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

Tabletop: The reference machine (155 keV, 2.6 keV/turn, r=9.65 cm) gets only ~0.8 mm/turn; a 10 kV dee at the same radius gives ~3-6 mm.

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

Tabletop: Small machines fare better because dr scales as dE/E; a 350 keV next machine at 10-20 keV/turn beats this 30 MeV machine's fractional separation by ~50x.

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

Tabletop: A deliberate few-mm source off-centering plus letting the beam run into the fringe (n rising to 0.2-0.4) can triple the next machine's turn spacing for free.

In practice, a coherent radial oscillation amplitude of the same size as the incoherent amplitude, is a good criterion for efficient extraction.

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

Tabletop: If a next machine's radial beam half-width is ~2-3 mm, aim for a ~2-3 mm coherent amplitude, no more.

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

Tabletop: In a weak-focusing field the last turns sweep n from ~0.1 to ~0.5; keep energy gain high there so n=0.2 is crossed in <~5 turns.

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

Tabletop: Gauss-level azimuthal field asymmetry matters at 0.59-0.89 T: it is both the knob (deliberate shim/coil bump) and the hazard (uncontrolled bumps de-center the beam).

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.

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

Tabletop: Scaled to 0.6-0.9 T and r~0.1 m, tens of gauss of first harmonic would be needed to force mm-scale separation - 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

Tabletop: A classical (weak-focusing) machine never has nu_r>1, so create the amplitude by ion-source off-centering instead and use the same nu_r~0.8 fringe region for precession.

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

Tabletop: At 350 keV a 100 mrad kick over 10 cm of arc needs only ~5.6 kV/cm - about 2.8 kV across a 5 mm gap; at nanoamps the septum needs no cooling (~0.1 mW).

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

Tabletop: A 3-5 kV, 5-10 kV/cm tabletop deflector sits ~300x below this limit; the practical amateur ceiling is set by feedthrough and edge-radius engineering (the ~26 kV/cm working rule), not bulk breakdown.

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

Tabletop: Direct amateur precedent: a 1 T / 472 keV university tabletop deflector at 28-32 kV; a next machine needs only ~1/10 the voltage, so generous edge radii make sparking a non-issue.

~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

Tabletop: Rutgers arced a 30 kV-rated feedthrough run at 35 kV and had to rebuild with the feedthrough inside vacuum plus a corona adapter - rate a next machine's feedthrough 2-3x over operating voltage.

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

Tabletop: Scaling by 2T: a next machine at 350 keV needs ~1/45 of MIT's voltage for the same geometry ratio - about 1-3 kV across a 3-5 mm entry gap, rising if a faster peel (larger DR) is wanted.

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

Tabletop: Plan a next machine around 10-25% extraction efficiency; with nA internal beam that is 0.1-0.25 nA external - still a countable, PIXE-usable beam. (Ladder rungs: botman p.2, jongen CYC2004 p.1.)

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

Tabletop: Do not chase single-turn extraction: accept multi-turn with dE ~ 2*e*Vdee (~20 keV at 10 kV dee), which PIXE tolerates. (Spread and dB/B: botman p.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

Tabletop: A next machine with R~10 cm and half-gap 1.27 cm allows only ~9 turns (needs ~17 keV/turn); shrinking the half-gap to 6-7 mm at the edge allows ~30 turns - borderline reachable with 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

Tabletop: At sub-MeV a 50 ug/cm2 foil costs ~10 keV of energy and some scattering; every other extraction problem (septum, HV, turn separation) vanishes if an internal-source H- beam and <=1e-6 Torr can be achieved.

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

Tabletop: A next machine's H- variant spends its whole life at the cross-section peak: ~25 m of path at 1e-6 Torr loses of order 5-10%, at 1e-5 Torr most of the beam - vacuum, not physics, decides this option. (70 MeV data: cyclotron_vacuum_model p.3.)

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

Tabletop: 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

Tabletop: If a next machine uses source off-centering (amplitude created at turn 1), expect full phase mixing over 30-100 turns: the amplitude survives but its direction smears - a trim bump near the extraction region is cleaner.

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

Tabletop: The reference machine already probes the internal beam; adding a two-finger (or shadow-bar) differential probe turns the existing radial probe into the diagnostic that decides septum placement.

