Design Guide

A slit Y, 0.5 cm by 1 cm, serves to define the deflected beam and sort out a given kind of ion with a small range of energies.

Oliphant & Rutherford, Experiments on the Transmutation of Elements by Protons (1933) — p. 262

Tabletop: In a cyclotron the machine itself is the analyzer, but any external beamline species check on the next machine can copy these modest slit and pole proportions.

Protons: T (Mev) = 3.12 x 10-4 B2R2 ... the radius R applies to the extent of the uniform magnetic field; the physical radius of pole faces must be larger by about one-half the gap length.

Livingston & Blewett, Particle Accelerators (1962) — p. 158

Tabletop: For 8-in poles at 5.9 kG with ~1.5-in gap, usable R is roughly 3.25 in, predicting ~115 keV; a wider pole or smaller gap directly buys energy as B^2R^2.

for particle oscillations about an equilibrium orbit to be stable for both axial and radial coordinates, the value of n must be in the range 0 < n < 1.

Livingston & Blewett, Particle Accelerators (1962) — p. 161

Tabletop: Map n(r) on the 8-in poles; any region where field rises with radius (n<0) defocuses axially and kills the beam.

the total decrease below the value of the central field out to the exit slit is about 2 per cent. The radial decrease can be larger (3 to 4 per cent) in small machines in which D voltage is relatively high.

Livingston & Blewett, Particle Accelerators (1962) — p. 161

Tabletop: The reference machine is the 'small, few-turn' case: aim for a smooth 3-4% droop center-to-edge rather than a flat field.

The n value rises almost linearly from zero at the center to 0.02 at 15 in. (where fringing effects start), then increases rapidly to 0.40 at 18.75 in. (exit-slit location) and to 1.0 at 19.25 in.

Livingston & Blewett, Particle Accelerators (1962) — p. 161-183

Tabletop: Scale directly: on 8-in poles keep n tiny out to ~3 in radius and take the beam off where n has climbed to ~0.4.

Precise machining of the surfaces in contact is necessary to make pole faces accurately parallel. The required machine tolerance is about 1/50,000 of the pole diameter.

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

Tabletop: For 8-in poles that is ~0.00016 in (~4 um) parallelism - a surface-grinder job; non-parallel poles show up as the sinusoidal azimuthal error in field maps.

For a designed flux density of 18 kilogauss in the gap of a 42-in. cyclotron ... the pole base would have to be about 52 in. in diameter to keep flux density in the base of the pole below the practical limit.

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

Tabletop: At 5.9 kG straight cylindrical poles are fine; only if a next machine pushes past ~12-15 kG does pole taper start paying for itself.

the longer the magnet gap the larger is the power required for excitation, varying approximately with the square of gap length ... use of 5- to 6-in. gaps for 42-in. poles and 8- to 9-in. gaps for 60-in. poles.

Livingston & Blewett, Particle Accelerators (1962) — p. 194

Tabletop: On 8-in poles the historical ratio suggests a ~1-in gap; every extra 1/4 in of gap costs both field (amp-turns) and usable radius.

The magnet field must be accurately regulated to maintain a steady beam ... A constant-current regulator is needed, capable of reducing fluctuations to better than 1/1000.

Livingston & Blewett, Particle Accelerators (1962) — p. 194

Tabletop: A modern current-regulated supply meets this easily, but verify ripple and thermal drift: 0.1% of 5.9 kG is 6 G, comparable to the whole shim budget.

obtained by the use of such stacks in the two shimming gaps, each consisting of four disks of 0.020-in. soft iron sheet of 6, 14, 18, and 22 in. diam.

Livingston & Blewett, Particle Accelerators (1962) — p. 195

Tabletop: Scaled to 8-in poles: a stack of 0.020-in disks of roughly 1.2, 2.8, 3.6, 4.4 in diameter is a proven starting recipe for the 2-4% droop.

At MIT the optimum ring section was 3/4 by 1/4 in. ... Shims which are too large produce a minimum in the radial field plot which would cause defocusing.

Livingston & Blewett, Particle Accelerators (1962) — p. 196

Tabletop: A small edge ring (order 0.15 x 0.05 in scaled, or trimmed empirically) can extend the reference machine's usable radius, but re-check the field plot at every operating current.

Most operators agree that a variation of less than 0.1 to 0.2 per cent is desirable ... After careful correction by use of sector-shaped and wedge-shaped shims, the errors were reduced to less than 0.1 per cent.

Livingston & Blewett, Particle Accelerators (1962) — p. 196-197

Tabletop: At 5.9 kG this means holding azimuthal wobble to ~6-12 G; an azimuthal bump acts like a field error that pumps radial oscillation amplitude.

the uncorrected field showed a median plane displaced 1/2 in. below the central plane ... adequately corrected by reducing excitation in the upper magnet windings relative to the lower ones.

Livingston & Blewett, Particle Accelerators (1962) — p. 197

Tabletop: The beam follows the magnetic plane, not the machined one; with separate top/bottom coil circuits (or a resistor across one layer) the builder can steer it back to mid-gap.

When this program was completed, the cyclotron was reassembled and on the first operation gave the highest beam intensities ever obtained, with no further empirical shimming.

Livingston & Blewett, Particle Accelerators (1962) — p. 197

Tabletop: The single strongest process lesson for a next machine: map first, shim from data - a weekend of Hall-probe mapping replaces months of trial-and-error beam chasing.

A local weak spot in the field (0.5 per cent low) was observed in the MIT magnet which was presumed to be due to a blowhole in the pole casting; it was corrected by a local spot shim.

Livingston & Blewett, Particle Accelerators (1962) — p. 197-284

Tabletop: Read the harmonic content of azimuthal maps like a diagnosis chart: 1st harmonic = tilt/centering, higher harmonics = discrete iron defects needing taped-on trial shims, then permanent installation.

To produce a field B of 1 weber/m2 (10 kilogauss) in a gap of 10 cm length, the number of ampere-turns required is 7.95 x 10^4 ... At 18 kilogauss ... the observed value of B is 0.73 of that predicted.

Livingston & Blewett, Particle Accelerators (1962) — p. 258-260

Tabletop: At the reference machine's 5.9 kG the linear formula is trustworthy: ~1.4e4 ampere-turns for a 3 cm gap; headroom for a hotter field on the next machine is cheap until ~10 kG, expensive after.

the edge of the usable region is inside the pole boundaries by about one-half the gap length ... Without shims the useful region was inside the pole edge by 0.6g; with the chosen ring-shaped shims it was inside by 0.45g.

Livingston & Blewett, Particle Accelerators (1962) — p. 260

Tabletop: With a 1.2-in gap on 8-in poles the builder loses ~0.6 in of radius to fringing; shrinking the gap or adding ring shims recovers usable radius.

A typical 'exploring' coil for a cyclotron magnet would have about 1000 turns of fine wire ... Total deflection should be zero after a full circle; this provides a check on the stability of the amplifier.

Livingston & Blewett, Particle Accelerators (1962) — p. 283-285

Tabletop: A pivoted-arm coil (or a modern Hall probe on the same fixture) sweeping circles at fixed radii is exactly the mapping jig an 8-in machine needs before shimming.

the magnetic field can be determined with high precision ... this resonance frequency represents an average value of the magnetic field from the center out to the exit radius ... an error of the order of 0.5 per cent is possible.

Livingston & Blewett, Particle Accelerators (1962) — p. 287-288

Tabletop: The reference machine's observed resonance peak vs magnet current is a magnetization-curve measurement of their own magnet - log it at every retune.

a common phenomenon ... is to find the median plane dished into a shallow saucer shape caused by asymmetries in the magnet iron or of the reinforcing iron in the foundations ... At MIT such a 'dished' median plane was corrected by connecting an external resistor in parallel with one of the coil layers.

Livingston & Blewett, Particle Accelerators (1962) — p. 288

Tabletop: Rebar in the floor or a nearby steel bench can dish an H-frame tabletop field; check for it and trim electrically rather than re-machining.

we will reduce the air gap between the poles of the magnet to 1.3 cm thereby increasing the magnetic field to roughly 0.75 T.

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

Tabletop: The cheapest field upgrade for a next machine is gap reduction (thinner chamber lids, pole pieces reaching into the chamber), before any coil or steel changes.

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

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

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

the magnet generates 2.7 T of magnetic field with a 1.25 inch pole separation... capable of accelerating protons to a maximum kinetic energy of 1.96 MeV

Dewan, Design and Construction of a Cyclotron Capable of Accelerating Protons to 2 MeV — MIT thesis (2007) — p. 7-8

Tabletop: The surplus-NMR-magnet route to MeV energies: small radius is fully compensated by high B (energy ~ B^2*r^2), so a 6-inch 2.7 T machine beats a 12-inch 1 T machine.

The magnet has tapered poles, the poles being tapered from 12-inch pole stems to 10-inch pole faces. There is a 0.7 inch thick shoulder at the pole face ... peripherally placed steel shims contribute to the uniformity of the field.

McGuire, The Iowa State University 1.5 MeV Undergraduate Cyclotron (1961) — p. 6-7

Tabletop: A concrete, machinable geometry for concentrating flux into an 8-10 inch pole face at ~1.7 T; the shoulder plus edge shims are what flatten B(r) near the outer orbit.

The magnet consists of coils of hollow copper tubing wound on a two-ton core of mild steel ... These deliver to the magnet 20 kilowatts of electric power, which is dissipated by water circulating through the coils.

McGuire, The Iowa State University 1.5 MeV Undergraduate Cyclotron (1961) — p. 6-7

Tabletop: Sets the scale of the jump from the reference machine's 0.59 T solid-copper-tubing magnet to a 1.7 T machine: hollow conductor and real water cooling become mandatory, and power goes to tens of kW.

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

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

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

This regulation system is capable of holding the 17,000 gauss field to within +/-4 gauss of its nominal value.

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

Tabletop: Sets a concrete stability target for a home magnet supply: a few parts in 10^4, achievable with a shunt, op-amp and pass bank.

an instrument operating on the principle of nuclear magnetic resonance is used ... The instrument may be read easily to one gauss accuracy.

McGuire, The Iowa State University 1.5 MeV Undergraduate Cyclotron (1961) — p. 9-10

Tabletop: A cheap DIY NMR gaussmeter (coil, oscillator, water sample) is a well-known amateur build and would let the builder set f = qB/2*pi*m exactly.

The pole gap is twenty-two inches, and, for any given radius, the gap variation is less than 0.005 inch.

Ramler & Parker, The Argonne 60-Inch Cyclotron — ANL-5907 (1959) — p. 10

Tabletop: Scaled to the reference machine's 8 in poles and ~2 in gap, a few-thousandths flatness/parallelism spec is achievable on a decent mill and is the tolerance to ask a machinist for.

Magnetic shimming consists of internal Rose rings and external stepped shims... The rings are 1/4 inch thick and 2 inches wide.

Ramler & Parker, The Argonne 60-Inch Cyclotron — ANL-5907 (1959) — p. 10-11

Tabletop: The classic two-knob shim architecture for extending the reference machine's flat-field region: perimeter ring for the edge, thin stacked discs for the interior gradient.

The magnet yoke, poles and tips, acceleration chamber lids, and shims are of soft iron forgings with the impurity analysis as follows: Carbon 0.12%...

Ramler & Parker, The Argonne 60-Inch Cyclotron — ANL-5907 (1959) — p. 11

Tabletop: A concrete steel spec to hand a supplier for a next machine's yoke stock: 1010/1018-class low-carbon steel is fine; avoid high-carbon or unknown scrap for pole tips.

the arms of the yoke carry a 25% smaller flux density than the maximum: only 1.2 T. This is achieved by increasing their cross-sectional area by 25%.

Heuer & Baumgartner, Design of a 2 MeV Cyclotron (2009) — p. 29

Tabletop: A ready sizing ratio for a next machine's H-frame: make every return-path section at least 25% larger in area than the pole face.

implement a .02'' convex taper from the center of the pole to the edge, to create sufficient bending of the magnetic field lines.

