, Extraction from Cyclotrons — CAS, CERN 96-02 (1996) — p. 14

Editorial note, tabletop extrapolation: At 350 keV a 100 mrad kick over 10 cm of arc needs E = theta*(2T/q)/L = 7 kV/cm - about 3.5 kV across a 5 mm gap. At nanoamp beams the septum's heat load is negligible whatever fraction it intercepts: 1 nA of 350 keV beam carries only 0.35 mW in total.

a criterion for the product of electric field E and potential V for a cyclotron deflector in order to avoid electric discharges: VE < 1.5 104 (kV)2/cm. The maximum sustainable voltage in a magnetic field is 20-30% lower.

Botman & Hagedoorn, Extraction from Cyclotrons — CAS, CERN 96-02 (1996) — p. 14

Editorial note, tabletop extrapolation: A 3-5 kV, 5-10 kV/cm tabletop deflector sits orders of magnitude below this bulk-discharge criterion - so at tabletop scale the practical ceiling comes from feedthrough, surface and edge-radius engineering (dg-353, dg-297, dg-295), not from the Smith-Grunder product.

At HV edges, electric field lines become so dense that breakdown becomes a major concern. 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: Direct amateur precedent: a 1 T / 472 keV university tabletop deflector ran at 28-32 kV. A lower-energy machine needs proportionally less deflector voltage (scaling roughly with beam energy at similar geometry - a 150 keV-class machine perhaps a third, not a tenth), and the edge-field formula stays the design check: generous radii reduce peak field, they do not make sparking impossible - finish and conditioning still rule (dg-295, dg-353).

Mammoflex M-1 HV cable has C of 56 pF per foot ... ~0.1 Joules at 30 kV ... ~0.4 Joules at 30 kV ... The bottom plate and deflector electrode - no pitting on the electrode noticed.

Ponter, Beam Energy Measurements with a New HV Deflection System and Ion Source Upgrades on the Rutgers 12-Inch Cyclotron (2010) — p. 43 (stored energy; repeated 45, 49) and 44 (pitting)

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: Rutgers' slide sequence recounts arcing a feedthrough run above its class and rebuilding with the feedthrough inside vacuum plus a corona adapter. The specific numbers, page-image verified 2026-09-06: cable stored energies ~0.1 J (5 ft) and ~0.4 J (20 ft) at 30 kV via 56 pF/ft Mammoflex M-1, and a feedthrough 'rated for 30 kV (we want to run it at 35)' - the overrun plan is the cautionary half of the lesson. Choose feedthrough rating from the manufacturer's figure, the vacuum-side geometry and test history, and never run a feedthrough above its rating. [Note revised 2026-08-23: 'rate 2-3x over operating voltage' was an invented margin.]

For DR = 0.1R: Va = 47,000 volts ... A typical figure, used in the MIT cyclotron, is a DR of 0.15R. ... The deflector gap is usually tapered.

Livingston & Blewett, Particle Accelerators (1962) — p. 163-166

Editorial note, tabletop extrapolation: Scaling by 2T: a next machine at 350 keV needs about 1/45 of MIT's voltage at the same normalized geometry - roughly 1-2 kV across a proportionally scaled entry gap - rising if a faster peel (larger DR) or a larger gap is wanted. Compute with the formula for the actual geometry (dg-590's worked example).

Emergent beam intensities up to 25 per cent of the resonant beam intensity have been obtained under optimum conditions; ... practical operating intensities would in this case be limited to 80 or 100 [micro]a.

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

Editorial note, tabletop extrapolation: Plan a next machine's deflector attempt around the classical rungs - tens of percent at best, and that under optimum tuning: with nA internal beam, 0.1-0.25 nA external is still a countable, PIXE-usable beam. The upper rungs belong to machine classes a tabletop deflector does not reach.

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

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

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

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

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

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

the negative hydrogen ion beam simply passes a thin carbon foil (e.g. pyrolytic graphite, typically 50 to 200 ug/cm2), which strips off the electrons.

Botman & Hagedoorn, Extraction from Cyclotrons — CAS, CERN 96-02 (1996) — p. 3-4

Editorial note, tabletop extrapolation: At sub-MeV a 50 ug/cm2 foil costs ~10 keV of energy and some scattering. The septum, HV and turn-separation problems genuinely disappear - replaced by the H- problems: an internal H- source, and the 1e-6 Torr-class vacuum that gas stripping of the fragile H- demands (dg-599).

the cross section of H- interactions with the gas molecules is maximal for the energy range (0.1 - 300) keV of the beam in the central region.

Calvo et al., Beam Stripping Interactions in Compact Cyclotrons — PRAB 24, 090101 (2021) — p. 14

Editorial note, tabletop extrapolation: A next machine's H- variant spends its whole life at the cross-section peak. Run the loss arithmetic explicitly through T = exp(-n*sigma*L) with measured H- detachment cross-sections - the 1e-15 cm2 class near the peak; fetch sigma(E) for the actual gas mix when designing. At that scale ~25 m of spiral at 1e-6 Torr loses of order 5-10%, and 1e-5 Torr costs most of the beam: vacuum, not physics, decides this option. (70 MeV data: cyclotron_vacuum_model p.3.)

Cited in: The Vacuum Budget of a Cyclotron

a 4 T magnetic field for the maximum achievable energy of 8.5 MeV in the AMIT cyclotron corresponds to a beam-rest-frame electric field of E = 160 MV/m. This entails a marginal beam fraction loss per unit length of 1.42e-6 m-1

Calvo et al., Beam Stripping Interactions in Compact Cyclotrons — PRAB 24, 090101 (2021) — p. 7-8, 14

Editorial note, tabletop extrapolation: At 0.889 T and 500 keV the rest-frame field is ~9 MV/m, where the exponential makes the lifetime effectively infinite - Lorentz stripping can be ignored entirely for a next machine.

the spreading of orbit centres for different HF phases due to HF mixing, is small for an originally well centreed beam, as in general the number of turns from the vr = 1 resonance till extraction is not so large.

Botman & Hagedoorn, Extraction from Cyclotrons — CAS, CERN 96-02 (1996) — p. 9

Editorial note, tabletop extrapolation: If a next machine uses source off-centering (amplitude created at turn 1, necessarily - it cannot be placed late), evaluate the phase-mixing integral from tracked particles in the actual field map before assuming the coherent centroid survives: individual amplitudes persist while the ensemble centroid can smear. A trim bump near the extraction region, where late placement IS possible, is the cleaner tool.

Figure 11 shows a differential probe measurement for this cyclotron in the extraction region. The separation between the probe fingers is 2 mm. The figure reveals the radial oscillation near extraction.

Botman & Hagedoorn, Extraction from Cyclotrons — CAS, CERN 96-02 (1996) — p. 11-12

Editorial note, tabletop extrapolation: Adding a two-finger (or shadow-bar) differential head turns the reference machine's existing radial probe into the diagnostic that informs septum placement - choose the finger spacing from the PREDICTED turn separation and beam width (2 mm was that machine's), and combine the measured pattern with orbit tracking and clearance requirements rather than reading placement off the probe alone.

the radial displacement amplitude is equivalent to about twenty turns, or to about two kilovolts, or about 1% spread in energy at the exit radius

Goodman, A Square-Wave Cyclotron Oscillator — ORNL-2403 (1958) — p. 12

Editorial note, tabletop extrapolation: Budget this effect for any future extraction work by evaluating D and Delta-r with the machine's own V, omega, gap and phase distribution and tracking the offsets to extraction - the ORNL equivalences are that machine's numbers, not a floor. Flat-topping reduces the phase-dependent part; neither AVF nor flat-topping removes the displacement wholesale.

for equal probability of sparking with given materials, the product of gap voltage and cathode gradient is a constant.

Smith & Grunder, Electrical Design of Electrostatic Deflectors for Sector-Focused Cyclotrons — UCRL-10654 (1963) — p. 8

Editorial note, tabletop extrapolation: For a next machine's deflector the trade falls out of a chosen VE number: a 3-mm gap at VE = 1.5e4 (kV)^2/cm predicts ~67 kV at ~220 kV/cm - far beyond tabletop needs (dg-590's few kV), which is the real point: tabletop deflectors sit deep inside the bulk-breakdown envelope, and surface/edge engineering rules instead (dg-591).

In order to provide an adequate margin for day-to-day operation, a design value of 1.5 X 10^4 should be used.

Smith & Grunder, Electrical Design of Electrostatic Deflectors for Sector-Focused Cyclotrons — UCRL-10654 (1963) — p. 33

Editorial note, tabletop extrapolation: The most quotable deflector design number in the collection: design to VE = 1.5e4 (kV)^2/cm and treat the tested 2.25e4 as commissioning margin - as the source machine practiced. Transfer it as a starting point under the usual conditions (electrode material, finish, conditioning - dg-353, dg-295), and verify on the actual electrodes.

stainless steel, inconel, molybdenum, K-monel, titanium, and nickel seem to be comparable and were the best materials. Copper, tantalum, and aluminum were intermediate. Silver showed the most severe spark damage. Carbon appeared to resist spark damage well, but would not remain baked out. Heard and Chupp claim that after baking out carbon electrodes and turning the voltage off for even a few minutes, the whole bake-in process had to start over again. The spark dust of K-monel and nickel was found to be magnetic. That from stainless steel and the other materials tested was not.