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

Tabletop: Sets the physics floor on energy spread from central bunching for any future extraction work; at the reference machine's and a next machine's energies the effect is small in absolute mm but the ~1%-class energy-spread scale is exactly what a deflector/slit design must budget for.

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

Tabletop: Directly. For a next machine's deflector, pick a VE number and the gap/voltage trade falls out; a 3-mm gap at VE=1.5e4 (kV)^2/cm predicts ~67 kV and ~220 kV/cm.

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

Tabletop: The single most quotable deflector design number, from an operating cyclotron with an in-tank vacuum no cleaner than an amateur's. Design a next machine's electrodes to 1.5e4 and treat anything above as commissioning margin.

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.

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

Tabletop: Make the next machine's deflector electrode 316 stainless (cheap, machinable, on the best-tier list); avoid copper or aluminum HV surfaces even though they are handy shop stock.

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

Tabletop: The reference machine's field (~6 kG) sits at the low edge of the 4-15 kG damage band, a real advantage. Conditioning the deflector at reduced field, then raising B, is nearly free insurance.

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

Tabletop: Directly sets deflector-supply philosophy - provide an adjustable, limited energy per spark (see UCRL-10655 crowbar) rather than either a stiff low-impedance supply or one that quenches sparks entirely.

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

Tabletop: A palm-sized tabletop electrode (~100 cm2) conditions in under an hour - or ~10 h if 316SS. 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

Tabletop: Directly. Measure the next machine's beam height at extraction radius, size the deflector field window ~2x that, and keep the HV bar as small and short as the trajectory allows.

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

Tabletop: 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.

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

Tabletop: 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

Tabletop: Cheap upgrade that scales down perfectly - line the grounded surfaces opposite the next machine's HV bar with thin tungsten (or at minimum molybdenum) sheet, edges overlapped.

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

Tabletop: Frees the mechanical design - cable runs and feedthrough capacitance in a tabletop deflector (tens of pF) are a non-issue provided the supply has adjustable spark-energy limiting.

When we increased the beam current, the carbon evaporated from the septum, contaminated the high-voltage electrode, and very little voltage could be held.

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

Tabletop: 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 contamination mechanism is temperature-driven, so thin-foil hot spots still apply. Default to tungsten/molybdenum septum, revisit carbon only with septum-temperature data.

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

Tabletop: The reference machine and a next machine use oil diffusion pumping, so expect the dirty-system dark-current regime; the ion-scrub recipe needs only a variac, a 480-V transformer, a limiting resistor, and the existing H2 feed - a directly copyable conditioning procedure.

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

Tabletop: Both halves are free instrumentation for a next machine - a three-point V(d) test during commissioning, and an insulated septum/ground-electrode current readout for beam steering (same trick as the reference machine's Faraday-cup practice).

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

Tabletop: The governing philosophy for any next machine's deflector supply - low stored energy is also the personnel-safety property. A sub-joule store at 50-100 kV is achievable and sufficient.

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

Tabletop: The 1963 'inexpensive silicon diodes + TV ceramic caps' recipe is today a standard multiplier stack; keep the two design features that matter - per-diode grading capacitors and high drive frequency (small energy per stage, fast regulation).

at the more sensitive positions of the crowbar current setting, the power supply can be turned off before a spark becomes visible.

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

Tabletop: The feature to replicate in a modern build - a solid-state inverter driving a CW stack gives the same microsecond drive-kill for free (gate shutdown on an overcurrent comparator), and the threshold should be an operator knob used during bake-in, per UCRL-10654.

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

Tabletop: A conservative, corona-quiet air-gradient number for amateur HV column layout; at 60 kV total a next machine's stack wants ~6 in of creep/clearance headroom or potting/SF6-free oil.

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

Tabletop: Historical for parts choice (modern fast-recovery diodes moot the issue) but the design insight stands - CW stacks feeding capacitive deflector loads tolerate slow diodes; spend money on voltage rating and grading instead.

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

Tabletop: Deflector voltage stability maps directly to extracted-beam steering stability; the lesson - regulation is limited by the divider, so buy/build the divider first - applies at any scale, and 0.01% is far beyond what a next machine needs (1% steers by ~1% of the deflection).

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

Tabletop: Two functions from one cheap HV resistor - ripple filter and spark-energy isolator (the isolation claim was independently tested in UCRL-10654 p.25). Put a 50-100 kOhm non-inductive resistor in the next machine's deflector feed.