Heuer & Baumgartner, Design of a 2 MeV Cyclotron (2009) — p. 31

Tabletop: A concrete starting number for 8-12 inch poles; the same 0.02 in figure was used on 12 inch poles at 1.6 T, so it scales directly to a next machine.

the edges of the pole have a 45 degree taper. This is to prevent magnetic saturation at the edges of the pole. The field due to the taper also fringes less sharply.

Heuer & Baumgartner, Design of a 2 MeV Cyclotron (2009) — p. 31

Tabletop: Trivial machining step for a next machine's pole tips that buys margin against edge saturation at higher fields.

at a dee radius of 6'' the field is 1.57 T, a .08 T drop off from 1.64 T directly at the center.

Heuer & Baumgartner, Design of a 2 MeV Cyclotron (2009) — p. 31

Tabletop: Gives the builder a sanity band for their own field maps: a few percent droop is by design, much more costs resonance synchronism.

we used the basic equation for an electromagnet... we decided a 2.13'' gap a reasonable size... we then concluded that we needed 720 turns to reach 1.6T.

Heuer & Baumgartner, Design of a 2 MeV Cyclotron (2009) — p. 32

Tabletop: Same sizing equation the reference machine's 538-turn magnet obeys; lets them trade gap, turns, and current for any next machine's target field on one line.

Our magnet is constructed out of 1060 steel, which saturates at around 1.7 T; above this magnetic flux density the yoke is unaffected by further excitation.

Heuer & Baumgartner, Design of a 2 MeV Cyclotron (2009) — p. 6, 29

Tabletop: Directly applicable: at 0.59 T the builder is far from saturation, but a next machine pushing past ~1.5 T must budget yoke cross-sections against the 1.7 T ceiling.

agreement to within less than two percent. In contrast, calculations of the flux density at Point G yield 0.39 T for the analogue method and 0.30 T for the computer

Leupold & Potenziani, A Permanent Magnet Circuit Design Primer — ARL-TR-946 (1996) — p. 10-11

Tabletop: If a next machine uses NdFeB anywhere (source magnets, PM cyclotron study), this back-of-envelope method sizes gap flux without FEA - but trust it for totals, not point fields.

The latter has a gap field of 2 T, as compared with only 0.8 T for the unclad structure... 7 kg mass of such an assembly compared to the 55 kg required to produce only 1.6 T

Leupold & Potenziani, A Permanent Magnet Circuit Design Primer — ARL-TR-946 (1996) — p. 15-16

Tabletop: Mostly a curiosity at cyclotron-gap geometry (where the gap dominates and cladding gains little), but valuable for compact PM ion-source or steering assemblies.

fields of twice the material remanence should be practicable, namely 2.0 to 2.5 T... Bw = 1.2 ln(15/2.5) = 2.1 T

Leupold & Potenziani, A Permanent Magnet Circuit Design Primer — ARL-TR-946 (1996) — p. 24-25

Tabletop: Shows what PM technology can do at small bore: not a cyclotron gap replacement, but a zero-power option for beamline analysis/steering dipoles on a next machine's extracted beam.

If the required fields are less than about half the remanence, open compact sources for fields in axially finite cavities can be made

Leupold & Potenziani, A Permanent Magnet Circuit Design Primer — ARL-TR-946 (1996) — p. 33

Tabletop: Quick feasibility screen: with Br ~ 1.3 T NdFeB, an open PM assembly tops out near ~0.6 T in a usable gap - marginally at the reference machine's current field, insufficient beyond.

When passive materials such as iron are operated close to or above saturation the approximation mu_p = infinity does not hold and the method of permeance estimation is not readily practicable.

Leupold & Potenziani, A Permanent Magnet Circuit Design Primer — ARL-TR-946 (1996) — p. 6

Tabletop: Same lesson as Tanabe from the PM side: all quick hand methods assume unsaturated iron, another reason to keep a next machine's yoke flux under ~1.5 T.

no unique mmf can be assigned to a conventional permanent magnet... the magnet mmf will always be that corresponding to the lowest point on the demagnetization curve reached

Leupold & Potenziani, A Permanent Magnet Circuit Design Primer — ARL-TR-946 (1996) — p. 8-10

Tabletop: Practical warning: alnico horseshoe magnets salvaged for a PM gap lose field every time the circuit is opened for chamber access; NdFeB tolerates gap changes reversibly.

required volume of PM material depends only on particle energy, magnet gap and PM working point and doesn't depend on pole radius or average magnetic field value.

Antokhin et al., Magnet System for PET Cyclotron Based on Permanent Magnets (2006) — p. 1

Tabletop: Scaling law that makes a permanent-magnet follow-on build thinkable: at ~1 MeV and a 2 cm gap the required NdFeB volume is a few percent of the 1 ton needed for 10 MeV.

To minimize weight and size of magnet system the average magnetic field value has to be high, limited by iron saturation ... average magnetic field value was chosen as 1.4 T provided of 2.3 T and 0.5 T of hill and valley region fields

Antokhin et al., Magnet System for PET Cyclotron Based on Permanent Magnets (2006) — p. 1

Tabletop: The hill/valley ratio (~4.6:1) and 45-degree sector angle are directly scalable to an 8-12 inch AVF pole set; iron saturation, not coil power, is the ceiling.

As hill gap providing enough beam intensity was chosen as 20 mm and then corresponding valley gap is 100 mm.

Antokhin et al., Magnet System for PET Cyclotron Based on Permanent Magnets (2006) — p. 1

Tabletop: Gives the gap ratio for a first AVF pole-tip design; a deep valley is also where an amateur puts the Dee/RF and pumping.

disagreement with calculation was found as the calculation average field value is 5 % higher than measured one ... the valley gap height was reduced from 100 mm to 70 mm

Antokhin et al., Magnet System for PET Cyclotron Based on Permanent Magnets (2006) — p. 2

Tabletop: Design in adjustability (a gap or shim you can still reduce after measuring), because your FEMM answer will be a few percent optimistic too.

Both cutting pole and shimming was applied to reach isochronous field. The resulting magnetic field strength is close to designed value and its shape is nearly isochronous

Antokhin et al., Magnet System for PET Cyclotron Based on Permanent Magnets (2006) — p. 2

Tabletop: Budget several map-machine-remap cycles for a next machine's pole profile; it is normal, not a sign of a bad design.

The temperature coefficient of gap magnetic field was measured as about -0.07%/0C. Such coefficient is acceptable for normal work of cyclotron.

Antokhin et al., Magnet System for PET Cyclotron Based on Permanent Magnets (2006) — p. 2

Tabletop: A PM cyclotron in an unheated garage will drift off resonance with the seasons: 10 degC swing = 0.7% field change, far more than the few-parts-in-10^4 the resonance wants.

The reason for increased radial oscillations is big first harmonic of magnetic field, which caused by non-symmetric structure of central part of cyclotron magnet ... to make symmetric central magnet part by setup second hole on opposite side with respect to ion source hole.

Antokhin et al., Magnet System for PET Cyclotron Based on Permanent Magnets (2006) — p. 2-3

Tabletop: A ten-fold reduction in orbit wander for the cost of drilling a second, unused hole - directly applicable to any asymmetric feature in the reference machine's pole or chamber center.

Bair = mu0 NI / (g + lambda/mu); ... Approximation ignoring iron reluctance (lambda/mu << g): NI = B g /mu0

Marks, Conventional Magnets for Accelerators — CAS lecture (2004) — p. 25

Tabletop: The correction term is exactly what bends the reference machine's excitation curve at high current; measuring B vs I against this formula reveals where the yoke saturates.

'Window Frame' Advantages: High quality field; No pole shim; Symmetric & rigid; Disadvantages: Major access problems.

Marks, Conventional Magnets for Accelerators — CAS lecture (2004) — p. 29, 31

Tabletop: Confirms the reference machine's H-frame as the right middle choice for a cyclotron (needs chamber access on both sides), with shimming accepted as part of the deal.

The 'shim' is a small, additional piece of ferro-magnetic material added on each side of the two poles... optimised to reduce the 6, 10, 14... pole error harmonics.

Marks, Conventional Magnets for Accelerators — CAS lecture (2004) — p. 29, 37

Tabletop: Edge shims are how a next machine can widen its flat-field fraction beyond the bare ~80% of pole radius without bigger poles.

typically +/- 1:104 within the 'good field region' of -12mm <= x <= +12 mm.

Marks, Conventional Magnets for Accelerators — CAS lecture (2004) — p. 41, 43

Tabletop: Sets the metric (not the number - a cyclotron needs far less) by which the builder should present their own field maps: normalized deviation over the beam region.

This profile provides the maximum rate of increase in gap with a monotonic decrease in flux density at the surface ie no saturation

Marks, Conventional Magnets for Accelerators — CAS lecture (2004) — p. 48-49

Tabletop: The mathematically optimal version of the Cyclotron Kids' 45-degree chamfer; worth machining on a next machine's pole edges if the builder pushes past ~1.4 T.

pressure @ 0.5T 99,472 Newton/m2... ~ 1 atmosphere

Tanabe, Iron Dominated Electromagnets, Lecture 10: Forces, Stored Energy, Fringe Fields, End Chamfering (2005) — p. 10-11

Tabletop: At the reference machine's 0.59 T the poles attract with ~1.4 atm over the 8-inch pole face — about 4,500 N (~1,000 lbf); clamps and any pole-retraction scheme must carry that load (chamber lids carry the separate atmospheric load — see the lid-deflection calculator). [Corrected 2026-08-20: previously printed as "~4500 lbf", the newton value mislabeled.]

Given the field = B0, pole width = a, Magnet Length = L and ramp time dt, the only design option available for changing the voltage is the number of turns, N.

Tanabe, Iron Dominated Electromagnets, Lecture 10: Forces, Stored Energy, Fringe Fields, End Chamfering (2005) — p. 12-16

Tabletop: Quick check on a next machine's supply matching: stored energy in a 10 inch, 1 T, 5 cm gap magnet is ~100s of joules, and turns count trades current for voltage against whatever surplus supply the builder finds.

This reduction is accomplished by reducing the saturation by making the yoke and back leg of the septum magnet as thick as possible.

Tanabe, Iron Dominated Electromagnets, Lecture 10: Forces, Stored Energy, Fringe Fields, End Chamfering (2005) — p. 17-19

Tabletop: Justifies generous H-frame cross-section on the next machine: extra return-path steel is the cheapest way to keep stray field away from ion gauges, turbo pumps and CRT-era instruments on the bench.

the fringe field is longer at the center of the magnet and drops off near the edges. This distribution is approximately quadratic and the integrated multipole field looks like a sextupole field.

Tanabe, Iron Dominated Electromagnets, Lecture 10: Forces, Stored Energy, Fringe Fields, End Chamfering (2005) — p. 20-21

Tabletop: Mostly relevant if the builder adds edge shaping for extraction: expect the field falloff at the pole rim to vary azimuthally with any non-axisymmetric pole feature, and fix it empirically with removable machined inserts.

the meshing package for POISSON is rather weak and often does not have the flexibility nor is robust enough to generate difficult detailed meshes easily.

Tanabe, Iron Dominated Electromagnets, Lecture 4: POISSON — A Two-Dimensional Magnetostatic Solver (2005) — p. 10, 19

Tabletop: Saves hours on shim-profile studies where dozens of geometry variants are compared; also justifies using FEMM instead for fiddly shim shapes.

It is a public access code (it's free), maintained under contract with DOE by Los Alamos National Accelerator Laboratory (LANL) personnel.

Tanabe, Iron Dominated Electromagnets, Lecture 4: POISSON — A Two-Dimensional Magnetostatic Solver (2005) — p. 2-4

Tabletop: Free tool that runs on a PC and is the same code the Houghton thesis used - the standard amateur path to pole-profile design.

nptc=31 means number of points on the circle, rint=20 means interpolation on 20 mm radius arc, rnorm=25 means multipole normalization at 25 mm ... nterm=14 means the maximum number of multipole terms.