Smith & Grunder, Electrical Design of Electrostatic Deflectors for Sector-Focused Cyclotrons — UCRL-10654 (1963) — p. 8

Editorial note, tabletop extrapolation: 316 stainless is the economical best-tier candidate for the next machine's deflector electrode (cheap, machinable, tested) - validate under the intended field, finish, gap and stored energy; copper and aluminum ranked intermediate in this test, which argues against them for HV surfaces where a best-tier metal is just as easy to use.

There seemed to be a critical magnetic field for each material beyond which the spark damage was severe and below which the spark damage was negligible. The critical fields ranged from 4 to 15 kG.

Smith & Grunder, Electrical Design of Electrostatic Deflectors for Sector-Focused Cyclotrons — UCRL-10654 (1963) — p. 7

Editorial note, tabletop extrapolation: The reference machine's ~6 kG is above the 4 kG end of the tested range, so no advantage can be assumed without knowing the chosen electrode material's own threshold. Conditioning at reduced magnet current is a hypothesis worth testing - it cannot prevent severe damage from later sparks at full field if the material's threshold sits below the operating point, so validate at full field before trusting it.

when a 0.0125-uF capacitor was added across the gap, the electrodes baked-in to 60 kV, a six-fold increase. Adding a 0.5-uF capacitor across the gap reduced the breakdown voltage to 5 kV.

Smith & Grunder, Electrical Design of Electrostatic Deflectors for Sector-Focused Cyclotrons — UCRL-10654 (1963) — p. 8

Editorial note, tabletop extrapolation: For the deflector supply, the transferable idea is that conditioning behavior depends on the discharge circuit, not just the gap: compute the total fault energy (all capacitance plus supply feed-through), current-limit and interrupt faults quickly, and establish any deliberate conditioning-energy setting by controlled test - not by defeating arc extinction.

all of them baked in in a similar fashion except 316 stainless steel, which required about ten times as many sparks to reach the ultimate breakdown voltage. It takes about 30 sparks per cm2 to bake in high-voltage-electrode surfaces. Since it takes about a second for the vacuum to recover following a spark, the bake-in time of an electrode is about 30 sec/cm2.

Smith & Grunder, Electrical Design of Electrostatic Deflectors for Sector-Focused Cyclotrons — UCRL-10654 (1963) — p. 13

Editorial note, tabletop extrapolation: Applying the source's scaling to a palm-sized ~100 cm^2 electrode gives about 50 minutes of spark time - or roughly 8.3 hours for 316 stainless - excluding setup, failed ramps and downtime. Write conditioning into the next machine's ops checklist as a scheduled activity, not a nuisance.

the high-voltage electrode should have the minimum possible surface area. This minimizes the amount of sparking required to bake out the cathode spots and reduces the amount of electrode contamination.

Smith & Grunder, Electrical Design of Electrostatic Deflectors for Sector-Focused Cyclotrons — UCRL-10654 (1963) — p. 16

Editorial note, tabletop extrapolation: Measure or track the next machine's actual beam envelope at extraction radius - vertical oscillations, alignment and median-plane shift included - set the field window from that worst case plus explicit margin, and keep the HV bar as small and short as the trajectory allows; the 88-inch's 2x is their outcome, not a sizing law.

The minimum radius of curvature of the high-voltage electrode should be large enough to prevent appreciable field-gradient magnification. In practice, the minimum radius should be no less than about half a gap.

Smith & Grunder, Electrical Design of Electrostatic Deflectors for Sector-Focused Cyclotrons — UCRL-10654 (1963) — p. 17

Editorial note, tabletop extrapolation: Direct machining rule - for a next machine's 3-mm deflector gap, radius every HV edge to at least 1.5 mm and polish.

At the smaller gaps the electrode vibrated like a tuning fork in a tuning-fork oscillator. ... The forces driving the electrode were electrostatic; the device that provided the pulsating force was the dark current. ... Simplifying this circuit by the techniques of network analysis the system reduces to that of a Colpitts oscillator. ... The period is 50 msec corresponding to a vibrational frequency of 20 cps. ... Curve 1 was taken before insulators were installed and electromechanical oscillation occurred, resulting in VE = 1.23 x 10^4 (kV)^2/cm; curve 2 was obtained with insulator supports which prevented electromechanical oscillation, crowbar was set at 0.4 A, resulting in VE = 1.47 x 10^4 (kV)^2/cm

Smith & Grunder, Electrical Design of Electrostatic Deflectors for Sector-Focused Cyclotrons — UCRL-10654 (1963) — p. 17

Editorial note, tabletop extrapolation: Very much in reach of amateur trouble - a small cantilevered electrode has low mass and compliance. Support a next machine's deflector bar on insulators at both ends and check the deflector voltage on a scope for slow oscillation buildup.

With the tungsten anodes, the VE number increased to 2.25 X 10^4 (kV)^2/cm, an increase of 17% in VE number. In addition, we found that the tungsten anodes resisted spark damage better.

Smith & Grunder, Electrical Design of Electrostatic Deflectors for Sector-Focused Cyclotrons — UCRL-10654 (1963) — p. 24

Editorial note, tabletop extrapolation: A cheap, historically demonstrated upgrade candidate: line the grounded surfaces opposite the next machine's HV bar with thin tungsten sheet, edges overlapped so only tungsten is exposed - then verify in the actual geometry, since breakdown gains depend on geometry, finish, stored energy and conditioning; molybdenum is a plausible substitute only on its best-tier spark-damage ranking (dg-744), not on this VE test.

we could compensate for deflector capacitance; at lower capacitance we could crowbar at higher spark currents, and vice versa.

Smith & Grunder, Electrical Design of Electrostatic Deflectors for Sector-Focused Cyclotrons — UCRL-10654 (1963) — p. 25

Editorial note, tabletop extrapolation: Cable and feedthrough capacitance in a tabletop deflector still stores 0.5*C*V^2 right at the gap, where a supply-side crowbar cannot intercept it - so it is a design input, not a non-issue: compute the local stored energy at maximum voltage and add local series impedance or other discharge-energy limiting, then set the crowbar point for the configuration as the source did.

A 500-µA beam of 32-MeV deuterons did not destroy the carbon septum. It did thoroughly contaminate the high-voltage electrode and insulators though. ... unless a solution appears to the carbon contamination problem, metal septums will be required for the high-energy beams.

Smith & Grunder, Electrical Design of Electrostatic Deflectors for Sector-Focused Cyclotrons — UCRL-10654 (1963) — p. PDF p. 28 (printed -24-)

Editorial note, tabletop extrapolation: A next machine's beam power is watts, not kilowatts, so a carbon septum's activation advantage may yet win at sub-MeV - but the mechanism is temperature-driven and thin-foil hot spots concentrate it, so default to a tungsten or molybdenum septum and revisit carbon only with septum-temperature estimates in hand.

Hydrogen is let into the vacuum tank until the pressure becomes 200 to 300 u. ... A discharge current of about 100 mA is maintained for about an hour.

Smith & Grunder, Electrical Design of Electrostatic Deflectors for Sector-Focused Cyclotrons — UCRL-10654 (1963) — p. 32

Editorial note, tabletop extrapolation: The reference machine and a next machine use oil diffusion pumping, so the dirty-system dark-current regime is the thing to MEASURE, not assume. The hydrogen ion-scrub is a historical conditioning procedure to adapt, not a weekend recipe: it needs an isolated, current-limited supply (a variac is not isolation and 480 V is lethal), controlled H2 admission with pressure regulation, a safe purge/exhaust path, and interlocks - reviewed against the actual apparatus before first use.

a deflector is limited by sparking phenomena and not from an extraneous cause can be tested simply by a log-log plot of the voltage versus gap to see that it follows a VE line.

Smith & Grunder, Electrical Design of Electrostatic Deflectors for Sector-Focused Cyclotrons — UCRL-10654 (1963) — p. 27

Editorial note, tabletop extrapolation: Free instrumentation for a next machine: run the V(d) test during commissioning with several repeated gap settings (conditioning history scatters single points). The report's practice of insulating each ground electrode and metering intercepted current as an alignment monitor is worth copying too - reported practice, scan re-read queued for the exact passage.

it stores only 2-1/2 joules and, at most, this is distributed among 1200 diodes. ... There is so little energy in a spark from this rectifier that it will not puncture even a piece of 5-mil aluminum foil.

Smith, Deflector Power Supply for Sector-Focused Cyclotrons — UCRL-10655 (1963) — p. 28

Editorial note, tabletop extrapolation: The governing philosophy for a next machine's deflector supply: limit the energy delivered per spark rather than trying to prevent sparks - low stored energy is an equipment-survival property, and a sub-joule store at 50-100 kV is achievable. It is not a personnel-safety property: such a supply remains dangerous to people, and in human contact the supply's follow-on current adds to the stored energy. Personnel protection stays with enclosure, interlocks, grounding and discharge practice (dg-522, dg-654).

Each circuit board consists of 100 Unitrode, Type UT71, silicon diodes connected in series. Each diode is shunted by a 250-pF, 500-V, ceramic capacitor to divide the inverse voltages equally.