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

Tabletop: Modern solid-state supplies mostly shrug at 150 G, but CRT-style meters, vacuum gauges, photomultipliers, and any remaining tubes near a next machine's yoke need the same treatment; mild steel is enough at this level.

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

Tabletop: Synchrocyclotron-specific hardware (a next machine's CW deflector needs no pulse), but the requirements chain - turn separation sets element aperture sets timing/rise budget - is the template for sizing ANY extraction element, including the 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

Tabletop: Scale perspective - deflecting-field requirement grows with beam rigidity, and at a next machine's 300 keV-1 MeV the equivalent job needs only tens of kV/cm CW (cf. UCRL-10654's 150-200 kV/cm at 50 MeV). Sub-MeV extraction is in the easy corner of this trade.

These tubes cannot be operated at plate voltages above 11,000 volts, even though rated at 16,000 volts, because, in operation, the plate voltage reversed in 0.3 us causing arcing between plate and grid.

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

Tabletop: 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 the exact role the 5C22 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

Tabletop: Classic paralleling technique still used in pulsed-power; relevant only if a next machine ever adds a pulsed element (fast chopper, kicker for time-of-flight work), but then it is the reference method.

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

Tabletop: Not needed for a CW deflector, but the de-aerated-oil corona cure, the 3x overvoltage proof test, and the interlaminar-voltage failure mode are transferable HV-construction craft for any oil-insulated amateur component.

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

Tabletop: The two lessons that outlive the hardware - charge-reversal duty is what kills capacitors (modern pulse caps are still specced by % reversal), and ESL budgets, not just C and V, set rise time. Cable-as-capacitor remains a legitimate cheap trick for one-off pulse work.

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.

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

Tabletop: Pulsed-modulator craft, not CW-deflector material; file under 'if a next machine ever needs a kicker' - it means the HV DC supply can be a quarter of the switch voltage.

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

Tabletop: A general commissioning lesson - extraction elements have one strong knob (voltage/field) that can buy back deficiencies in the others; design in voltage headroom (UCRL-10654's derating serves the same end from the other side).

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

Tabletop: 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

Tabletop: The siting logic transfers even though the numbers are synchrocyclotron pole-edge values - put the next machine's septum/regenerator equivalent just inside where the field map says the beam dies (n -> 0.2 walkout or resonance), and know that every mm inward is 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

Tabletop: The workflow (measured field -> amplitude-dependent tunes -> impulse-matrix tracking -> element strength) is exactly the CYCLOPS-lite pipeline planned for a next machine; the specific peeler-regenerator field shapes are synchrocyclotron machinery and need not transfer.

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

Tabletop: The gauss-radian bookkeeping is a handy unit for ANY azimuthally-localized field bump (harmonic coils, shims, channel compensation) on a next machine; the percent-of-B0 scale of effective perturbations is a useful sanity anchor. The specific values are 100+ MeV synchrocyclotron numbers.

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

Tabletop: The general warning transfers - any radial-field-gradient extraction element has an off-midplane Br that pumps vertical motion, so check axial kicks in the next machine's tracker for the deflector fringe and any field bump, and expect to lose the large-axial-amplitude tail 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

Tabletop: Direct analog for a next machine - the septum and exit-channel iron (or the deflector entrance fringe) perturbs the last internal turns; model that perturbation in the tracker and compensate upstream (harmonic coil/shim) instead of trying to null the channel's leakage to zero.

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

Tabletop: A genuinely tabletop-compatible extraction assist - an electrode pair driven by a small independent oscillator. For a next machine (nu_r ~ 1) the required frequency is near the orbital frequency's sidebands; worth a tracker experiment before committing hardware.

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.

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

Tabletop: kV/cm-class rf on a small electrode is trivially available at a next machine's scale (hundreds of volts across a few mm). The scheme was never demonstrated on hardware in this report - treat as 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

Tabletop: Directly supports the next machine's plan-of-record (electrostatic deflector, no fixed magnetic channel) - an educational machine that will run at more than one field/energy point wants its extraction strength on a knob, not in iron.

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

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

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

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

Tabletop: Sets expectations for any resonant/precessional scheme on a next machine - extraction is a many-turn statistical process, so judge schemes in the tracker by turns-to-extraction and septum-hit fraction, not single-pass kick size.