Tanabe, Iron Dominated Electromagnets, Lecture 4: POISSON — A Two-Dimensional Magnetostatic Solver (2005) — p. 7

Tabletop: Turns a simulation into the same harmonic numbers you get from a measured field map, so simulation and Hall-probe map can be compared directly.

nbsup, nbslo, nbsrt and nbslf means the boundary condition at the upper, lower, right hand, and left hand boundaries. = 0 means Dirichlet (flux parallel) and =1 means Neumann (flux perpendicular) boundaries.

Tanabe, Iron Dominated Electromagnets, Lecture 4: POISSON — A Two-Dimensional Magnetostatic Solver (2005) — p. 8

Tabletop: Halves the mesh and run time for the symmetric H-frame cross-section the builder would model.

The iron yoke area uses mat=2, which uses the BH curve for a 'generic' iron whose magnetic properties approximate the behavior of 1010 steel.

Tanabe, Iron Dominated Electromagnets, Lecture 4: POISSON — A Two-Dimensional Magnetostatic Solver (2005) — p. 9

Tabletop: Removes the main excuse for not simulating: home-built yokes are usually A36/1018 mild steel and the default curve is close enough for first-pass design.

Note that all regions must close, that is the first and last coordinates are equal ... Negative currents in the right hand coil gives positive flux on the horizontal centerline.

Tanabe, Iron Dominated Electromagnets, Lecture 4: POISSON — A Two-Dimensional Magnetostatic Solver (2005) — p. 9

Tabletop: The two mistakes that make a first POISSON run fail; also shows amp-turns (not turns and amps separately) are what the model needs.

efficiency ~ 0.98 For magnets with well designed yokes.

Tanabe, Iron Dominated Electromagnets, Lecture 6: Excitation, Coil Design, System Design and Water Flow (2005) — p. 4-6, 12

Tabletop: Lets the builder size a next machine's amp-turns to ~2% accuracy with hand arithmetic before any FEA.

It is necessary to add a small weld bead, electrically connecting all the laminations. The core can then be grounded to a single ground point.

Tanabe, Iron Dominated Electromagnets, Lecture 8: Core Fabrication, Assembly, Installation and Alignment (2005) — p. 23

Tabletop: Single-point grounding of the yoke also matters on a solid-core machine carrying RF and HV nearby - one deliberate ground, no accidental loops.

The electrical bussing connection creates a loop around the beam line, resulting in a small solenoidal field... the in and out conductors should be placed close to each other.

Tanabe, Iron Dominated Electromagnets, Lecture 8: Core Fabrication, Assembly, Installation and Alignment (2005) — p. 24-26

Tabletop: Cheap to get right on a next machine: dress the coil leads as a twisted/adjacent pair and keep supply cables from encircling the chamber.

Magnet alignment specifications... typically call for < +250 um precision transversely and vertically and < +500 um longitudinally... The cost of retrofit is high.

Tanabe, Iron Dominated Electromagnets, Lecture 8: Core Fabrication, Assembly, Installation and Alignment (2005) — p. 3, 27

Tabletop: For a single-magnet cyclotron the numbers relax, but the lesson holds: machine reference flats and leveling features into the next machine's yoke before assembly.

A true kinematic support system must have at least and at most six linearly independent supports.

Tanabe, Iron Dominated Electromagnets, Lecture 8: Core Fabrication, Assembly, Installation and Alignment (2005) — p. 38-41

Tabletop: A next machine's stand with three adjustable feet plus lateral stops gives repeatable leveling of the median plane without fighting a warped frame.

Solid iron yokes are often used in simple, flat pole contour magnets.

Tanabe, Iron Dominated Electromagnets, Lecture 8: Core Fabrication, Assembly, Installation and Alignment (2005) — p. 4-5

Tabletop: Settles the question for a next machine: a one-off DC cyclotron magnet should be solid steel; laminations buy nothing at quantity one.

The BH characteristics of iron are variable and depend on the chemistry of the iron (dominated by the Carbon content, which is highly variable from heat to heat).

Tanabe, Iron Dominated Electromagnets, Lecture 8: Core Fabrication, Assembly, Installation and Alignment (2005) — p. 7, 9

Tabletop: Practical purchasing rule: buy a next machine's pole and yoke stock as one lot from one heat, and expect top/bottom asymmetry if pieces come from different sources.

IV > 150 V-Amperes or I > 30 Amps or V > 130 Volts or when the magnet stored energy is > 5 joules.

Tanabe, Iron Dominated Electromagnets, Lecture 9: Coil Fabrication, Testing and Electrical Safety (2005) — p. 12-13

Tabletop: The reference machine's magnet exceeds several of these thresholds; a simple sheet-metal or polycarbonate coil cover including the hot cooling fittings brings the machine to lab-standard electrical safety.

Shimming of pole edges or shims based on equation: dB(r)/B(r) = gamma(r)^2 * df_p(r)/f_p(r)

Zaremba, Magnets for Cyclotrons (2005) — p. 10

Tabletop: At 160 keV-1 MeV gamma ~ 1.0002-1.001, so isochronism errors are dominated by mechanical field errors, not relativity - this formula converts the reference machine's measured phase-slip vs radius directly into required shim thickness profile.

The maximum kinetic energy T determines magnetic rigidity: B*rho = sqrt(T^2+2T*E0)/(300*Z)

Zaremba, Magnets for Cyclotrons (2005) — p. 19

Tabletop: For 1 MeV protons B*rho = 0.145 T*m: at 1 T that is a 14.5 cm final orbit radius, which immediately sizes the next machine's pole diameter (with overhang and fringe allowances added).

small gap: reduced number of At of coils, pole radius reduced, orbits close to outer edge; large gap: large space: injection, extraction, probes, easier vacuum pumping

Zaremba, Magnets for Cyclotrons (2005) — p. 22

Tabletop: Frames the central tradeoff for a next machine: shrinking the reference machine's gap raises B for the same 538 turns, but everything (dee aperture, ion source, probe) must still fit and pump through it.

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

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

Tabletop: The most common amateur failure mode is a magnet that works but leaves no port for the probe or pump; run this five-item checklist on every layout iteration for a next machine.

coil cooling estimation: dT(C) = 60*P(kW)/(4.19*N(l/min))

Zaremba, Magnets for Cyclotrons (2005) — p. 30-32

Tabletop: The cooling formula is immediately usable: a next machine's 5 kW coil at 4 L/min runs ~18 C water rise; the flutter formulas matter only if the builder adds sector (AVF) pole faces.

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

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

Tabletop: If a next machine goes AVF to escape the weak-focusing energy ceiling, these are proven starting numbers: 3 or 4 sectors, half-open valleys, and a modest nu_z ~ 0.2 target.

calculation results and measurements differ less than 3 percent

Zaremba, Magnets for Cyclotrons (2005) — p. 4, 35

Tabletop: The reference machine's Poisson/FEMM workflow is the professional one; a >3% mismatch between model and Hall-probe map means the model geometry or BH data is wrong, not the method.

Achieving the following homogeneity values is reasonable but nevertheless challenging. Dipole: dB/B0 <= 0.01%

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 10

Tabletop: A useful upper bar; a weak-focusing cyclotron deliberately wants a controlled radial gradient, but azimuthal variation should be held near this level to avoid a first harmonic.

The total required aperture size is the sum of the good field region, the vacuum chamber thickness (0.3-2 mm) and a margin for installation and alignment (0-5 mm).

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 14

Tabletop: Explains why the pole gap must exceed the chamber's internal height by a centimetre or so; useful when trading gap (and hence amp-turns) against chamber wall thickness.

where h is the magnet gap height in [m] ... eta is the efficiency (typically 99%), mu_0 is the permeability of free space ... Note that Eq. (5) is only approximate and neglects fringe fields and iron saturation.

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 15

Tabletop: First-cut sizing for a next machine: at a 2 cm gap and 1.0 T you need ~8000 A-turns per pole, which sets conductor/current density before any FEMM run.

It is good practice to keep the iron yoke reluctance smaller than a few per cent of air reluctance ... such that the magnetic flux in the iron remains smaller than 1.5 T ... the efficiency is better than 99%.

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 15

Tabletop: The single most useful yoke-sizing rule for an H-frame homebuilt magnet: pick return-leg area = flux/1.5 T and the magnet behaves predictably.

l_mag = l_iron + 2hk ... Typical values of k are between 0.3 and 0.6. A precise determination of k is only possible with measurements or numerical calculations.

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 16

Tabletop: Quantifies the fringe-field bulge at the pole edge - the region where a tabletop cyclotron's outermost orbits actually live.

Total flux in the return yoke is Phi = integral B da ~= B_gap (w + 2h) l_mag ... where h is the gap height and w the pole width.

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 17

Tabletop: For an 8-inch pole with a 1-inch gap this says design the yoke for ~25% more flux than the naive pole-area estimate.

U_magnet = U_gap + 2 U_coil + U_yoke = B^2/(2 mu_0) (V_gap + 2 V_coil/6 + (1/mu_r) V_yoke)

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 18

Tabletop: Tells you the inductance and therefore how fast a bench supply can ramp the magnet and how big the flyback/crowbar protection must be.

Typically, the dipole produces a gradient across the pole of 0.1% with respect to the central field ... the window-frame design provides a very homogenous field quality even without shims.

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 18-20

Tabletop: Validates the reference machine's H-frame choice for a cyclotron (two-fold symmetry, lighter than a C) and warns that shimming will still be needed.

Sheet thickness 0.3 <= t <= 1.5 mm ... Coercivity Hc < 65 A/m ... Coercivity spread dHc < +/- 10 A/m

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 23

Tabletop: For a DC cyclotron magnet solid mild steel is fine, but this gives the numeric target for 'good' steel and explains why scrap-plate yokes vary.

In normal operation, the magnet is always cycled to its maximum value, irrespective of the required field, to ensure that hysteresis effects are reproducible.

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 26

Tabletop: Free operational fix for run-to-run field shifts in a home cyclotron - important because resonance is set by B and the beam vanishes on a few-gauss error.

l_avg = pole perimeter + 8 x clearance between pole and coil + 4 x coil width

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 27, 33

Tabletop: Gives copper length, hence resistance and power, straight off a sketch - exactly what a garage builder needs before ordering tubing.

the maximum current density for voluminous coils which are almost entirely enclosed in the magnet yoke should not exceed 1 A/mm2 ... The current density in direct water-cooled coils can be typically as high as 10 A/mm2.

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 28-29, 31

Tabletop: The reference machine's 538-turn solid copper tubing coils sit in the air-cooled regime; this rule says they must stay under ~1-2 A/mm^2 unless they switch to hollow conductor with water flow.

The velocity of the cooling medium ... should be sufficiently high to guarantee a turbulent flow but low enough (u_avg <= 5 m/s) to avoid erosion and vibration. A maximum permitted temperature of less than 60 C on the coil surfaces was found to be good practice.

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 31

Tabletop: Gives hard numbers for a home chilled-water loop: exceed 5 m/s and you erode the tubing; exceed 60 C and the insulation ages fast.

Q_water = 2.388 x 10^-4 P/dT ... d = 5.59 x 10^-3 (P/(dT Kw))^0.368 (l/dp)^0.21

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 32-34

Tabletop: Lets the builder compute the hollow-conductor bore and pump requirement for a next machine's 5-20 kW magnet with a spreadsheet, no CFD.

NI_dipole = Bh/(eta*mu0), where the magnet efficiency, eta... The magnet efficiency for a well designed yoke is eta >= 98%.

Tanabe, Iron Dominated Electromagnets: Design, Fabrication, Assembly and Measurements — SLAC-R-754 (2005) — p. 116-117, 129

Tabletop: One-line check of the reference machine's 538 turns: at 0.59 T and their gap this formula predicts the required current within a couple percent if the H-frame iron is unsaturated; a measured efficiency well below ~95% signals a saturated or gappy flux path.

The BH relationship becomes highly nonlinear at B >= 1.5 Tesla and the material exhibits fully saturated behavior at B >= 2.0 Tesla.

Tanabe, Iron Dominated Electromagnets: Design, Fabrication, Assembly and Measurements — SLAC-R-754 (2005) — p. 249-251

Tabletop: Sets the iron budget for the next machine: yoke and pole cross-sections should be sized so flux density stays under ~1.5 T anywhere on the return path, and pole-tip fields much above 1.8 T are not worth chasing with iron.