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

Editorial note, tabletop extrapolation: Today this is a standard multiplier stack; keep the two features that matter - per-diode grading capacitors (transient sharing; add static resistors or integrated HV rectifiers for dc sharing) and high drive frequency, which buys regulation into a varying load. What frequency does NOT buy is low stored energy: 0.5*C*V^2 is set by the capacitors, so compute the stack's accessible spark energy and add local limiting before pointing it at a sparking deflector.

typically, it takes a few microseconds ... The recycling time is 1 sec. ... the power supply can be turned off before a spark becomes visible.

Smith, Deflector Power Supply for Sector-Focused Cyclotrons — UCRL-10655 (1963) — p. PDF 28 carries the quoted sentence; the two performance figures are on PDF 19

Editorial note, tabletop extrapolation: The feature to replicate in a modern build: fast drive-kill on spark detection with an operator-adjustable threshold, used deliberately during bake-in (UCRL-10654's practice). A solid-state inverter's gate shutdown gives the fast drive-kill - but killing drive is not a crowbar: energy already stored in the output stack and cable still feeds the spark (dg-285), so pair gate-kill with a dump path or series resistance rated for that stored energy.

The spacing between boards is about 2 in. and provides a nominal maximum design gradient of 10 kV per in.

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

Editorial note, tabletop extrapolation: For an amateur HV column, run the real layout numbers: air clearance and surface creepage separately, field stress at conductor curvatures, contamination and altitude derating, and a controlled HV test - matching the historical 10 kV/in exactly (6 in at 60 kV) leaves zero headroom by construction.

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

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

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

for a stability of 0.01% the temperature difference between resistors must be within about 3 C.

Smith, Deflector Power Supply for Sector-Focused Cyclotrons — UCRL-10655 (1963) — p. 21

Editorial note, tabletop extrapolation: Deflector voltage stability maps directly (first-order) to extracted-beam steering stability, so buy or build the divider first - and set the actual tolerance from a beam-clearance budget at the septum (beam size, orbit spacing, drift) rather than assuming either 0.01% is needed or 1% is fine.

We can attenuate this ripple by using an RC filter consisting of a series resistance connecting the Cockcroft-Walton to the deflector, and a capacitance which is the deflector capacitance.

Smith, Deflector Power Supply for Sector-Focused Cyclotrons — UCRL-10655 (1963) — p. 30

Editorial note, tabletop extrapolation: Pick R from the measured deflector capacitance, ripple frequency, allowable voltage drop and the discharge-energy model - and note what the resistor cannot do: the 0.5*C*V^2 already ON the deflector side discharges into the arc regardless. Size the part honestly (dc dissipation I^2*R, pulse rating, voltage grading) - at the report's own 5 mA, 100 kOhm burns 2.5 kW only if run continuously at that current, so check the real duty before calling any resistor cheap.

the deflector oscillators are located close to the magnet yoke of the cyclotron in a field of about 150 G, magnetic shields had to be put over the 4CW2000 oscillator tube and the 3D22.

Smith, Deflector Power Supply for Sector-Focused Cyclotrons — UCRL-10655 (1963) — p. 19

Editorial note, tabletop extrapolation: Map the field where equipment will sit and shield or relocate per COMPONENT tolerance: transformers, inductors, Hall sensors, relays and fans all care about DC field to different degrees, PMTs need residual fields far below 150 G (high-permeability or multilayer shields), and a mild-steel can's attenuation depends on geometry, seams and saturation - the cited caps are proof the approach works, not a universal thickness spec.

the increase in radius of the burst of ions per rf cycle is approximately 0.1 inches and the deflector bars are spaced one inch apart, the pulse must occur within +/- 5 rf cycles.

Kerns et al., High Voltage Pulser for 184-inch Cyclotron Electric Deflector — UCRL-95 (1948) — p. 8

Editorial note, tabletop extrapolation: Synchrocyclotron-specific hardware (a CW deflector needs no pulse), but the requirements chain - turn separation sets element aperture sets timing budget - is the template for sizing ANY extraction element, including a next machine's septum entrance.

The electric field between the deflector bars necessary to shift the particle center of rotation enough to allow it to pass through the magnetic channel is about 75,000 volts per centimeter.

Kerns et al., High Voltage Pulser for 184-inch Cyclotron Electric Deflector — UCRL-95 (1948) — p. 8

Editorial note, tabletop extrapolation: Scale perspective without a false law: the required field follows from the integrated kick theta ~ q*INT(E dl)/(p*v) - beam rigidity, electrode length, needed displacement and septum clearance all enter, which is why UCRL-10654 quotes 150-200 kV/cm at 50 MeV while this machine used 75 kV/cm at 200 MeV. Compute a sub-MeV machine's requirement from its own kick integral; it will come out modest, but earn the number.

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

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

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

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

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

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

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

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

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

the capacitor must withstand a complete reversal of charge in 0.3 us 100 times a second without failure.

Kerns et al., High Voltage Pulser for 184-inch Cyclotron Electric Deflector — UCRL-95 (1948) — p. 14

Editorial note, tabletop extrapolation: Two lessons that outlive the hardware: (1) reversal fraction and reversal time belong in a pulse capacitor's complete duty spec - alongside peak/RMS current, dV/dt, temperature and derating, all of which shorten life too; (2) ESL budgets, not just C and V, set rise time. The paralleled-coax alternative is a distributed pulse-forming line, not a lumped capacitor - engineer it as one (impedance, delay, termination, voltage rating, stored energy).

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

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

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

the effective rise time is about 0.15 us, 50 percent more than that desired. ... it is felt that increasing the peak voltage compensates for the longer rise time of the pulse.

Kerns et al., High Voltage Pulser for 184-inch Cyclotron Electric Deflector — UCRL-95 (1948) — p. 16

Editorial note, tabletop extrapolation: A commissioning lesson in trade-offs: extraction elements have one strong knob (voltage/field) that can sometimes buy back deficiencies in the others - design in voltage headroom, but check what the slower edge costs in turn selectivity and what the higher voltage costs in breakdown and switch margin before leaning on it.

The extraction requirements, simply stated, are: (a) The precession must be arrested (b) Sufficient gain per turn must be obtained (c) Losses owing to axial blowup must be minimized.

Stubbins, Extraction of Synchrocyclotron Beams Near the Maximum Energy — UCRL-3476 (1956) — p. 7

Editorial note, tabletop extrapolation: The cleanest checklist in this collection for what a next machine's precessional-assist extraction must accomplish - phase-lock the precession to place orbit maxima at the septum azimuth, then count gain-per-turn against septum thickness. Machine-class independent.

The synchronous radius suitable for deflection in the cyclotron is just inside the radius at which normal beam destruction occurs.

Stubbins, Extraction of Synchrocyclotron Beams Near the Maximum Energy — UCRL-3476 (1956) — p. 7

Editorial note, tabletop extrapolation: The siting logic transfers, the threshold does not: put a next machine's septum or regenerator equivalent just inside where its OWN analysis says the beam dies - measured field map, tune calculation and tracking, not a universal n = 0.2 wall (linear radial stability formally extends to n = 1, and real loss radii are set by resonances, apertures and field errors). And every mm inward is extracted energy given away.

The determination of the required perturbation for extracting the beam of a synchrocyclotron is made in seven steps.

Stubbins, Extraction of Synchrocyclotron Beams Near the Maximum Energy — UCRL-3476 (1956) — p. 6

Editorial note, tabletop extrapolation: The workflow (measured field -> amplitude-dependent tunes -> impulse-matrix tracking -> element strength) is exactly the CYCLOPS-lite pipeline planned for a next machine; the peeler-regenerator field shapes themselves are synchrocyclotron machinery and need not transfer. Treat the sine-ratio gain coefficient as branch- and model-specific once the re-read pins its definitions - it is singular near its denominator zeros, so no monotone smaller-interval-more-gain rule survives unqualified.

When B0 is in gauss, B-theta is in gauss-radians.

Stubbins, Extraction of Synchrocyclotron Beams Near the Maximum Energy — UCRL-3476 (1956) — p. 17

Editorial note, tabletop extrapolation: The gauss-radian bookkeeping is a handy unit for ANY azimuthally localized field bump (harmonic coils, shims, channel compensation) on a next machine. What fraction of B0 an effective bump needs is geometry-dependent - the same integrated strength over 20 or 60 degrees is a 3x different local field - so compute the integral for the actual bump, without a stock percent anchor.

For a 1-in. axial amplitude this disturbance is about twice as strong as that occurring in the radial motion from the same field perturbation.

Stubbins, Extraction of Synchrocyclotron Beams Near the Maximum Energy — UCRL-3476 (1956) — p. 18

Editorial note, tabletop extrapolation: The transferable warning: any radial-field-gradient extraction element has an off-midplane Br ~ z*dBz/dr whose vertical effect can focus or defocus depending on gradient sign and trajectory - include the deflector fringe and any field bump in the next machine's 3-D tracking rather than assuming the sign or which particles go first.

The computation enables one to modify the regenerator field to account for the channel effect, and, thus, the maximum effort of corrective shimming for the channel is not required.

Stubbins, Extraction of Synchrocyclotron Beams Near the Maximum Energy — UCRL-3476 (1956) — p. 20

Editorial note, tabletop extrapolation: Direct analog for a next machine: the septum and exit-channel iron (or deflector entrance fringe) perturbs the last internal turns - model that perturbation in the tracker and consider compensating upstream (harmonic coil, shim, or the bump program) as ONE option alongside local shielding or shimming of the channel itself; co-optimize rather than nulling one element in isolation.