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

Tabletop: The architecture for any timed kick against an extraction gap, on a next machine or a small synchrotron - a coarse condition (frequency, turn count, integrated field) opens a window, and the RF itself supplies the fine phase. Two easy measurements replace one impossible one.

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

Tabletop: Classic measurement doctrine - move precision to a fixed low frequency where stability is cheap. The same trick (mix dee RF down, detect at fixed IF) is how a modern amateur frequency/turn marker gets crystal accuracy with 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

Tabletop: General fast-timing wisdom for beam-pulse and kick timing chains - every smoothing stage costs latency; calibrate the chain end-to-end and remove the constant part in the threshold or delay setting rather than chasing zero-delay filters.

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

Tabletop: Matters wherever a resonant pickup watches a changing frequency - including a synchrotron RF ramp or an FM-tuned marker on a cyclotron; if the ramp rate changes, the timing calibration silently moves.

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

Tabletop: A self-calibration idiom worth copying into any comparator/discriminator in the DAQ - trim to observed threshold at session start (their multivibrator = today's comparator with drifting offset), and slow drift stops moving the physics timing.

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

Tabletop: Directly applicable to pulse chains fed by beam pickups or PMTs at low rep rate - stabilize on detected peak height at the discriminator input, and amplitude drift stops translating into time walk.

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

Tabletop: A complexity-avoidance rule with 2026 force - blanking a known-bad time window (one line of firmware now) beats analog cleverness whenever the artifact's timing is predictable.

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

Tabletop: Calibrates ambition - microsecond-class event timing off a tiny RF sample needed no exotic parts in 1952; any modern comparator + MCU implementation should beat it by orders of magnitude, so the architecture (not the hardware) is the thing to copy.

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

Tabletop: Sets expectations for any future extraction gate on a next machine - design the septum/deflector with in-vacuum adjustability and count a 30-40% extracted fraction as success on a first small machine.

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

Tabletop: At reference-machine and next-machine energies activation is negligible, but the selection logic transfers to the planned higher-power machines and to the business plan's licensing story - prefer aluminum/graphite for probes, septa, and slits anywhere protons above a few MeV are contemplated.

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

Tabletop: DIRECT - this is the canonical two-stage architecture for any external line on a next machine. The optical condenser/analyzer analogy (illuminated slit as object) is the cleanest possible statement of why "focus first, analyze second" beats one clever magnet.

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

Tabletop: The conceptual mechanism to have in hand before any extraction attempt on a next machine; it needs nu_r to pass unity with a controlled first harmonic — both quantities a FEMM-fed tracker can compute for a candidate pole design.

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

Tabletop: The right figure of merit for any next machine's beamline or extraction simulation — track a small grid of particles and judge the deformed shape, not just the centroid; five to two dozen particles sufficed in 1961.

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

Tabletop: The doctrine transfers whole to any resonance-crossing scheme on a small machine — cross fast where the map is ugly; the diagnostic (superimpose the accelerated beam path on static phase plots) is a cheap tracker post-processing step.

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

Tabletop: The quantitative ancestor of "dee volts buy extraction" — the reference machine's ~800 V nominal dee is why it is internal-beam-only, and the next machine's 5-13 kV target is what would make any future extraction scheme even thinkable.

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

Tabletop: 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

Tabletop: 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 deflector septum or foil design on a next machine.

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

Tabletop: Per-element thermal interlocks scale down perfectly — the same philosophy belongs on the next machine's RF amplifier dummy load, water-cooled dee stubs, and any powered septum, and matches the fail-safe interlock doctrine in the 1974 ORNL safety survey.

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

Tabletop: Every conductor near the pole gap feels J x B; thin walls, septa, and coil leads need either stiffening or a measured demonstration that deflection at full excitation stays elastic - and motors, encoders, and anything with a magnetic circuit belong outside the fringe field.

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 (c. 1950) — p. 116

Tabletop: The corpus's commissioning-order lesson (internal beam -> then extraction) stated as an explicit 1951 schedule decision. For a next machine, budget the probe and its lock as first-beam hardware and hold extraction hardware at the drawing stage until the field and RF are proven.

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 (c. 1950) — p. 116

Tabletop: The RF-ground deflector-plate trick (steal the existing dee field, add DC only as a supplement) and the adjustable-channel flux-vs-resolution trade are scale-free ideas for any future extraction study on a next machine; the phase-floor analysis is the kind of computation this collection's deflector cluster (nyo-9360 etc.) expects before metal is cut.