At high fields, the top of the pole can saturate. The right hand figure illustrates a tapered pole which is wider at the top... a radius at the pole corner, reducing this magnetic flux stress concentration.

Tanabe, Iron Dominated Electromagnets: Design, Fabrication, Assembly and Measurements — SLAC-R-754 (2005) — p. 251-252

Tabletop: Cheap insurance for the next machine's pole design: a root taper and corner radius cost one lathe operation and keep the field map valid from low current to full excitation.

A general rule of thumb is that the length of the fringe field beyond the edge of the steel pole tip is = h, = h/2, or = h/3, for the dipole, quadrupole or sextupole

Tanabe, Iron Dominated Electromagnets: Design, Fabrication, Assembly and Measurements — SLAC-R-754 (2005) — p. 252-253

Tabletop: Tells the builder where their usable field really stops on an 8 inch pole: with a ~2 inch gap the field is already dying ~1 inch inside the pole edge, which sets the practical maximum orbit radius and extraction geometry.

The angle of the cut is unimportant. However, a 45 degree angle cut is convenient and distributes the same angle at two points and minimizes saturation effects due to the sharp corners.

Tanabe, Iron Dominated Electromagnets: Design, Fabrication, Assembly and Measurements — SLAC-R-754 (2005) — p. 253-254

Tabletop: If the next machine's pole edge is chamfered or radiused to soften the field falloff for extraction, use ~45 degrees and bolt-on machinable end pieces so the shape can be iterated (Tanabe converged in two iterations on SPEAR3).

the field quality can be improved by adding smooth bumps near the edge of the pole, causing the flow lines to squeeze through a narrower gap

Tanabe, Iron Dominated Electromagnets: Design, Fabrication, Assembly and Measurements — SLAC-R-754 (2005) — p. 63-65

Tabletop: The classic Rose-shim trick: a machined or stacked-shim ring at the edge of the 8 inch poles buys field uniformity (and hence more usable radius) far more cheaply than a bigger magnet.

The canonical expressions... are used to estimate the amount of pole overhang required to achieve a desired field quality... for both unoptimized and optimized pole contours.

Tanabe, Iron Dominated Electromagnets: Design, Fabrication, Assembly and Measurements — SLAC-R-754 (2005) — p. 64-66

Tabletop: Directly sizes how much of the reference machine's 8-12 inch pole diameter is usable good field; e.g. for dB/B=1e-3 an unoptimized pole needs ~1.6 half-gaps of extra pole beyond the outermost useful orbit.

the radial sector poletips have the greatest average falloff - so great that it amounts to be an unusable field. The spiral sector AVF field is a compromise between the two.

Koeth & Krutzler, Field Mapping in Cyclotron Magnets (2015) — p. 10

Tabletop: Direct guidance for a next machine's pole-tip upgrade at the 8-12 inch scale; also warns that narrow spiral vanes saturate at large radius (measured field fell below simulation).

this analysis approach can be used to quickly assess a field during design, relegating the laborious task of phase space mapping and determining the limits of stability to the few the final contenders.

Koeth & Krutzler, Field Mapping in Cyclotron Magnets (2015) — p. 10-11

Tabletop: A cheap, quantitative design filter that works from measured maps of a home-built magnet, no orbit code required.

The aggregate of lead screw pitch and motor resolution correlates to 800 steps per inch. To further minimize the potential for backlash, field measurements are only made while stages are moving in the 'forward' direction.

Koeth & Krutzler, Field Mapping in Cyclotron Magnets (2015) — p. 2

Tabletop: A 1/800 inch (0.03 mm) grid is more than enough for an 8-12 inch pole and is buildable from surplus stepper/leadscrew parts.

There are field profile differences in excess of 1% between zero of half-second dwell times. However, there is no measureable difference between dwell times of 2.5 and 2.0 seconds.

Koeth & Krutzler, Field Mapping in Cyclotron Magnets (2015) — p. 3

Tabletop: Directly applicable: any DIY gaussmeter-plus-stepper mapper on an 8-inch magnet needs this calibration or the map carries 1% systematic error.

Four needles were used to scale both dimensions; the fifth needle was used to break the symmetry, removing orientation ambiguities.

Koeth & Krutzler, Field Mapping in Cyclotron Magnets (2015) — p. 3-4

Tabletop: Trivially cheap (iron nails plus a few turns of magnet wire) and it ties the field map to the mechanical chamber center, which is what you actually need for placing the ion source and target.

After 1600 travel manipulations were executed by 2.4 million motor steps, the probe carriage reproducibly returned back to the distal point within the digital dial indicator's resolution of 0.0000 inches

Koeth & Krutzler, Field Mapping in Cyclotron Magnets (2015) — p. 4

Tabletop: Cheap insurance: an afternoon of cycling the homemade stage validates every field map you take afterwards.

the sequence of standard deviations was fit to a parabola from which the minimum standard deviation, i.e. the center locations, could be inferred ... the centers of each measurement circle were found to be coincident to 10-4.

Koeth & Krutzler, Field Mapping in Cyclotron Magnets (2015) — p. 5-6

Tabletop: Exactly the analysis the builder needs for a symmetric-pole next machine: it also tells you how far the magnetic center sits from the mechanical center of the chamber.

we choose a reference circle to have a radius half that of the maximum ion radius ... the reference circle is swept to maximize the 4th harmonic, while minimizing the second, third, and fifth.

Koeth & Krutzler, Field Mapping in Cyclotron Magnets (2015) — p. 6-7

Tabletop: Applies if a next machine moves to sectored pole tips; on a 12-inch machine the whole analysis is a spreadsheet/Octave job on the map you already took.

ferromagnetic materials lose their advantages above their saturation field (typically 2 T).

Humphries, Principles of Charged Particle Acceleration (1986) — p. 104, 108

Tabletop: Defines the absolute ceiling of the iron-magnet approach for a next machine (~1.6-1.8 T practical); beyond that only superconductors or air-core help.

production of a field of 1 T in a gap with a 0.02 m spacing requires 16-kA turns (160 turns of wire if a 100-A supply is available).

Humphries, Principles of Charged Particle Acceleration (1986) — p. 111

Tabletop: Numerically the same worked example the builder needs: their 538 turns at ~30 A across ~5 cm predicts ~0.4 T ideal - the shortfall vs measured maps the iron's contribution.

The vertical field magnitude decreases away from the magnet over a scale length comparable to the gap width.

Humphries, Principles of Charged Particle Acceleration (1986) — p. 140, 526

Tabletop: Rule of thumb for a next machine's layout: reserve roughly one gap-height of radius at the pole edge as unusable fringe, and shield any deflector with a grounded septum.

fx = (gamma mo vz/qBo)/tan beta = rgo/tan beta.

Humphries, Principles of Charged Particle Acceleration (1986) — p. 141

Tabletop: If a next machine ever extracts a beam, angling the magnet exit edge focuses the diverging beam without any extra magnet.

The bending magnets were shaped to produce a field with index in the range 0 < n < 1.

Humphries, Principles of Charged Particle Acceleration (1986) — p. 159, 521

Tabletop: The outer bound that pairs with Koeth's n<0.2 refinement: the reference machine's field must fall (n>0), but slowly, all the way to full radius.

Tmax = 48 (Z RB)2/A, where Tmax is given in MeV, R in meters, and B in tesla.

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

Tabletop: The master sizing formula: the reference machine's 0.59 T at ~0.09 m gives ~135 keV; 1 MeV needs (R*B) ~ 0.144 T-m, e.g. 1.2 T at 12 cm.

Have real sinusoidal solutions for 0<n<1; this condition is true in a classical cyclotron

Antaya, Cyclotron Basics — MIT 8.277, Unit 10, Lecture 14 (2010) — p. 36-37

Tabletop: Confirms the reference machine's flat-pole H-frame inherently provides weak focusing from its natural radial falloff - the design task is controlling how fast n rises, not creating it.

Almost (but not quite) spherical: Efficient cyclotron magnetic circuits include more iron laterally than axially

Antaya, Cyclotron Basics — MIT 8.277, Unit 10, Lecture 14 (2010) — p. 48-50

Tabletop: The B^2 energy leverage argues for pushing the next machine's field toward the iron limit (~1.5-1.8 T) before enlarging poles: doubling B quadruples energy at fixed radius while iron mass stays fixed.

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

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

Tabletop: Directly actionable option for a next machine: targeting 0.89 T instead of 0.59 T puts the machine on the 13.56 MHz ISM band where used generators, amplifiers, and matchboxes are plentiful and legal.

A radially decreasing field can be described as Bz = B0(r0/r)^n for n >= 0, where n = 0 implies a uniform field and n > 0 implies a restoring force.

Chun, The Cyclotron Magnet and RF Oscillator (2003) — p. 7-9

Tabletop: Exactly the reference machine's problem class and size: machine a gentle crown or stepped 'lump' into the 8-inch poles (or shim equivalently) targeting ~2-3% center-to-edge fall-off for axial focusing.

a pole piece with a flat surface at the edge with a thickness sufficient for the screws and a kind of lump in the middle with a flat top

Chun, The Cyclotron Magnet and RF Oscillator (2003) — p. 8

Tabletop: Directly applicable fabrication pattern for a next machine's contoured pole caps that still bolt on.

For educational applications a six to nine-inch pole piece is an economical range; for inducing light element reactions ... a somewhat larger machine, say, 12 to 15 inches

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 11-12

Tabletop: Directly frames the next machine's decision: staying at 8 inches keeps it a demonstration machine; nuclear-reaction goals argue for 12-inch-class poles and higher field.

Ampere-Turns = 2.02 x gauss x inches gap

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 13

Tabletop: Directly applicable; e.g. 5900 G x 2 in gap needs ~24,000 A-turns before iron reluctance and leakage corrections.

Lbs. force on conductor = 1/1750 x kilogauss x amperes x inches length; Lbs. force between pole faces = 1/1.735 (kilogauss)^2 x (inches^2 area)

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 13

Tabletop: Directly applicable: at 5.9 kG on 50 in^2 poles that is ~1000 lb of attraction a next machine's bolts and spacers must carry.

most soft irons begin saturating in the vicinity of 16 kilogauss, though some may be operated as high as 21 kilogauss

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 2

Tabletop: Directly applicable; the reference machine's 0.59 T (5.9 kG) gap field leaves large iron margin, so a next machine could roughly double the field before core saturation dominates.

Ratio Gap Height/Gap Diameter ... Multiplying Factor: 1/2 -> 2; 1/4 -> 1.5; 1/10 -> 1.2, region of small cyclotrons

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 2

Tabletop: Directly applicable sizing rule: for an 8-inch pole with ~1.5-2 inch gap (h/D ~ 1/4), design coils and yoke for ~1.5x the gap flux.

the length of the pole cores and the distance from pole cores to return yokes is at least twice and preferably three times the gap height

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 3

Tabletop: Directly applicable to a next machine's H-frame; coil space usually forces compliance automatically, but check it when shortening the frame.

the return yoke must accordingly be designed so that its total cross sectional area is a good deal greater than that of the cores, say, at least 25 percent greater

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 3

Tabletop: Directly applicable: for 8-inch (50 in^2) cores, provide >= 63 in^2 of total yoke steel around the flux return path.

It is important that the contact surfaces between yoke pieces and between yoke and pole cores be flush to eliminate additional air gaps

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 3

Tabletop: Directly applicable; a few thousandths of an inch of unintended air gap is a noticeable fraction of a small machine's ampere-turn budget.

top and bottom of the vacuum chamber should be thin, circular steel plates ... to decrease the magnetic gap as much as possible. To prevent field bypassing, the tank wall must be non-magnetic, preferably brass

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 5

Tabletop: Directly applicable chamber architecture for a small machine; every millimeter of chamber wall inside the gap costs ampere-turns.

it is advantageous to keep the gap between the magnet poles small. This tight spacing made the design of the vacuum chamber more difficult, but it was essential.