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

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

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

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

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

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

The possibility of changing the electrical frequency and gradient to match operating conditions eliminates difficulties arising in magnetic extraction systems for variable-energy machines.

Stubbins, Radiofrequency System for Extracting Particles from a Cyclotron — UCRL-8578 (1958) — p. 4

Editorial note, tabletop extrapolation: Supports the next machine's plan-of-record (electrostatic deflector, no fixed magnetic channel) in spirit: an educational machine running several field/energy points wants extraction strength on a knob. A plain electrostatic deflector carries the voltage knob - not the source system's frequency knob - and that adjustability is exactly what a fixed B-bump lacks.

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.

because of the precession of orbits all particles are ultimately perturbed to larger radial oscillation amplitudes.

Stubbins, Radiofrequency System for Extracting Particles from a Cyclotron — UCRL-8578 (1958) — p. 9

Editorial note, tabletop extrapolation: Sets expectations for any resonant/precessional scheme on a next machine: the growth is episodic over many turns, so judge schemes in the tracker by turns-to-extraction and septum-hit fraction rather than single-pass kick size - the detailed evolution is deterministic and scheme-dependent, so track your own.

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

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

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

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

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

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

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

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

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

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

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

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

the bias adjustment is made with reference to the actual critical firing voltage.

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

Editorial note, tabletop extrapolation: A self-calibration idiom worth copying into any comparator/discriminator in the DAQ: trim to the observed threshold at session start (their multivibrator = today's comparator with drifting offset). That removes the threshold error present AT calibration - within-session drift, and aging that changes delay or hysteresis rather than threshold, still need periodic re-trim or monitoring.

the automatic pulse-height circuit had to work on a peak-reading principle.

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

Editorial note, tabletop extrapolation: Directly applicable to pulse chains fed by beam pickups or PMTs at low rep rate: stabilize on detected peak height at the discriminator input. This compensates multiplicative gain drift in the stages inside the loop and reduces amplitude-induced time walk - pulse-shape changes, baseline shifts and discriminator drift are outside it, so keep a timing calibration (or constant-fraction discrimination) as well.

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

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

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

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

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

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

A very effective adjustable beam deflector has been developed; under the best conditions, 38% of a 1000 ua internal beam has been deflected.

Howard (ed.), Electromagnetic Research Division Quarterly, period ending 31 December 1951 — ORNL-1269 (1952) — p. 40

Editorial note, tabletop extrapolation: Sets expectations for any future extraction gate: design the septum/deflector with in-vacuum adjustability - the quoted 'very effective' unit was fully adjustable and even so extracted 38% at BEST. Tens of percent is the documented ballpark for classical deflectors (dg-496, dg-595); define success for your machine before the attempt, and account for where the undeflected majority goes (dg-260).

The extreme radioactivity induced in type 304 stainless steel makes its use undesirable, the use of an aluminum alloy is now being investigated.

Howard (ed.), Electromagnetic Research Division Semiannual, period ending 20 March 1953 — ORNL-1531 (1953) — p. 18

Editorial note, tabletop extrapolation: At sub-MeV energies on ordinary structural metals activation is small where it occurs at all - thresholdless capture and deuteron operation are the exceptions - and the selection logic transfers whole: thermal adequacy is not the whole selection. Prefer aluminum or graphite for probes, septa and slits anywhere protons above a few MeV are contemplated, and let the licensing story inherit the same reasoning.

Cited in: Shielding a Small Cyclotron

in order to produce a suitable object for the analyzing magnet, we introduce a second magnet whose sole function is to focus as much of the beam as possible on a precision slit.

Bromley & Bruner, The Design of a Focusing and Analyzing System for the 27-inch Cyclotron Beam — NYO-3823 (1954) — p. 4

Editorial note, tabletop extrapolation: DIRECT for any ANALYZED external line on a next machine - the canonical two-stage architecture: a condenser focuses as much beam as possible onto a precision slit, and that illuminated slit becomes the analyzer's cleanly defined object. Lines that only transport or irradiate skip the apparatus; the slit's shielding is the companion rule (dg-966).

introduction of the field bump has caused a discontinuous jump in the location of the central stable orbit in the phase diagram

Blosser & Gordon, Computational Study of a Resonant Extraction System for a 3-Sector Cyclotron — MSUCP-9 (1961) — p. 24

Editorial note, tabletop extrapolation: The conceptual mechanism to have in hand before a regenerative extraction attempt on a next machine: it needs nu_r to pass unity with a controlled first harmonic, both of which a FEMM-fed tracker can compute for a candidate pole design. It is one extraction method - electrostatic deflection, stripping, or simply large natural turn separation do not require crossing nu_r = 1. [Note revised 2026-08-23: earlier wording read as if this were prerequisite to any extraction.]

stretching and rotation are fine but not twisting, filamentation, etc.

Blosser & Gordon, Computational Study of a Resonant Extraction System for a 3-Sector Cyclotron — MSUCP-9 (1961) — p. 24

Editorial note, tabletop extrapolation: The right figure of merit for any next machine's beamline or extraction simulation - track a grid of particles and judge the deformed shape, not just the centroid. Five to two dozen particles sufficed in 1961 for the smooth cases; check convergence by refining the grid where the map is nonlinear, since a sparse grid can miss filamentation entirely.

The essential design requirement of such a system is a turn program which avoids regions of large flow rate gradient in the static phase space.

Blosser & Gordon, Computational Study of a Resonant Extraction System for a 3-Sector Cyclotron — MSUCP-9 (1961) — p. 45

Editorial note, tabletop extrapolation: The doctrine transfers to schemes where a static phase-plot analysis applies: superimpose the accelerated beam path on static phase plots (cheap tracker post-processing), identify the large-flow-gradient regions - especially near unstable fixed points - and compare candidate turn programs by accelerated tracking. Crossing faster reduces exposure to a bad region but can excite other resonances non-adiabatically, so test, don't assume.

volts per turn substantially lower than the designed 280 kev/turn would result in sharp reduction of both extraction efficiency and optical quality.

Blosser & Gordon, Computational Study of a Resonant Extraction System for a 3-Sector Cyclotron — MSUCP-9 (1961) — p. 45

Editorial note, tabletop extrapolation: The quantitative ancestor of 'dee volts buy extraction': the reference machine's uncalibrated ~1.3 kV dee is one reason it is internal-beam-only, and a next machine's 5-13 kV target is what would make an extraction scheme thinkable - thinkable, not feasible, until the turn separation (delta_r ~ r*delta_E/2E), phase width, septum clearance, tune and bump design are actually computed.

beams entering the extraction region approximately centered on the equilibrium orbit behave as well or better than beams entering with substantial displacement.

Blosser & Gordon, Computational Study of a Resonant Extraction System for a 3-Sector Cyclotron — MSUCP-9 (1961) — p. 45

Editorial note, tabletop extrapolation: The project-level lesson for a next machine — run the cheap simulation before committing hardware to any orbit-dynamics intuition, including intuitions published by people as good as Blosser and Gordon.

This septum will use only 40 kW of power, a factor of four smaller than if the original thickness were kept to the end

Rainwater et al., The Columbia University Nevis Synchrocyclotron Major Modification — NEVIS-189 / R-774 / CU-295 (1971) — p. 13

Editorial note, tabletop extrapolation: A current-septum channel is beyond tabletop needs, but the geometric principle - septum thickness need only be minimal on the first intercepting turn - applies to any conductive deflector septum on a next machine, subject to the beam-clearance check downstream. (Extraction FOILS are a different problem: stripping, scattering, heating and lifetime set foil thickness, not turn separation.)

each wire will have its own thermocouple to sense any rise in the cooling water temperature which will shut off the current in the channel

Rainwater et al., The Columbia University Nevis Synchrocyclotron Major Modification — NEVIS-189 / R-774 / CU-295 (1971) — p. 13

Editorial note, tabletop extrapolation: Per-element thermal interlocks scale down perfectly - the RF amplifier dummy load, water-cooled dee stubs, any powered septum - and match the fail-safe doctrine (dg-1110). A coolant-temperature sensor only responds after heat reaches the water: pair it with a flow interlock (dg-202's return-orifice practice) so loss of flow trips the supply without waiting for temperature to say so.

with the coils energized to 3500 amperes, revealed a negligible deflection of the inner walls (about 0.002 inch) which eliminated the possibility of future collapse

Cyclotron Staff, Report of Cyclotron Operation 1 July – 31 December 1969 — NRL Memorandum Report 2103, Naval Research Laboratory (1970) — p. 27

Editorial note, tabletop extrapolation: Every conductor near the pole gap feels J x B: thin walls, septa and coil leads need structural qualification, and a displacement measurement at above-operating excitation is one ingredient of it, not the whole - add the load calculation, yield and buckling margins, fatigue for cycled excitation, and fault-current loads. Motors, encoders and anything with a magnetic circuit belong outside the fringe field regardless.

Machining work will begin after the oscillator is operating and an internal beam produced.

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (1951) — p. 116

Editorial note, tabletop extrapolation: The commissioning-order lesson as an explicit 1951 schedule decision: internal beam first, extraction hardware behind it. A sensible default for a next machine - the probe and its lock as first-beam hardware, extraction machining held until the internal beam teaches you the real orbit - a default, not a law.

a minimum of 80 kv dee to ground r.f. potential is necessary in order that the ions do not enter the region of decelerating phase at any time within the dees.