Baumgartner, The Cyclotron Kids' 2 MeV Proton Cyclotron — Cyclotrons 2013, WE1PB05 (2013) — p. 1-2

Tabletop: The central trade for a next machine: every millimeter of gap saved is field (and energy ~B^2) for free.

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

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

Tabletop: The reference machine's 0.59 T machine resonates at ~9.0 MHz; any next machine's field choice instantly fixes the oscillator/tank tuning range via this 15.23 MHz/T constant.

Increased cross section reduces flux through yoke to 1.2T

Baumgartner & Heuer, The Cyclotron Kids 14-Inch Accelerator (2010) — p. 8

Tabletop: Simple area-ratio rule the builder can apply when welding a next machine's frame from surplus plate: yoke area ~ 1.3-1.5x pole area keeps 1010-grade steel comfortably linear.

Slight taper on pole applies a corrective Lorenz force to the beam. Made with freeware! Poisson Superfish

Baumgartner & Heuer, The Cyclotron Kids 14-Inch Accelerator (2010) — p. 8

Tabletop: Confirms the standard amateur approach for the reference machine's scale: put the field index into the pole profile (taper/gap growth with radius) rather than relying on accidental fringing.

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

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

Tabletop: An existence proof at exactly the reference machine's energy: modest dee voltage (1-2 kVpp), 1e-5 torr, and a machined pole profile suffice below ~300 keV; heroic RF and UHV are not prerequisites.

1st successful operation was recorded by slowly sweeping B-field to locate resonance condition. September 16, 1999

Koeth et al., The Rutgers 12-Inch Cyclotron for Students (2010) — p. 8

Tabletop: The standard commissioning move for a next machine: B-field is the easy knob to sweep since the RF stays matched at fixed frequency.

the field index value n=0.2 must not occur inside the maximum ion orbit radius to avoid coupled resonances

Morrow, Focusing in the Houghton College Cyclotron — Houghton College thesis (2015) — p. 2, 39

Tabletop: This is the single design criterion for weak-focusing pole shaping on a 100 keV-1 MeV tabletop machine; it is computable from a measured B(r) curve.

the magnetic field changes too quickly near the edge of the shim. This is a result of making the shim too thick.

Morrow, Focusing in the Houghton College Cyclotron — Houghton College thesis (2015) — p. 25, 44, 46

Tabletop: Warns the builder off the obvious first shimming attempt; the useful shims are thinner than are convenient to fabricate and hold in place.

weak magnetic focusing can be achieved by producing a magnetic field in which Bz linearly decreases.

Morrow, Focusing in the Houghton College Cyclotron — Houghton College thesis (2015) — p. 26-27

Tabletop: Gives a single, plottable acceptance test for a shimming attempt on the reference machine's 8-inch poles - no orbit code needed to reject a bad shim.

the magnetic field actually increases in magnitude out to around r = 5 cm at which point it begins decreasing again. This is problematic because it yields a negative field index

Morrow, Focusing in the Houghton College Cyclotron — Houghton College thesis (2015) — p. 51-53

Tabletop: A concrete trap when adding any iron or coil near the center of an 8-inch pole; check the sign of dB/dr everywhere, not just at the edge.

the difference in radius is minimal - about 0.2 cm - and comes at the steep cost of a ~20% reduction in maximum magnetic field from 1.27 T to 1.07 T. As such, this modification was considered insufficient.

Morrow, Focusing in the Houghton College Cyclotron — Houghton College thesis (2015) — p. 53-54

Tabletop: Saves a next machine's builder from spending months on trim coils inside a small gap; also note trim coils steal gap height.

As the vacuum chamber radius is 2.2 cm larger than the radius of the magnet poles, these lids act as wide pole faces that draw the magnetic field lines out to larger radii.

Morrow, Focusing in the Houghton College Cyclotron — Houghton College thesis (2015) — p. 54-55

Tabletop: The highest-leverage cheap upgrade in this batch: swapping aluminium chamber lids for steel roughly doubles theoretical proton energy on a machine essentially identical to the reference machine's.

Pole face: 150mm, Pole gap: 39mm, Current: 70A ;NOTE: this is a slice down the middle of the magnet

Morrow, Focusing in the Houghton College Cyclotron — Houghton College thesis (2015) — p. 60-68

Tabletop: Zero-cost simulation path for a hobbyist; the appendix geometry file is a working starting template for an 8-15 cm pole magnet.

much of the beam current is being lost by the time the beam reaches larger radii... This could be done by adding shims of ferromagnetic material between the chamber and pole faces.

Fuller, Exploring the Capabilities of the Houghton College Cyclotron — Houghton College thesis (2013) — p. 52-53

Tabletop: Predicts the current-vs-radius profile the builder should measure, and the standard shim fix if a next machine loses beam before full radius.

once the iron magnet poles become saturated (at about 2 T) the maximum energy is determined by R

Loucks, Initial Results from the Houghton College Cyclotron — Houghton College thesis (2007) — p. 18

Tabletop: Frames the next machine's tradeoff space: pushing the reference machine's 0.59 T toward 1.2-1.5 T is cheap energy gain (E ~ B^2), but above ~1.8 T iron stops helping and only pole diameter buys more.

the value of n for the cyclotron must be between 0 and 1; it has been determined empirically the index should increase with r roughly linearly between 0 and 1

Loucks, Initial Results from the Houghton College Cyclotron — Houghton College thesis (2007) — p. 21-23

Tabletop: The core magnet-shimming target for the next machine: map B(r) with a Hall probe, compute n(r) by finite differences, and add edge shims until n(r) is a clean 0-to-1 ramp over the dee radius.

the maximum field is limited by available water cooling and the power supply... To achieve the maximum field, using 70 A, the magnet requires 6.1 L/min

Loucks, Initial Results from the Houghton College Cyclotron — Houghton College thesis (2007) — p. 35-36

Tabletop: Do the L/min bookkeeping for the whole next machine (magnet + diffusion/turbo + RF amp) before buying a chiller; the cooling loop is a first-class design constraint, not an afterthought.

the dBz/dr term was approximated by dBz/dr, where dr is the difference between two radii (1 cm)

Loucks, Initial Results from the Houghton College Cyclotron — Houghton College thesis (2007) — p. 36-38

Tabletop: A directly copyable measurement rig for a next machine's field map: rotating grooved aluminum disc plus angular scale gives B(r,theta) with hardware the builder already owns.

With the chamber in place, the separation between the pole tips is 3.81 cm, giving a maximum magnetic field of 1.28 T at 70 A ... requiring 18 C water flowing at 0.8 gallons per minute (at 50A)

Yuly, The Houghton College Cyclotron: a Tool for Educating Undergraduates — Cyclotrons 2013, WE1PB01 (2013) — p. 2-3

Tabletop: A purchasable-magnet benchmark almost exactly at the reference machine's scale; the 0.8 gpm figure sizes a chiller for a ~kW-class coil.

12 inch diameter poles pieces forming a 4-inch gap to which upper and lower pole tips up to 1-inch thick can be easily attached and removed.

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

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

upper and lower pole tips up to 1-inch thick can be easily attached and removed - we currently have four sets of pole tips.

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

Tabletop: Probably the single best architecture decision the builder can copy: a next machine with bolt-on tips can iterate field profiles cheaply.

The magnet's upper and lower coils are independently energized enabling an intentional axial field imbalance so as to vertically shift the accelerating plane.

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

Tabletop: Cheap beam-height trim for a next machine: two supplies (or a shunt rheostat on one coil) instead of re-machining anything.

if n = 0.2 is to be avoided (vx=2vz), then the rate at which the vertical field decreases must be moderated such that n=0.2 occurs at the final ion radius.

Koeth, Undergraduate Education with the Rutgers 12-Inch Cyclotron (2015) — p. 3

Tabletop: The quantitative pole-taper design rule for a next machine: map n(r) from the field profile and keep 0 < n < 0.2 out to full beam radius.

The n=0.2 location occurs near r=3.5 inches, well within the 5 inch DEE radius, so as to allow the ion displacement to grow.

Koeth, Undergraduate Education with the Rutgers 12-Inch Cyclotron (2015) — p. 5

Tabletop: Shows how little margin there is between good and bad tapers on an 8-12 inch machine; motivates measuring n(r), not guessing it.

The axial tune... can be summarized by: vz2 = -k + F(1+tan2xi) and the radial tune is written as: vr2 = 1+k

Koeth, Undergraduate Education with the Rutgers 12-Inch Cyclotron (2015) — p. 6

Tabletop: If a next machine ever gets sector pole tips (to allow a rising average field), these two lines are the whole first-order design calculation.

The energized wire loop simply needed to be tossed towards the gap and it would reproducibly snap to the nearest stable orbit.

Koeth, Undergraduate Education with the Rutgers 12-Inch Cyclotron (2015) — p. 7

Tabletop: A zero-cost field-quality diagnostic the builder can run on the existing magnet this weekend.

F = ((<B^2> - <B>^2)/<B>^2) is called the flutter and represents the hill to valley field difference

Beeckman, Cyclotron Magnets — ECPM37 lecture, Groningen (2009) — p. 25-26

Tabletop: The complete design equation set for an AVF follow-on build; every term is measurable from a 2-D Hall-probe map of the built magnet.

N large: high maximum energy, F small and quasi circular orbits -> spiral compulsory

Beeckman, Cyclotron Magnets — ECPM37 lecture, Groningen (2009) — p. 26, 28

Tabletop: Explains when the extra machining pain of spiral tips pays off; at 8-12 inch pole size with N=4 a modest spiral is worth more than more sectors.

It implies that N must be larger than 2 (lower limit of the pi stop-band) and there is an energy limit for every N value T = (N/2 - 1)E0

Beeckman, Cyclotron Magnets — ECPM37 lecture, Groningen (2009) — p. 27-28

Tabletop: Rules out 2-sector 'butterfly' pole tips that look easy to machine; N=3 or 4 is the practical amateur choice and neither limits sub-MeV protons.

Constant gaps : B(r) naturally decreasing. The larger the gap, the stronger the decrease ... Coil field : B(r) naturally increasing. Important only when iron becomes saturated

Beeckman, Cyclotron Magnets — ECPM37 lecture, Groningen (2009) — p. 32

Tabletop: Explains the negative field index a flat-pole tabletop magnet already has - and why a bigger gap gives more weak focusing but less field.

Trim coils increase the gap ... Very weak except in superconducting machines ... Model it before implementing it to avoid unexpected effects

Beeckman, Cyclotron Magnets — ECPM37 lecture, Groningen (2009) — p. 33, 47

Tabletop: Settles the shim-vs-trim-coil question for a small warm magnet the same way the Houghton thesis did empirically: iron wins.

The iron shaping methods zoo: Change the ratio of hill/valley spanned angle with radius ... Prevent field decrease at large radii ... Decrease the gap along radius ... Lateral edges milling ... Iron inserts ... Change local saturation

Beeckman, Cyclotron Magnets — ECPM37 lecture, Groningen (2009) — p. 34-46

Tabletop: A ranked menu of things the builder can machine on 8-inch pole tips, each demonstrated on a real cyclotron; movable flaps in particular give post-build adjustability.

Laminated: Limited thickness : 300 mm max, usual 200 mm. Good magnetic and mechanical properties. Slight anisotropy.

Beeckman, Cyclotron Magnets — ECPM37 lecture, Groningen (2009) — p. 57

Tabletop: For an amateur the practical read is: mild-steel plate stock is fine for a DC magnet; note the anisotropy if you stack plate for pole tips.

small gap: reduced number of At of coils, pole radius reduced, orbits close to outer edge, no space, very sensitive to errors : vertical losses. large gap: large space: injection, extraction, probes, easier vacuum pumping, lower field

Beeckman, Cyclotron Magnets — ECPM37 lecture, Groningen (2009) — p. 65

Tabletop: Frames the central decision for a next machine (the reference machine's chamber must fit in the gap) with the actual list of consequences on both sides.

step0: Squeeze requirements and extract juice; step1: Get starting numbers from hand calculation; step2: 2d global model; step3: 3d global model; step4: 2d cuts for detailed local objects ... 2d calculations must be preferred.