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (1951) — p. 116

Editorial note, tabletop extrapolation: Two transferable ideas for any future extraction study: run the phase-floor analysis BEFORE cutting metal (the computation this collection's deflector cluster expects), and consider using the machine's existing RF field for deflection with DC as supplement - after resolving the geometry from the re-read, since a deflection field needs a potential difference and the as-summarized grounded-plate-vs-grounded-dee-edge description cannot be right as written.

Der Teilchenstrahl braucht dabei nicht einmal ausgelenkt zu werden [tr.: the particle beam does not even need to be extracted]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 27

Editorial note, tabletop extrapolation: A radial probe drive with a Faraday cup is the first detector to build on any small machine, and extraction is properly a separate later project - which, when undertaken, teaches its own lessons (septum design, transport, external diagnostics; the COLUMBUS Wien-filter plan, dg-1512, is that next chapter). Wait until internal beam is reproducible across days.

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.

A copper target will be placed in the chamber, which will as a result of the beam be impregnated with deuterons. More ions from the beam will collide with the trapped deuterons, undergoing one of two reactions, d(d,n)3He or d(d,p)3H. Since neutrons are the desirable result of the reaction, no extraction system will be required. ... the outgoing neutrons will be produced with 2.8 MeV. The electrically neutral neutrons will pass through the chamber walls and can then be used for inelastic scattering measurements.

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 48

Editorial note, tabletop extrapolation: A beam-loaded (drive-in) copper target avoids separately fabricating a deuterated target and removes extraction from the critical path. Physics notes on the thesis's numbers: D(d,n)3He neutrons at ~150 keV bombarding energy are angle-dependent, roughly 2.1-3.0 MeV in the lab - 2.8 MeV is one point on that curve, not the spectrum - and the thesis does not analyze dose or shielding beyond its concrete room, so the radiological planning is entirely on the builder.

An extractor system was designed with a negatively charged deflection plate, but the cyclotron also had a Faraday collector that was a small metal plate that could be inserted into the beam. ... The cyclotron was not successfully tested by the publication of Ref [20]

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

Editorial note, tabletop extrapolation: The design logic worth keeping: pair any extraction ambition with an internal probe so beam existence is confirmed independently of extraction working. 'Designed' documents intent - the extractor was never demonstrated (the machine never ran), so this is a proposed geometry, not a precedent.

The aim of this project is to deflect the ion beam and guide it through a Wien Filter to measure the speed and energy of the ions.

Wolf & Prechtl, COLUMBUS — A Small Cyclotron for School and Teaching Purposes — THPO001, Proceedings of Cyclotrons2022 (2022) — p. 3

Editorial note, tabletop extrapolation: A Wien filter is a realistic first external beamline element for a low-energy machine: it measures VELOCITY directly and yields energy only once the species is known (or paired with a separate analyzer) - which is exactly why it also cross-checks species assignments. It needs crossed electric AND magnetic fields; at keV energies both are modest, but 'electrostatic-only' it is not.

A thin, curved, grounded sheet formed the septum and separates the main accelerating volume and the deflection channel. A slightly greater curved high voltage (HV) electrode was concentrically arranged to complete the deflection channel with and average 0.31 inch gap spacing. The deflector tangentially intercepted the spiraling cyclotron beam at a radius of 4.0 inches and transported the beam to a radius of 4.5 inches in 43° of azimuth. The deflection channel had a nominal radius of curvature of 7 inches.

Koeth, Ponter, Hoffman, Schneider & Krutzler, Rutgers 12-Inch Cyclotron Electrostatic Deflector (2010, rev. 2011) — p. 1

Editorial note, tabletop extrapolation: The most fully dimensioned extraction geometry in the amateur literature at this scale — a 12-inch machine intercepting at 4.0 inches. As orientation: the channel's radius of curvature is 1.75× the orbit radius, the gap ~7.5% of the orbit radius, and the channel spans 43° to gain 0.5 inch (ratios computed here). Applying those ratios to another machine is geometric illustration only — rigidity, turn separation, septum thickness and fringe fields all enter — so recompute the field and voltage (dg-1660) and verify by tracking before cutting metal.

Since this was much larger than the entering ion's radius of curvature of 4 inches, ions that entered the un-energized channel would impinge on the septum and quickly be lost, certainly unable to traverse the length of the channel. High voltage (HV) applied to the electrode generates a deflecting transverse electric field. Only an appropriate negative electric field will partially negate the magnetic field's bending force permitting the successful transmission of ions. A greater field will cause the ions to terminate on the deflector and be lost, and a lesser field will cause the ions to terminate on the septum, only ions of the correct q/m ratio and velocity will be permitted completely through the channel to be successfully detected.

Koeth, Ponter, Hoffman, Schneider & Krutzler, Rutgers 12-Inch Cyclotron Electrostatic Deflector (2010, rev. 2011) — p. 1

Editorial note, tabletop extrapolation: A useful commissioning property: with the channel un-energized the direct orbit ends on the septum, so ramping HV from zero and watching a signal grow is strong evidence you are steering real beam. Suppressed direct transmission is not a null instrument, though — scattered ions, secondaries, light leakage and pickup can all reach an exit detector, so take an HV-off background and shield the optics before crediting counts to extracted beam. The same geometry is what lets the channel double as a velocity/q-over-m filter (dg-1673, dg-1675).

This determines the necessary electric field; we must multiply the electric field by the HV electrode-septum gap spacing to determine the required applied potential. Using the values of ρo and ρ1 listed above, we find that for protons in a 1.0 Telsa magnetic field, a transverse electric field of 4.2 MV/m is required. The nominal electrode-septum spacing is 0.31 inches, thereby setting the electrode voltage at 33 kV.

Koeth, Ponter, Hoffman, Schneider & Krutzler, Rutgers 12-Inch Cyclotron Electrostatic Deflector (2010, rev. 2011) — p. 2

Editorial note, tabletop extrapolation: The sizing equation a tabletop extraction design starts from, checked against the printed numbers: with rho_0 = 0.1016 m, rho_1 = 0.1778 m the magnitude comes to 4.17 MV/m, and times 0.31 inch gives 32.8 kV — agreeing with the printed 33 kV (computed). Scaling: with field scaled by b and ALL lengths by s, the required field goes as b²s and the voltage as b²s² — so half the field at two-thirds scale needs ~1/6 the field and ~1/9 the voltage, which is what makes a modest HV supply workable on a smaller machine. ("Telsa" is the source's typo for Tesla.)

The deflection channel was constructed as a modular assembly that could easily be removed from and replaced within the cyclotron chamber, as shown in Figure 2. Two aluminum plates separated by stainless steel posts formed the skeletal structure. The septum's curve was machined as a stepped shelf along the inside edge of the top and bottom structural plates. A thin (0.005 inch thick) stainless steel strip was seated against the step forming the septum. Thin strips of aluminum matching the septum's curvature were bolted onto the shelf clamping the septum in place and holding its curvature – see Figure 3.

Koeth, Ponter, Hoffman, Schneider & Krutzler, Rutgers 12-Inch Cyclotron Electrostatic Deflector (2010, rev. 2011) — p. 3

Editorial note, tabletop extrapolation: A septum-forming pattern that avoids specialty tooling: machine the curve as a stepped shelf in the structural plates and let 0.005-inch shim stock take the shape when clamped by matching strips. The modularity choice paid off operationally in this program — the deflector came out repeatedly during the arcing investigation — so if inspection cycles are anticipated, build it as a drop-in cartridge; how easy the machining is depends on the shop doing it.

The high voltage electrode was machined 3/8 inch thick from 7075 aluminum; each corner was rounded with a radius also of 3/8 inch. The curvature of 3/8-inch was based on the anticipated voltage, including a significant margin of error. The electric field resulting from a curved metallic surface follows [displayed equation Emax = 0.9V / ( r ln( (r+a)/r ) )] Where r is the radius of the curved surface, and a is the distance of the closest approach, limiting Emax to a conservative 170 kV/inch. In addition, the electrode was highly polished.

Koeth, Ponter, Hoffman, Schneider & Krutzler, Rutgers 12-Inch Cyclotron Electrostatic Deflector (2010, rev. 2011) — p. 3

Editorial note, tabletop extrapolation: A reusable first-pass electrode-sizing estimate: pick the corner radius so the curved-surface Emax stays under the working limit you are willing to accept. Worked with this memo's own parameters from its earlier sections (gap a = 0.31 in, V = 33 kV): r = 0.375 in gives Emax = 131 kV/inch — computed here, comfortably under the authors' stated 170 kV/inch, which is their conservative working limit for polished aluminum in their vacuum, not a universal breakdown value. Satisfying the estimate does not certify holdoff: the full field map, insulator flashover, surface condition and conditioning still decide.

It was supported from the back by stem of two T-shaped Teflon insulators. Bosses were machined in the tips of each arm of the T-insulators, the bosses were seated in detents in top and bottom plates. The T-insulator stems were deeply counter-bored and finished with a blank through hole. Two tapped holes on the rear of the HV electrode, and Nylon screws secured the electrode to the base of the T-insulators, which can be seen in place in Figues 3 and 4. Electrical connection was made to the HV electrode by directly seating a HV ceramic vacuum feed-through conductor into a third and final clearance hole in the back of the electrode, and is captured by a set screw.

Koeth, Ponter, Hoffman, Schneider & Krutzler, Rutgers 12-Inch Cyclotron Electrostatic Deflector (2010, rev. 2011) — p. 3

Editorial note, tabletop extrapolation: Three compact construction choices from a working HV-in-vacuum assembly, with their plausible rationales: the deeply counter-bored insulator stem (surface-path length — verify creepage on the actual geometry), Nylon fasteners in the high-field region (less grounded metal near the electrode), and the feedthrough conductor seated directly into the electrode (no in-vacuum HV wire to dress). None is a proven remedy on its own; qualify the PTFE, Nylon and feedthrough for voltage, temperature, charging and outgassing, and check the fields the real geometry makes.

After initial operation, internal arcing between the HV electrode and the grounded housing clearly indicated secondary electron emission. The evidence was in pitting, shown in Figure 4 on the internal surfaces of the top and bottom structural plates - the bulk of which occurred directly above and below the perimeter of the HV electrode. A general rule-of-thumb places the threshold for damage from arcing at 1 Joule. Locations of the closest approach, such as directly below the centerline did not show much pitting, exonerating field emission based brake-down. Further, damage was only noted on the top and bottom plates, not the deflector electrode, suggesting secondary electrons were emitted on the electrode, accelerated away from the HV electrode, tightly following the vertical magnetic field lines.

Koeth, Ponter, Hoffman, Schneider & Krutzler, Rutgers 12-Inch Cyclotron Electrostatic Deflector (2010, rev. 2011) — p. 3

Editorial note, tabletop extrapolation: A post-mortem method for any HV campaign: read the damage map. On this deflector, pitting sat above and below the electrode perimeter — displaced along the vertical field lines — while the closest-approach points and the electrode itself were clean, which the authors read as magnetically guided secondary electrons and against field emission. Treat such patterns as evidence to corroborate (trajectory modeling, polarity tests, conditioning behaviour), not as unique proof — field emission can light a discharge whose energy lands elsewhere. The 1 Joule damage threshold is the authors' quoted rule of thumb. (The source's figure reference appears to be to Figure 5, captioned "Pitting observed from arcing"; "brake-down" is the source's spelling.)

Several steps were taken to mitigate the arcing. First, the polished HV electrode was coated with Aerodag-G graphite lubricant to reduce the coefficient of secondary electron emission. Three thin coatings of Aerodag-G were applied from an aerosol dispenser using an alcohol based propellant. The coated electrode was then baked at 125° C for 1 hour in standard atmosphere. Care was taken in handling the electrode as not to scrape the coating. However, from the handling it did receive, the coating was found to be surprisingly robust. Secondly, a clearance slot parallel to the deflection electrode was machined into the top and bottom structural plates which, shown in Figure 6, was intended to further reduce the electric field between them.

Koeth, Ponter, Hoffman, Schneider & Krutzler, Rutgers 12-Inch Cyclotron Electrostatic Deflector (2010, rev. 2011) — p. 4

Editorial note, tabletop extrapolation: A cheap surface treatment with the full recipe as this program ran it: Aerodag-G colloidal graphite, three thin aerosol coats (alcohol-based propellant), one hour at 125°C in air — and they found the coating surprisingly robust in handling. Before copying: formulations change, so check the current product's SDS/TDS, outgassing and adhesion for your vacuum. Note the sequence — polish for field uniformity first, then coat for low secondary emission. The clearance slot machined above and below the electrode was INTENDED to reduce the field there (the source's own wording); verify such a slot with a field calculation.

Initially only a constant-voltage regulated 30 kV power supply was available. For safety, the supply required a current limiting series resistor of 75 MΩ in the event of a short or arc. Even though the supply was capable of providing 30 kV, the leakage current from corona reduced the maximum achievable deflector electrode voltage to 28 kV. Even so, 28 kV was sufficient to just bring the beam to the edge of the screen, as seen in Figure 10.

Koeth, Ponter, Hoffman, Schneider & Krutzler, Rutgers 12-Inch Cyclotron Electrostatic Deflector (2010, rev. 2011) — p. 4

Editorial note, tabletop extrapolation: A planning number for tabletop extraction: budget the series resistor's IR drop, because corona current through a 75 megaohm resistor cost these authors ~2 kV out of 30 kV, about 7%. The current-limiting resistor is reported as the authors' own required practice for their supply; the lesson to carry over is that the supply must be specified above the design electrode voltage, not at it.

Subsequently, a surplus Bertan 205A-50N 50 kV power supply was ordered and installed. This supply was also only a constant voltage supply requiring a 150 MΩ current limiting resistor. The resistor was housed in an acrylic tube, capped at both ends, which was then externally covered with a grounded copper mesh. The resistor housing was installed in a relatively inaccessible location at the top and backside of the magnet yoke.

Koeth, Ponter, Hoffman, Schneider & Krutzler, Rutgers 12-Inch Cyclotron Electrostatic Deflector (2010, rev. 2011) — p. 5

Editorial note, tabletop extrapolation: This is the source's own construction practice for a stack of HV resistors on a small machine: an insulating tube for standoff plus an outer grounded screen so the assembly presents a defined, grounded surface rather than a floating one, and physical placement out of casual reach. Reported here as what they did, with their numbers.

The Mammoflex cable is rated for 60 kV and had a capacitance of 56 pF per foot. After installation of the new supply and cable, mysterious behavior was noticed and is still not fully explained. At sufficiently high voltages (~ 30kV) arcing inside the chamber occurred – both light and audible snapping were observed. Coincident with the internal arcing, external arcing was observed between the shield of the Mammoflex cable (of the 6 foot segment between the resistor and chamber) and chassis ground, such as the magnet frame. One such arc terminated on the upper magnet coil, causing the magnet power permanent damage, requiring costly repair. The stored energy in the 6 foot cable at 30 kV is about 0.2 Joules, not much lower than the rule-of-thumb damage threshold of 1 Joule. It is also known that the focusing influence of the magnetic field can enhance the damage of an electrical discharge.

Koeth, Ponter, Hoffman, Schneider & Krutzler, Rutgers 12-Inch Cyclotron Electrostatic Deflector (2010, rev. 2011) — p. 5

Editorial note, tabletop extrapolation: The most expensive lesson in the document, and it scales down unchanged: HV cable capacitance is a stored-energy reservoir whose shield is not automatically at ground everywhere. Computing from the paper's own numbers, 56 pF/ft × 6 ft = 336 pF, and ½CV² at 30 kV is 0.15 J — the source's "about 0.2 J" at the same order (computed here). Neither 0.2 J nor the 1 J rule of thumb is a safety boundary; cable length is the variable a builder controls directly.

After consulting an experienced high voltage engineer, it was suggested that due to the rapid formation of the internal arc, the segment of HV cable between the resistor and chamber was effectively a Blumlein HV pulse generator [5], several steps were taken to suppress the arcing. First, the HV cable length was reduced to the bare minimum required, thereby minimizing the stored energy in the cable. To limit the discharge current, 68 Ω, 2 Watt carbon resistors were placed in series with the cable shield at the resistor box. However, streamers traveling greater than 1 inch in air were still observed bypassing the 68 Ω resistors. The resistors were subsequently tested and found to be undamaged and properly functioning. A 5 MΩ HV resistor was then next installed in series with the center conductor and the chamber just prior to the HV vacuum chamber bushing. This has been found to suppress the arcing. … Finally, to ensure machine safety, the HV coaxial cables have been routed clear of any sensitive electronics in the event of a reoccurrence.

Koeth, Ponter, Hoffman, Schneider & Krutzler, Rutgers 12-Inch Cyclotron Electrostatic Deflector (2010, rev. 2011) — p. 5

Editorial note, tabletop extrapolation: A rare documented failed-fix-then-working-fix sequence at exactly this scale: shorten the cable (less stored energy), try shield-side series resistance (bypassed — streamers jumped more than an inch of air around the 68 Ω resistors, which survived undamaged), then put 5 MΩ in the CENTER CONDUCTOR at the chamber bushing — which suppressed the arcing here, plausibly because that is where series resistance can actually limit the discharge current into the arc. Component values are this installation's; buy any such resistor for working voltage and impulse energy, and route HV cables away from electronics as they finally did.

Initial beam measurements were performed with the cyclotron operating at an RF frequency of 14.900 MHz at 400 watts input power and magnetic field of approximately 1 Tesla (the magnetic field is adjusted for maximum beam current on the original adjustable faraday collector). Once beam was established, the adjustable faraday collector was fully retracted, allowing the accelerated beam to encounter the entrance slit of the deflection channel. The deflector HV supply was slowly ramped while observing the phosphor screen. A clearly visible green spot appeared on the left most edge of the phosphor screen, and continued to move towards the right with increased HV until the maximum limit of the power supply was reached.

Koeth, Ponter, Hoffman, Schneider & Krutzler, Rutgers 12-Inch Cyclotron Electrostatic Deflector (2010, rev. 2011) — p. 5

Editorial note, tabletop extrapolation: A copyable extraction-TUNING order (not a full commissioning procedure — interlocks, remote observation and radiation monitoring are separate obligations): establish and optimize internal beam on the existing movable collector first, retract it, then ramp the deflector slowly with the phosphor screen as the live indicator. Separating the two optimizations matters on a small machine where field tune and deflector voltage are interactive. (The quoted passage begins on p.5 and its closing sentence is on p.6.)