Beeckman, Cyclotron Magnets — ECPM37 lecture, Groningen (2009) — p. 68

Tabletop: A workflow a solo builder can actually execute, and it puts pencil-and-paper (Zickler-style) sizing ahead of any software.

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

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

Tabletop: Shows the exact arithmetic used to go from a required <B> to hill/valley fields and sector angle - reusable at any scale.

CHOICE : nu_z = 0.2. Flutter and spiral not too large. Field gradient can be strong. Spiral angle of pole completely determined since n, N, F and nu_z are known

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

Tabletop: Gives a numeric focusing target to design toward instead of 'as much focusing as possible' - and 0.2 is achievable with weak focusing at the reference machine's energies.

the field B = mu0 nI/h is proportional to the total current in the solenoid, is inversely proportional to the magnetic gap and is independent on the pole surface, a rather counter-intuitive fact to most people.

Beeckman, Cyclotron Magnets — ECPM37 lecture, Groningen (2009) — p. 70-71

Tabletop: The core sizing identity for a home magnet: shaving the pole gap buys field for free, whereas making the poles bigger does not.

Steel (0.9% C) 50 / 1000; Iron (99.8%) 150 / 5000; Iron (99.95%) 10,000 / 200,000

Beeckman, Cyclotron Magnets — ECPM37 lecture, Groningen (2009) — p. 72-73

Tabletop: Concrete reason to buy A36/1018 low-carbon plate rather than whatever scrap steel is on hand for an H-frame yoke.

The 3D geometry is modelled with a 2D code in axisymmetry using pseudo-materials. The stacking factor is the proportion of the circle occupied by the real material. Each pseudo-material is defined by a modified B-H curve

Beeckman, Cyclotron Magnets — ECPM37 lecture, Groningen (2009) — p. 74

Tabletop: Lets a hobbyist study an AVF pole set in free 2-D codes (POISSON/FEMM) before committing to a 3-D solver.

YOU must be in control of the mesh, not the code. A limited amount of quadratic elements is much more effective to accuracy than many linear elements

Beeckman, Cyclotron Magnets — ECPM37 lecture, Groningen (2009) — p. 83

Tabletop: Explains noisy field-index curves out of a home simulation: n and nu_z are derivatives, so mesh quality matters far more than for B itself.

Is the rest of the universe far enough ? TEST IT! ... Codes are very good in the computation of small changes between 2 models but less good at absolute values.

Beeckman, Cyclotron Magnets — ECPM37 lecture, Groningen (2009) — p. 85-86

Tabletop: Practical simulation hygiene: use FEMM/POISSON to compare shim options (differences), and use the Hall probe for the absolute field.

The radial decrease in field strength is at a rate of one percent in 13 inches out to a radius of 20 inches ... These shims reduce azimuthal variations to less than 0.2%.

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 15, 35

Tabletop: The fractional numbers transfer, not the inches: aim for a smooth ~1-3% total field fall-off center-to-edge on the 8-inch pole and shim azimuthal asymmetry to the few-per-mille level.

The shims were machined from 2 1/4 in. steel plate on a vertical boring mill ... The magnetization curve taken at the center of the tank with the contour shims in place is also shown.

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 35

Tabletop: Directly applicable method: leave gap allowance for removable machined shim rings/plates so a next machine's field shaping is a measurement-and-remachining loop, not a magnet rebuild.

By means of auxiliary coils wound on the pole pieces it is possible to control the position of the beam with respect to the median plane of the tank.

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 35

Tabletop: Directly applicable and cheap for a next machine: a few dozen turns on one pole with a bipolar bench supply gives a knob for vertical beam centering instead of mechanical re-shimming.

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

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

Tabletop: Directly applicable: map the reference machine's H-frame fringe field with a hall probe and keep the LDMOS amplifier, its magnetics, and instrumentation outside the ~60 G contour.

The U-shape of the magnet gives direct access to the top of the vacuum chamber and permits the use of an overhead crane for transferring the assembled dee system.

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 7, 9

Tabletop: The principle (design the yoke around how you will service the chamber, not vice versa) is directly applicable to a next machine's H-frame layout.

a magnetic load of 1,055,000 lb and a vacuum load of 60,000 lb could be expected ... mating surfaces of pole bases and yoke pieces to be planes within 0.005 in. T.I.R.

Livingston & Howard (eds.), The Oak Ridge Relativistic Isochronous Cyclotron — ORNL-2648, OSTI 4275955 (1958) — p. 118

Tabletop: Direct transfer of tolerancing practice: face-grind a next machine's pole and yoke mating surfaces and check with a dial indicator; magnetic attraction, not atmosphere, is the structural design load.

The magnet is of a conventional closed-yoke design with a 1/1 ratio of pole base cross section to yoke cross section.

Livingston & Howard (eds.), The Oak Ridge Relativistic Isochronous Cyclotron — ORNL-2648, OSTI 4275955 (1958) — p. 118-119

Tabletop: Directly applicable: 1018/1010-class steel is the right iron for a next machine, and yoke area comparable to (Wouters says 25% above) pole area is the design corridor.

Approximately 1/8-scale model magnets were energized ... A complete grid of points 1/4 in. apart is thus obtained over the entire model.

Livingston & Howard (eds.), The Oak Ridge Relativistic Isochronous Cyclotron — ORNL-2648, OSTI 4275955 (1958) — p. 29, 31

Tabletop: Inverted for the builder: their whole magnet is model-sized, so a dense XY hall-probe map on a ~5 mm grid with attention to probe positioning and current regulation (the two dominant error terms) is the equivalent discipline.

The error due to probe position varies depending on the field gradient ... techniques available to us at this time fall short of the desired 0.1% accuracy.

Livingston & Howard (eds.), The Oak Ridge Relativistic Isochronous Cyclotron — ORNL-2648, OSTI 4275955 (1958) — p. 31

Tabletop: Directly applicable to a next machine's shimming: regulate magnet current (not just set it) while mapping, and index the probe mechanically, or the map noise will exceed the shim effects being measured.

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

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

Tabletop: The coupled optimization transfers: for a next machine, pick dee voltage and magnet gap together, since every kV of dee needs clearance that costs ampere-turns.

the design of the beam deflection system will be worked out simultaneously with the design of the magnet ... all the problems which arise from trying to obtain deflected beams after the machine is built would be avoided.

Livingston & Howard (eds.), The Oak Ridge Relativistic Isochronous Cyclotron — ORNL-2648, OSTI 4275955 (1958) — p. 85-86

Tabletop: Directly applicable lesson for a next machine: if an extracted beam is ever wanted, reserve the azimuthal slot, field-edge profile, and feedthrough ports now, even if the deflector comes later.

power varies inversely with volume of conductor, so to a first approximation it can be chosen at will ... a well-designed coil will have a 'packing ratio' greater than 0.5.

Livingston & Blewett, Particle Accelerators (1962) — p. 273-277

Tabletop: If a next machine's coils run hot, the fix is more copper, not more cooling: doubling conductor volume halves dissipation at the same ampere-turns.

The voltage breakdown strength of a resin-impregnated layer of glass cloth or cotton mesh is usually over 100 volts/mil ... necessary to utilize mica-sheet or mica-flake insulation to obtain the higher voltage-to-ground insulation.

Livingston & Blewett, Particle Accelerators (1962) — p. 278

Tabletop: Potting the reference machine's coils stops the slow insulation abrasion that coil hum causes; their low coil voltage means the resin-glass numbers alone give ample margin.

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

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

Tabletop: Two directly portable specs: DI-water loop quality for any hollow-conductor coil, and tight dee-water temperature control if a next machine water-cools the dee.

The circulating pumps and heat exchanger are sized to handle a 1000-kw heat load, with the normal operating load being about 300 kw.

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

Tabletop: For a next machine dissipating ~1-5 kW, buy the chiller/radiator rated for ~3x that; margin is what makes long runs boring.

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

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

Tabletop: Explains RF drift during long runs at the reference machine's power levels; cooling the tank coil stabilizes tune.

When properly cooled, our 1/4''x1/4'' hollow copper conductor can safely carry up to 120A. Allowing a margin of safety, we designed our magnet to operate at 110A.

Heuer & Baumgartner, Design of a 2 MeV Cyclotron (2009) — p. 32

Tabletop: Direct conductor rating for the exact class of hollow-conductor coil a next machine would use in place of the reference machine's refrigeration tubing.

Using this type of winding allows for a more uniform field than a simple spiral winding.

Heuer & Baumgartner, Design of a 2 MeV Cyclotron (2009) — p. 32-33

Tabletop: The reference machine's 538 turns of copper tubing could be rebuilt as ~10 potted double-pancakes per pole with a cooling manifold, easing fabrication and repair.

Our magnet can achieve a maximum temperature of 173 oF and will normally operate at no more than 142 oF.

Heuer & Baumgartner, Design of a 2 MeV Cyclotron (2009) — p. 33

Tabletop: Sets the thermal design point for any potted coil in a next machine; consistent with Tanabe's <30 C rise rule for long potted-coil life.

The value of number of turns (N) is chosen to match power supply and interconnection impedances.

Marks, Conventional Magnets for Accelerators — CAS lecture (2004) — p. 35-36

Tabletop: The reference machine's 538 turns were set by their supply; for a next machine, pick the surplus supply first, then wind N = NI_required/I_supply.

Power distribution cables... are generally limited to a current density of <1.5 to 2 Amps/mm2.

Tanabe, Iron Dominated Electromagnets, Lecture 6: Excitation, Coil Design, System Design and Water Flow (2005) — p. 21

Tabletop: The go/no-go line for whether a next machine's coil design can skip water cooling: at or below ~1.5 A/mm^2 in the copper, air cooling can suffice.

the optimum is flat and appears to be j=4 Amps/mm2. However, a higher design value (the canonical j=10 Amps/mm2 value) is generally chosen.

Tanabe, Iron Dominated Electromagnets, Lecture 6: Excitation, Coil Design, System Design and Water Flow (2005) — p. 29-30

Tabletop: For a home machine where power cost matters and coils are hand-wound, the ~4 A/mm^2 end of the range is the better choice; the reference machine's tubing coil runs even lower.

f = 64/Re for laminar flow Re < 2000. For turbulent flow (Re>4000), the friction factor is gotten by solving a transcendental equation.

Tanabe, Iron Dominated Electromagnets, Lecture 6: Excitation, Coil Design, System Design and Water Flow (2005) — p. 32-34

Tabletop: The complete hydraulic sizing recipe for any hollow-conductor or tubing-wound coil at the reference machine's scale.

Desirable temperature rise... < 10 deg. C. Maximum allowable temperature rise (assuming 20 deg. C. input water) < 30 deg. C for long potted coil life.

Tanabe, Iron Dominated Electromagnets, Lecture 6: Excitation, Coil Design, System Design and Water Flow (2005) — p. 40, 45

Tabletop: One-line flow-rate calculator: a 1 kW coil on a next machine needs ~0.4 gpm for a 10 C rise.

For water velocities > 15 fps, flow vibration will be present resulting in long term erosion of water cooling passage.

Tanabe, Iron Dominated Electromagnets, Lecture 6: Excitation, Coil Design, System Design and Water Flow (2005) — p. 42

Tabletop: Hard upper bound when the builder sizes pump and passage diameter for a next machine's hollow-conductor coil.

Pressure drop can be decreased by a factor of eight if the number of water circuits are doubled.

Tanabe, Iron Dominated Electromagnets, Lecture 6: Excitation, Coil Design, System Design and Water Flow (2005) — p. 47

Tabletop: Argues for manifolded pancake sub-coils on a next machine instead of one long series water path through 538 turns.

If the design hole diameter is increased, the required pressure drop is decreased dramatically. If the fabricated hole diameter is too small... pressure drop can increase substantially.

Tanabe, Iron Dominated Electromagnets, Lecture 6: Excitation, Coil Design, System Design and Water Flow (2005) — p. 48

Tabletop: When choosing hollow conductor for a next machine, err to the larger bore; also a reason to flow-test each pancake before potting.