The magnetic field was then approximately halved, 0.44 Tesla, and the measurements repeated. The RF frequency was held fixed at 14.900 MHz. The deflector voltage was stepped in 0.5 kV increments and a photograph of the phosphor screen was taken. Vertically stitching the sequence of images reveals the admittance of two different ions. Given the deflector voltage and magnetic field strength, the q/m values were determined. Accounting for the deflection voltage, analysis of the lower beam spot, centered at 6.0 kV, shows a q/m of 1.0 – the signature of a proton, H+. … A similar analysis was performed for the peak observed at 3.0 kV, corresponding to an ion with q/m of ½, such as 2H+ or 4He++.

Koeth, Ponter, Hoffman, Schneider & Krutzler, Rutgers 12-Inch Cyclotron Electrostatic Deflector (2010, rev. 2011) — p. 6

Editorial note, tabletop extrapolation: A genuinely cheap species diagnostic: a voltage step, a camera, and image stitching replace a dedicated spectrometer, with the 2:1 deflector-voltage ratio giving RELATIVE q/m directly. The source's own hedge carries the limitation: equal-q/m species (2H+, 4He++, H2+…) are indistinguishable by this measurement alone, and absolute identification still leans on the field and geometry calibration. Fig. 11 shows the resulting strip from 1.5 kV through 8.0 kV in 0.5 kV steps.

For the 12-Inch Cyclotron values, V=28 kV, ρ=4.125 inches, d=0.31 inches, ∆ρ=2.757 inches, εr=0.118 inches, we arrive at a ∆T=25 keV for a nominal 500 keV proton beam, a 5%. The resolution will be worse than this figure, as the entire entrance slit is admitting ions, which may have an angular component as well. These effects will be thoroughly studied in a future deflector document.

Koeth, Ponter, Hoffman, Schneider & Krutzler, Rutgers 12-Inch Cyclotron Electrostatic Deflector (2010, rev. 2011) — p. 7

Editorial note, tabletop extrapolation: For anyone whose internal deflector doubles as an energy diagnostic: apply the formula to YOUR channel — the ~5% here belongs to the listed Rutgers parameters, and the authors themselves call it optimistic (finite slit, angular spread). Worked checks: T_nom = (28 kV × 4.125)/(2 × 0.31) × (1 + 4.125/2.757) = 465 keV, consistent with the quoted nominal 500 keV; and subtracting the paper's own printed T+ and T− expressions yields a 2·εr factor and 24 keV, where the printed combined ΔT expression reads "1 +" — an apparent typesetting slip for "2", flagged here with both computations shown.

A scaled version of the of the 12-Inch Cyclotron's deflector will be the basis of the 19-Inch cyclotron deflection system. The 19-Inch cyclotron projects has a design constraint limiting the HV potential to 50 kV as a second 50 kV Bertan supply has been purchased. The stated goal is to extract and transport the 19-Inch Cyclotron's beam to a diagnostic and experimental chamber. As such, the extracted beam will need to traverse the rapidly falling vertical fringe field. The 19-Inch extraction design will incorporate an increase the deflection channel's gap, reducing the extraction field, through the region of declining magnetic field.

Koeth, Ponter, Hoffman, Schneider & Krutzler, Rutgers 12-Inch Cyclotron Electrostatic Deflector (2010, rev. 2011) — p. 7

Editorial note, tabletop extrapolation: The authors' design intent for a machine not yet built, not an achieved result. The transferable idea, stated correctly: an extracted particle crosses the fringe at roughly constant speed, so the magnetic bending force falls locally as B — the channel needs progressively less counter-field on the way out, and widening the gap along the channel is one way to deliver that at a single electrode potential. Derive the gap profile from the measured fringe map plus tracking, not from a scaling law; the B²-type relation (dg-1660) applies to the equilibrium-orbit sizing calculation, not to this traverse.

A high-voltage electrostatic beam deflection channel has been designed, constructed, and commissioned in the Rutgers 12-Inch cyclotron. A 500 keV proton beam has successfully been intercepted at it's nominal cyclotron radius of 4.0 inches and brought a radius of 4.5 inches in 43° of azimuth. This project has provided the experience necessary to confidently design an extraction channel for the 19-Inch cyclotron project. … [Figure 10 caption:] First image of 500 keV protons on phosphor screen.

Koeth, Ponter, Hoffman, Schneider & Krutzler, Rutgers 12-Inch Cyclotron Electrostatic Deflector (2010, rev. 2011) — p. 7

Editorial note, tabletop extrapolation: Read the achievement precisely: internal deflection onto a screen 0.5 inch further out in radius — not extraction from the chamber. For a small-machine builder that is the right first milestone: it proves the channel geometry, the HV system and the diagnostic before any attempt on the fringe field (the 19-inch extraction intent, dg-1676, is the stated next step).

An IEEE-488C GPIB interface has been purchased for the Bertan HV 205A-50N power supply, enabling remote computer control. There is a planned project to automate the sweeping of the cyclotron magnetic field and HV deflector while recording the beam current, effectively turning the cyclotron into a very sensitive accelerator based q/m spectrometer.

Koeth, Ponter, Hoffman, Schneider & Krutzler, Rutgers 12-Inch Cyclotron Electrostatic Deflector (2010, rev. 2011) — p. 5

Editorial note, tabletop extrapolation: Stated as a plan, not an achievement. The idea is well matched to a tabletop machine that already has a current-collecting screen: a two-axis sweep of field and deflector voltage recorded against collector current turns the manual photograph-stitching method (Fig. 11) into a quantitative spectrum with no new hardware in the vacuum. Modern equivalents of the GPIB link are trivial by comparison.

The cyclotron was tuned for maximum deuteron beam current on the radial probe, which was set to radius of 4 inches – this is just prior to the beam entrance into the deflection channel.[6] The probe was then fully retracted, allowing the beam to enter the deflection channel. … A deflector voltage of 16 kV placed the deuteron beam onto the phosphor screen, confirming the energy at 250keV. After fine-tuning of the RF and magnetic field the beam's stability was monitored for a few minute period. Neutrons were not detected. ... The radial probe was slowly inserted until neutrons were detected. The target position was adjusted for maximum measured neutron dose rate, which was found to be at a radius of 3 inches, for an inferred energy of 150 keV with a measured beam current of 100nA, as respectively depicted in figures 8 and 9. This was the crossover point of increasing beam energy and decreasing beam current.

Koeth, Neutron Production with a 12-Inch Cyclotron (2017) — p. 4

Editorial note, tabletop extrapolation: A counter-intuitive operational result: the best NEUTRON position was not the highest-energy position — dose rate peaked with the target at 3 inches (~150 keV, 100 nA), the crossover of rising energy and falling current. Two honesty notes: the maximum is of measured dose rate at a fixed detector, and moving the target also moves the source-detector geometry, so scan radius with geometry-corrected readings and simultaneous target current; and the 250 keV no-neutrons observation was beam-on-PHOSPHOR, not a controlled deuterated-target comparison at that energy. The method — scan the movable target for yield rather than assuming maximum radius — is the transfer. Note the Fig. 9 beam-current axis is labelled microamps while the text quotes 100 nA at r = 3 inches; the axis label appears to be a source misprint and no rule here relies on Fig. 9's magnitudes.

The deflection channel has a nominal radius of curvature, ρ1, of 7 inches and tangentially intercepts the cyclotron beam at a radius, ρo, of 4.0 inches and transports it to a radius of 4.5 inches over 43° of azimuth.

Koeth, Rosenberg, Krutzler, Ponter, Schneider & Hoffman, Rutgers 12-Inch Cyclotron: Dedicated to Training Through Research and Development — WEPPT024, Proceedings of Cyclotrons2013 (2013) — p. 2

Editorial note, tabletop extrapolation: PDF p.2 = printed p.367. A dimensioned energy-analyser example at tabletop scale, with the governing combined-field orbit relation in closed form. Because the electric field selects velocity at known magnetic rigidity, it yields an absolute energy number rather than the inferred radius-times-field estimate. Before rescaling: the relation as written is the ideal nonrelativistic form and its sign follows the chosen field direction (with ρ1 > ρ0 the deflecting field opposes the magnetic bending) — define the convention, then check the design with a field map or trajectory run, since gap, fringes and orbit geometry set the real calibration.

In a 1 Tesla field, a potential of 33 kV is required to produce a transverse electric field of 4.2 MV/m

Koeth, Rosenberg, Krutzler, Ponter, Schneider & Hoffman, Rutgers 12-Inch Cyclotron: Dedicated to Training Through Research and Development — WEPPT024, Proceedings of Cyclotrons2013 (2013) — p. 2

Editorial note, tabletop extrapolation: PDF p.2 = printed p.367 (gap on PDF p.3 / printed p.368). The three numbers are mutually consistent on computation — 4.2 MV/m across 0.31 inch (7.9 mm) is 33 kV, and the paper's own formula with ρ1 = 7 in, ρ0 = 4 in, B = 1 T returns 4.2 MV/m for the computed ~494 keV proton at 4 inches — so the set can be trusted as a worked example. Another machine recomputes from its own orbit radii, field and electrode gap; the voltage scales with the gap and the geometry, and can land well above or below this.

the HV electrode’s corners were rounded so as to limit the maximum E field to a conservative 170 kV/inch.

Koeth, Rosenberg, Krutzler, Ponter, Schneider & Hoffman, Rutgers 12-Inch Cyclotron: Dedicated to Training Through Research and Development — WEPPT024, Proceedings of Cyclotrons2013 (2013) — p. 3

Editorial note, tabletop extrapolation: PDF p.3 = printed p.368. Read the numbers as design practice, not as an allowance: Rutgers rounded and polished the electrode so the peak local field stayed at their chosen conservative 170 kV/inch (6.7 MV/m) while the channel ran 4.2 MV/m — the ratio is the geometric peak-enhancement they permitted themselves, not a demonstrated breakdown margin. What transfers: control the peak-to-working field ratio by geometry, polish, and seat the feedthrough conductor directly in the electrode; then condition and test at the actual gap, pressure and surfaces, and put a current-limiting series resistor in the HV line (here 75 MΩ) so the inevitable arc is survivable.

Pitting, Fig. 6, on the internal surfaces of the top and bottom lids only occurred directly above and below the perimeter of the electrode … Evidence suggested the internal arcing was initiated by secondary electron emission. … however, locations of highest E-field, such as directly below the electrode’s centerline did not show pitting, exonerating field emission based brake-down. Further, no damage was observed on the deflector electrode.

Koeth, Rosenberg, Krutzler, Ponter, Schneider & Hoffman, Rutgers 12-Inch Cyclotron: Dedicated to Training Through Research and Development — WEPPT024, Proceedings of Cyclotrons2013 (2013) — p. 3

Editorial note, tabletop extrapolation: PDF p.3 = printed p.368. A transferable diagnostic method, reported with the source's own interpretation: they read the pitting pattern — under the electrode perimeter, absent at the highest-field centerline, electrode itself undamaged — as evidence for secondary-electron-driven breakdown and against field emission. The pattern is evidence, not proof (field-emitted electrons also strike remotely); the practical takeaway is to read the chamber lids after any HV campaign, and to expect onset at whatever voltage YOUR gap and surfaces condition to — 30 kV was this channel's.

the polished HV electrode was coated with Aerodag-G graphite lubricant in order to reduce the coefficient of secondary electron emission

Koeth, Rosenberg, Krutzler, Ponter, Schneider & Hoffman, Rutgers 12-Inch Cyclotron: Dedicated to Training Through Research and Development — WEPPT024, Proceedings of Cyclotrons2013 (2013) — p. 3

Editorial note, tabletop extrapolation: PDF p.3 = printed p.368. A named, commercially available consumable applied to a polished in-vacuum HV electrode — about as accessible a candidate treatment as exists for secondary-emission trouble. The sequence matters: polish first, then coat — and note the coating did not by itself end the arcing; the 5 MΩ chamber-end resistor did (dg-1826). Check the current product's formulation, adhesion, particulates and vacuum compatibility before copying.

One such arc terminated on the upper magnet coil, causing costly damage to the magnet power supply.

Koeth, Rosenberg, Krutzler, Ponter, Schneider & Hoffman, Rutgers 12-Inch Cyclotron: Dedicated to Training Through Research and Development — WEPPT024, Proceedings of Cyclotrons2013 (2013) — p. 3

Editorial note, tabletop extrapolation: PDF p.3 = printed p.368. A concrete, expensive failure chain for anyone adding HV to an existing machine — and it is two-stage: the internal deflector discharge excited the charged cable (the Blumlein mechanism, dg-1826), and the resulting EXTERNAL arc terminated on the magnet coil and took out the magnet supply. The warning that transfers: HV transients couple into unrelated subsystems through cabling, grounds and stray capacitance, so an HV fault must be analyzed as a whole-machine event, not a deflector event.

the segment of HV cable between the series resistor and chamber formed a Blumlein HV pulse generator explaining the apparent ground-to-ground arcing … A 5 MΩ HV resistor was also installed in series with the coaxial center conductor and the chamber just prior to the HV vacuum chamber bushing. This suppressed all arcing and deflector operation at full potential is routine.

Koeth, Rosenberg, Krutzler, Ponter, Schneider & Hoffman, Rutgers 12-Inch Cyclotron: Dedicated to Training Through Research and Development — WEPPT024, Proceedings of Cyclotrons2013 (2013) — p. 3

Editorial note, tabletop extrapolation: PDF p.3 = printed p.368. The craft lesson: a protective series resistor at the supply end leaves the cable beyond it as a charged transmission line that dumps into any internal arc. The fix that worked here — a second resistor at the chamber bushing — is cheap and retrofittable; 5 MΩ is the value that worked in THIS installation. Size yours from the downstream cable's capacitance and stored energy at your voltage, and buy the resistor for the job: working-voltage, impulse-energy and creepage ratings, or the protective part becomes the next flashover.

A 0.005 inch thick, curved, grounded stainless steel sheet forms the septum and separates the main accelerating volume and the deflection channel.

Koeth, Rosenberg, Krutzler, Ponter, Schneider & Hoffman, Rutgers 12-Inch Cyclotron: Dedicated to Training Through Research and Development — WEPPT024, Proceedings of Cyclotrons2013 (2013) — p. 2

Editorial note, tabletop extrapolation: PDF p.3 = printed p.368. A buildable worked example at tabletop scale: 5-thou stainless shim, curved and grounded, forms the septum, with the concentric HV electrode at an average 0.31 inch gap — formable without a machine shop. Choose your own thickness from stiffness, supports and intercepted beam power rather than copying the number. The design choice worth copying outright is modularity: the whole channel removes as a unit, which is what keeps a crowded small chamber serviceable. (The 0.31 inch average gap figure is on p.3.)

This was verified by simulation: 385, 405, and 425 keV ions were admitted to the deflector resulting in a comparable target image … The bands are compilations of revolutions. Ions with sufficient radial extent in the nth turn are captured by the channel and form the outer (right most) band in Fig. 8. Those not intercepted continue on for another revolution, nth+1, of acceleration, and thus have a greater rigidity and hence are deflected less forming the second band, and so it goes for the third band, or nth+2 turn. … Considering the finite width of the deflector entrance slit and channel, the resolution has been calculated to be 10% at 500 keV.

Koeth, Rosenberg, Krutzler, Ponter, Schneider & Hoffman, Rutgers 12-Inch Cyclotron: Dedicated to Training Through Research and Development — WEPPT024, Proceedings of Cyclotrons2013 (2013) — p. 3

Editorial note, tabletop extrapolation: PDF p.3 = printed p.368. A small machine can display individual turns as separate bands on one screen — the source's own account: outermost band the nth turn, successive bands nth+1 and nth+2 at greater rigidity, verified by admitting 385/405/425 keV ions in SIMION. Two metrics must not be conflated: adjacent-band SEPARATION (~20 keV here) is an image-structure statement, while the calculated 10% at 500 keV (~50 keV) is the absolute-energy resolution set by the entrance slit and channel width — so the screen resolves turn structure without being a 20 keV spectrometer. Band spacing tracks energy gain per turn; converting it to dee volts needs the gap-crossing count and phase, not just the image.

Since Qx(r=0) begins at 1, any radial offset simply displaces the equilibrium orbit by the same. As the ions gain energy and spiral towards larger radii, Qx(r) begins to drop, causing the location of maximum radial displacement to azimuthally process. This continues until a tight inter-turn bunching occurs on one side of the machine while large turn to turn spacing develops on the other, as shown in Fig. 4. Historically this has been exploited to increase extraction efficiency by placing the septum between turns.

Koeth, Beam Physics Demonstrations with the Rutgers 12-Inch Cyclotron — WEPPT025, Proceedings of Cyclotrons2013 (2013) — p. 2

Editorial note, tabletop extrapolation: PDF p.2-3 = printed p.370-371 (the turn separation is photographed in Fig. 4). Directly useful to a small-machine builder attempting extraction: a deliberate radial offset makes the azimuth of maximum displacement precess as Qx falls, concentrating turns on one side and opening turn-to-turn gaps on the other — historically where the septum goes. Choose the azimuth by orbit tracking and low-current measurement; and note that on this machine the offset comes from translating the whole chamber, which moves dees and probes with it — offsetting the source alone is the finer instrument.

Sufficient data has been taken with this feasibility-study cyclotron to warrant progression to a twelve inch magnet. It is reasonable to expect one million volt protons with a magnetic field of 1.2 Tesla, and an fr of 18 MHz. Such a magnet system is currently being obtained. ... The use of a solid state amplifier is precluded once power requirements exceed 500 Watts. ... Finally, after the twelve inch system has proved operable, a tangential accessory vacuum port will be added with the intention to extract the proton beam.

Koeth, The Construction and Operation of a Nine Inch Cyclotron (undated scan; the machine ran 1995–1999) — p. 8

Editorial note, tabletop extrapolation: Design intent, not achievement — every number is a plan as of September 1999. What transfers is the staging philosophy: prove the concept on a small borrowed magnet (~184 keV, 9 inches) before committing to the larger machine. The "solid state precluded above 500 W" line is the author's 1999 equipment landscape, not a law — modern LDMOS amplifiers run solid-state into the kilowatts (the same lineage's later 1.5 kW AL-82 tube chain and pulsed operation, dg-1756/dg-1804, show the options both ways). The 1 µA figure on the same page is what "could have been achieved" with more source work — expectation, not measurement. Ellipses mark omitted text. (The first two quoted sentences begin on p.8.)