A single water circuit in a coil assembly should be wound from a single continuous length of conductor. Splices 'buried' within the potted insulation should not be allowed.

Tanabe, Iron Dominated Electromagnets, Lecture 9: Coil Fabrication, Testing and Electrical Safety (2005) — p. 14-16

Tabletop: For a next machine wound from copper refrigeration tubing: buy one continuous coil per water circuit, keep the shop swarf away from the winding, and verify the bore is clear before the tubing is buried in the stack.

A sick coil will exhibit waveforms whose frequency and/or damping rate changes as the voltage increases or will exhibit hash at the peak of the damped sinusoid.

Tanabe, Iron Dominated Electromagnets, Lecture 9: Coil Fabrication, Testing and Electrical Safety (2005) — p. 17-24

Tabletop: A signal generator, capacitor and scope let the builder certify the next machine's coils before they are trapped under the yoke; also hipot potted coils at 2x operating voltage + 1 kV with < 2 mA/kV leakage.

Water flow calculations made for the preliminary design may be unreliable for a coil designed with many tight turns... due to the added flow impedance of tight radius turns.

Tanabe, Iron Dominated Electromagnets, Lecture 9: Coil Fabrication, Testing and Electrical Safety (2005) — p. 25

Tabletop: The reference machine's 538-turn tubing coil is exactly the many-tight-turns case; a bucket-and-stopwatch flow test at operating pressure is the real spec, not the straight-pipe pressure-drop formula.

Water hoses should be at least one meter long and use nonconducting material to prevent current leakage from the magnet.

Tanabe, Iron Dominated Electromagnets, Lecture 9: Coil Fabrication, Testing and Electrical Safety (2005) — p. 3

Tabletop: The reference machine's water-cooled copper-tubing coil sits at supply potential; a meter of plastic hose per lead and interlock-on-return are exactly the cheap practices that prevent shocks and detect a blocked circuit at home scale.

The normal set-point of Klixons is about 89 C... One thermal interlock is installed on each water circuit.

Tanabe, Iron Dominated Electromagnets, Lecture 9: Coil Fabrication, Testing and Electrical Safety (2005) — p. 5-6

Tabletop: A $5 thermal snap-switch soldered to the coil exit tube, in series with the magnet supply enable, is the single best protection against cooking the next machine's winding on a lost-water event.

Inter-turn insulation thickness is normally between 0.3 mm and 1.0 mm, the ground insulation thickness should be between 0.5 mm and 3.0 mm depending on the applied voltage.

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 28-29

Tabletop: Sets realistic packing-factor expectations for a hand-wound 538-turn coil and how much window the insulation eats.

For a bending radius of three times the conductor width we can expect a keystoning of 3.6% ... we can ignore the effect of keystoning by systematically choosing a bending radius four times larger than the conductor width.

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 30

Tabletop: Directly applicable to bending copper tubing for a 538-turn homemade coil: tight bends also pinch the cooling bore and risk insulation damage.

An aspect ratio of c:b between 1:1 and 1:2 should be chosen, and the packing factor fc somewhere between 0.6 and 0.8.

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 33

Tabletop: Turns the amp-turn number into an actual coil window size before you buy tubing or start winding.

This implies that for a given flow, the pressure drop is reduced by a factor of eight by doubling the number of cooling circuits.

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 33

Tabletop: Explains why splitting a big coil into 2 or 4 hydraulic circuits lets a modest garage chiller pump do the job.

Water resistivity higher than 0.1x10^6 Ohm m; pH-value between 6 and 6.5; dissolved oxygen below 0.1 ppm

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 34

Tabletop: If a next machine uses water-cooled coils at high voltage, tap water will leak current and corrode; a small DI cartridge loop is the fix.

power distribution cables are convectively cooled and are limited to <= 1.5 Amps/mm2

Tanabe, Iron Dominated Electromagnets: Design, Fabrication, Assembly and Measurements — SLAC-R-754 (2005) — p. 128-129

Tabletop: The reference machine's copper-tubing winding at 538 turns: if any leg of the circuit (bus, jumper, lead) runs above ~1.5 A/mm^2 without water flow it will run hot; size leads accordingly.

Normally, a good value for the current density is j = 10 Amps/mm2 for water cooled coils... The value of the packing fraction is typically f ~ 0.5 for small conductors.

Tanabe, Iron Dominated Electromagnets: Design, Fabrication, Assembly and Measurements — SLAC-R-754 (2005) — p. 129

Tabletop: Lets the builder size a next machine's coil cross-section on one sheet of paper: gross coil area ~ NI/(j*f) = NI/5 in mm^2 for water-cooled copper.

Flow velocity v <= 4 m/sec to avoid flow vibration and erosion... An acceptable coil temperature rise which protects the coil epoxy encapsulation from damage is dT <= 30 C.

Tanabe, Iron Dominated Electromagnets: Design, Fabrication, Assembly and Measurements — SLAC-R-754 (2005) — p. 134-135

Tabletop: Direct water-cooling design window for a next machine's hollow-conductor coil; also warns that a lazy laminar-flow circuit cools far worse than the handbook film coefficient suggests.

Kilowatt-Tons = (0.118)Cu (Mega-ampere turns)^2 (inches mean turn length)

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 13

Tabletop: Directly applicable trade study tool: the product of coil dissipation and coil weight is fixed by NI and geometry, so more copper always buys less heat.

The coils should be wound so that they occupy approximately a rectangular cross section around the poles ... Either too flat or too tall a coil intercepts more leakage flux and thus wastes turns.

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 3

Tabletop: Directly applicable guidance for a next machine's coil geometry.

operate close-wound naturally air-cooled coils at a current density not exceeding 750 amps per square inch of conductor area. For intermittent operation this may be raised to 1000 amps per sq. in.

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 3

Tabletop: Directly applicable thermal sizing rule for a next machine's magnet coils.

Most coil designs favor large conductor areas and correspondingly high amperages; this reduces total voltage and simplifies both the insulation and the winding problems.

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 3

Tabletop: Directly applicable when choosing wire gauge and supply for a next machine's coils.

flat donuts of 1/16 in. copper sheet ... having a 1/4 in. copper pipe soldered to the outer edges ... such coils should operate steadily at 1300 amps per sq. in.

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 4

Tabletop: Directly applicable cheap upgrade: 1/16-inch copper donut plates with soldered edge tubing between pancakes nearly doubles allowable steady excitation.

These windings saturate the iron (~20 KG) at somewhat less than ten amperes; at this current the temperature becomes excessive in less than an hour

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 4

Tabletop: Directly applicable cautionary datum: quote coil ratings as (current, time-to-overheat) pairs, not just maximum field.

The magnet coil circuit must never be broken at high currents, of course, unless adequate surge protection is provided.

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 5

Tabletop: Directly applicable; a next machine with tens of henries of coil inductance needs a freewheel diode/varistor dump path or it will arc its switchgear.

The Dee capacitance is approximately 76 pF. The secondary coil inductance of 0.87 uH or more in parallel with the Dee capacitance yields a resonance as high at 19.5 MHz

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

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

An alarm warns the operator when the coil temperature has reached a predetermined value, usually 70 to 80 C ... one to three hours are required for the temperature to reach equilibrium.

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 33

Tabletop: Directly applicable: put a thermocouple in the next machine's winding and log it; a coil that is fine at 30 minutes can still cook at 2 hours.

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

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

Tabletop: Directly applicable to the homemade dee-tank coil, which sees circulating RF current far above the dee's DC feed current.

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

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

Tabletop: Reject nickel-plated hardware (and nickel underlays beneath chrome or silver) anywhere RF current flows in the resonator, coil, or ground-return path.

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

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

Tabletop: Buy the tank-coil tubing as electrolytic/electrical-grade (C10100/C11000) copper, not generic plumbing tube, for up to ~20% lower RF resistance.

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

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

Tabletop: Budget the resonant step-up assuming coil Q of a few hundred (loaded lower still), not textbook thousands, when sizing the amplifier for 5-13 kV dees.

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

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

Tabletop: When characterizing the dee resonator with a VNA or Q meter, treat the reading as a lower bound and keep leads/fixture capacitance minimal.

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

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

Tabletop: At 9 MHz a 3-4 inch diameter tank coil can reach Q well over 1000, directly multiplying dee voltage per watt of drive.

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

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

Tabletop: For a 9 MHz matching/tank inductor, space the turns so the wire fills 45-70% of the pitch; close-winding bare tubing throws away Q to proximity effect.

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

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

Tabletop: Make the resonator coil short and fat (roughly half as long as its diameter), not the long skinny solenoid that fits most easily in a corner.

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

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

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

Measurement of the capacitance with an L-C meter yields a value of 78.1pF. Nice agreement seen!

Koeth, Theoretical Calculations and Measurements of the DEE Voltage in the Rutgers 12 Inch Cyclotron (2005) — p. 1

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

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

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

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

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

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

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

the induced voltage on the capacitive pickup facing the DEE was calibrated against forward power at lower levels. Extrapolation allowed us to measure forward power levels up to 1300 watts

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

Tabletop: Exactly the measurement chain the builder needs for the LDMOS upgrade: calibrate their pickup at 5-50 W against a scope probe, then trust the pickup alone at 100-500 W.

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

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

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

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

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

Tabletop: A bench L-C meter trick the builder can use to characterize their coupling loop; M of tens of nH is the expected scale for a matched half-turn loop.

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

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

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

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

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

Tabletop: A benchmark for the reference machine's ~9 MHz tank: if their measured Q0 is far below ~900, there is excess loss (bad joints, steel in the return path) worth hunting down.

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

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

Tabletop: The builder need not agonize over loop position vs tap point: any combination that nulls reflected power delivers identical dee voltage, so pick the mechanically stable one.

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

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

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

It is not necessary to operate at 2000 watts, as shown above 1000 watts produces a peak-to-peak DEE voltage of approximately 15kV.

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

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

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

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

Tabletop: Lets the builder use an unshielded collector at nA levels: a ~100 uH-mH choke at the feedthrough kills 9 MHz pickup without blocking DC beam current.

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

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

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

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

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

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

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

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

Tabletop: Make the source mount adjustable by a few mm in both directions and tune position for beam, not for geometric center.

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

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

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

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

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

Tabletop: At 1.3 kV and 160 keV the reference machine's ions make ~60+ turns; doubling dee voltage halves turns and dramatically relaxes both field-uniformity and vacuum (scattering) requirements.

The gap between chamber lids was chosen to be 5 in., leaving 1 1/4-in. clearance between D's and lids ... resulting in a D-voltage limit of about 70 kv due to breakdown.

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

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

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

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

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

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

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

Tabletop: Hood or collimate the reference machine's source so only ~1/3 of the dee aperture height of plasma column is exposed; more column means RF load, not more beam.

The only general rule is: The simpler the physical structure and the shorter the leads and connections, the less subject is the oscillator to parasitics.

Livingston & Blewett, Particle Accelerators (1962) — p. 185-187

Tabletop: If the next machine goes two-dee push-pull, watch for the push-push mode (no accelerating voltage, oscillator happily locked); a single-dee-plus-dummy design sidesteps it.

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

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

Tabletop: The reference machine's ~1.3 kV dee sits right in classic multipactor territory; surface conditioning, low pressure, and the ability to snap the drive up fast are the standard escapes.

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

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

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

dust should be controlled and all grease removed (even fingerprints), and under no circumstances should steel wool or coarse abrasives be used in cleaning.

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

Tabletop: After every chamber opening, budget an hour of gradually raised dee voltage for conditioning before expecting stable beam.

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

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

Tabletop: The same logic favors the reference machine's self-excited or PLL-followed drive: let the dee resonator define frequency so mechanical drift retunes the drive instead of killing the beam.

about 50 per cent thicker than the depth of the groove to allow for compression ... 1/4-in. gaskets have proved adequate for even the largest seals ... Conductivity for rf currents through such a seal can be assured by half-covering the gasket with a thin copper-foil strip.

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

Tabletop: Directly usable rules for the reference machine's lid and port seals; the copper-foil RF bridge over elastomer joints prevents mysterious Q loss and local heating.

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

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

Tabletop: A concrete tuning rule for the builder: don't tune RF to the central field value; split the difference toward the outer-radius field.

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

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

Tabletop: Quantifies how little phase budget a mistuned tabletop machine has; explains failed runs where beam dies at small radius.

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

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

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

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

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

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

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

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

Tabletop: Sets expectations if a next machine attempts a deflector: losing two-thirds of the beam at the septum is normal, not failure.

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

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

Tabletop: Direct rule for the reference machine's source-to-puller spacing and any dee-to-ground clearance: a few-kV dee needs sub-mm minimum, but leave margin because sputtered metal films spoil the 'clean surface' assumption fast.

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

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

Tabletop: When insulating the reference machine's extraction or dee leads with PTFE sheet or heat-shrink, use the bulk (70 kV/mm-class) figure with a 5-10x safety factor, not the datasheet film value.

Compared to T or Pi networks, the L network uses only one combination of inductance and capacitance. This simplifies the microcontroller tuning algorithm.

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

Tabletop: If the builder automates their dee match at 9 MHz, a stepper-driven L-network is the simplest topology whose tuning can't get lost in redundant solutions.

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

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

Tabletop: Exactly sized for the reference machine's 100-500 W upgrade: a homebrew 30 dB coupler plus AD8307 boards gives continuous forward/reflected monitoring across their whole power range.

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

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

Tabletop: A ~$5 coupler build that brackets the reference machine's 9 MHz band; the shield-through-toroid trick is the detail that makes homebrew directivity respectable.

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

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

Tabletop: Tells the builder not to chase SWR below ~1.1 on a homebrew bridge - that residual is the instrument, not the match.

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

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

Tabletop: The builder already lives in this instrument ecosystem; a Bird 43 (or borrowed one) transfers absolute power calibration to permanently installed cheap sensors.

actuates stepper motors to alternately adjust a variable capacitor and a variable inductor to reduce VSWR to less than 1.5:1

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

Tabletop: SWR 1.5:1 is the protection threshold for the reference machine's LDMOS amp too; coordinate-descent on C then L converges fine for the single-resonance dee load.

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

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

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

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

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

Tabletop: At sub-MeV this limit is distant (10 kV dee -> ~3 MeV proton ceiling), but the same physics governs field-flatness tolerance: fewer turns forgives more field error.

Low energy proton in 1 T field: 15.23 MHz

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

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

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

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

Tabletop: For the builder: 1 MeV at 2 kV/gap (2 gaps) is ~250 turns with final-orbit spacing ~0.2 mm at r=12 cm - explaining why higher dee voltage directly eases both extraction and vacuum requirements.

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

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

Tabletop: Reassurance and ceiling in one number: at 1 MeV gamma-1 = 0.001, ~0.4 deg/turn - a next machine is nowhere near the relativistic limit, and the classical (non-AVF) architecture is fine to several MeV.

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

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

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

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

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

Tabletop: Direct benchmark for the reference machine's resonator: if measured Q is far below ~1000, hunt for lossy joints; and thermal drift of a Q~1600 circuit needs active or frequent retuning at 9 MHz.

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

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

Tabletop: Cyclotrons run 1e-5 to 1e-4 torr with gas feed - squarely in the gray zone - so the reference machine's spark limit will move with operating pressure, and tests at base pressure overstate what they can hold with gas flowing.

r.f. power should never be left on for prolonged periods under these circumstances, else the risk is run of cracking the glass dee insulators. The power and length of application should be gradually increased

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

Tabletop: Directly applicable startup ritual at the reference machine's 1.3 kV dee level; persistent glow during conditioning signals organic contamination (grease, oil, rubber) in the tank.

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

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

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

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

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

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

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

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

Tabletop: Directly applicable to the reference machine's amplifier: wide copper sheet/strap grounds and a short feed run, with magnetically sensitive parts (and LDMOS heat sinks) out of the fringe field.

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

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

Tabletop: Directly applicable; the reference machine's beam-current, bias, and gauge lines all need feedthrough RC/choke filtering at 9 MHz.

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

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

Tabletop: Directly applicable home-lab safety baseline for a next machine.

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

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

Tabletop: Directly relevant to any thin-lid chamber on a next machine squeezed into a small magnet gap: plan support posts (clear of the beam spiral) from the start.

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

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

Tabletop: Confirms the single-dee choice for a next machine unless dee voltage becomes the binding constraint.

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

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

Tabletop: For any HV feed on a next machine (deflector, source bias): keep cable runs minimal - stored cable energy, not the supply, does the arc damage.

We've encased the resistor in a grounded shield, and the coax shields go through 68 Ohm, 2 watt resistors

Ponter, Beam Energy Measurements with a New HV Deflection System and Ion Source Upgrades on the Rutgers 12-Inch Cyclotron (2010) — p. 44-52

Tabletop: A ready-made HV-distribution recipe for the reference machine's deflector or PIG source bias; note even this shielding didn't stop arcs until the cable-energy fix - resistors limit damage, they don't prevent flashover.

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

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

Tabletop: This is essentially the reference machine's current architecture, validated: a ham antenna tuner really can match a dee, at the cost of low Q and ~1-2 kV ceilings.

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

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

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

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

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

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

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

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

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

Record Input Power 2kW: 8.4 kVpeak

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

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

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

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

Tabletop: A free end-to-end check for the builder: the RF power at which beam vanishes measures the true dee voltage through pure geometry, independent of every probe.

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

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

Tabletop: At 100-500 W the next machine will drift off resonance within minutes of turn-on; this phase-lock autotuner (or the equivalent PLL driving their signal source) is the fix.

Beam Inferred DEE Voltage

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

Tabletop: The builder can cross-check their 1.3 kV estimate by measuring where the first half-turn lands - the beam itself is the most honest voltmeter.

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

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

Tabletop: Bring the reference machine's dee and extraction voltages up over tens of minutes on first pump-down, watching for micro-discharge pulses; a gap that arcs at 15 kV cold will often hold 20+ kV after patient conditioning.

They found that at a critical angle of 31.5 deg, the surface charge was zero... by screening the section of the insulation surface near the cathode... the breakdown voltage was raised by a factor of approximately 2.5.

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

Tabletop: Free flashover margin for the next machine's source stalk and dee-stem insulators: cone the insulator ends at ~30 degrees toward the negative electrode and recess the triple junction behind a metal skirt.

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

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

Tabletop: Budget ~2 kV per mm of insulator surface path in vacuum (before sputter contamination); a 20-kV extraction stalk wants >=10 mm of clean creepage plus corrugations.

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

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

Tabletop: The classic failure of home-built HV feedthroughs: a loose PTFE sleeve over a rod arcs in the annular air film; pot it, oil-fill it, or evacuate the annulus so Paschen cannot be satisfied.

The optimum ratio as r_i/r_o = 1/e. This optimum ratio minimizes the stresses within the coaxial electrode arrangement, independent of the material of the dielectric used.

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

Tabletop: Sizes the reference machine's HV stalk directly: for a grounded 25-mm-bore chamber port, a ~9-mm center conductor minimizes field stress; and never leave a sharp-edged washer or nut on the HV end.

This phenomenon causes the cathode grid material from the IEC device to be deposited on the high-voltage (HV) stalk. That can in time cause premature breakdown at the stalk.

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

Tabletop: In the reference machine's small chamber everything sees the source; a simple washer-stack or skirt shielding the feedthrough ceramic from the chimney slit will multiply time-between-cleanings.

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

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

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

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

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

Tabletop: Essential for interpreting the reference machine's magnet scans: a peak at one-third field is a subharmonic, not a mystery species, and H2+ vs H+ vs They peaks can be disentangled this way.

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

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

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

the RF generator was adjusted in steps of 0.5 MHz ... adjusted in steps of 0.1 MHz near the maximum voltage ... a third sweep was performed using steps of 0.01 MHz

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

Tabletop: A simple, scope-only resonance-finding recipe the builder can use after any mechanical change to a next machine's dee or stem.

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

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

Tabletop: Quantifies the reference machine's architecture choice: an antenna-tuner match (like their current setup) gives kV-class dee voltage; multi-kV needs a high-Q tank coil instead.

when the CT2591 HV probe was placed near the dee, the overall capacitance changed slightly. This would, of course, change the value of the resonant frequency.

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

Tabletop: When the builder cross-checks NanoVNA SWR sweeps against probe measurements, a few-percent frequency disagreement is expected instrumentation loading, not a fault.

the real voltage was roughly 11,300 times the pickup voltage ... the probe had to be recalibrated every time the frequency was adjusted.

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

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

a SWR of 1:1 and forward power of 15.43 W were measured

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

Tabletop: Reassurance for commissioning a next machine: hunt for first beam at tens of watts with a clean match before scaling power - beam detection, not power, is the bottleneck.

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

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

Tabletop: At the reference machine's sub-MeV energies relativistic slip is negligible (~0.1%), so dee voltage matters mainly through path length and gas scattering - but this rule sets the fixed-frequency ceiling for any future MeV-class ambition.

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

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

Tabletop: An off-the-shelf, cheap, replaceable filament choice plus the RF-bypass detail that keeps the filament supply alive next to a live Dee.

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

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

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

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

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

Tabletop: The reference machine's 9 MHz sits in this sweet spot; for a next machine, avoid pushing frequency (i.e., field) past where cheap RF parts and simple technique still work.

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

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

Tabletop: Formula transfers directly: at 9 MHz, ~50 pF and Q~1000, 5 kV on the dee costs only tens of watts, telling the builder exactly how much amplifier a higher-voltage dee on a next machine needs.

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

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

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

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

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

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

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

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

Tabletop: Order-of-magnitude expectation transfers: most RF power goes to resonator and ion-loading losses, so judge a next machine's RF sizing on resonator dissipation, not beam power.

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

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

Tabletop: Scaled down: any sliding or bolted joint in the reference machine's dee-stem/coil path should be a broad, clean, plated, firmly clamped contact - RF joints, not wires, set small-resonator Q.

The ceramic 'Lapp' coils originally used for introducing cooling water to the tube and the plate line failed whenever the oscillator voltage was increased to give 200 kv. They have since been replaced with choke coils wound from copper tubing.

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

Tabletop: The principle (a conductive-liquid line into an RF-hot electrode must itself be an insulator or a choke) applies whenever a next machine adds cooling or bias plumbing to the dee.

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

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

Tabletop: Transferable architecture: paralleled small supply modules (or PA pallets) with individual protection give a home machine graceful degradation.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Tabletop: Standard practice for any kW-class dee driver a home builder assembles from LDMOS boards.

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

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

Tabletop: Useful if the builder builds a broadband solid-state dee driver: the devices have huge low-frequency gain and will oscillate without this.

The real issue was the third harmonic, though; in general, it was only down 10 dB down and on some bands only 8 dB down.

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

Tabletop: A cyclotron dee tank is narrowband, but the same rule holds: measure what the PA actually emits before designing filtering or worrying about RF interference from a garage machine.

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

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

Tabletop: Relevant if the builder drives the dee with a broadband solid-state PA instead of a tube: protect the FETs from the highly reactive dee load.

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

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

Tabletop: Schedule tuning time (this cost the author three months); the same applies to a homemade dee tank and matching network.

I also added a limiting power resistor (20 ohms at 50w) in series with 50v to the TIP102 as a precaution...with this resistor in place, a short on the 12v line will limit the current and prevent a catastrophic failure.

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

Tabletop: Cheap fault-tolerance rules for any homebuilt high-voltage/high-current RF deck; voltage-derating the caps matters more with the reactive load a dee presents.

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

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

Tabletop: Size the RF chain for the dee power you actually need plus ~10-15%; the same relay/coupler/filter tax applies to a cyclotron dee drive.

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

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

Tabletop: Skip decorative silver plating on the dee and coil; a jobbing-shop bright-silver finish would raise, not lower, resonator loss at 9 MHz.

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

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

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

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

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

Tabletop: A sub-micron corrosion-protection flash on copper is harmless at 9 MHz; a mid-thickness medium-conductivity coating is the worst case to avoid.

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

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

Tabletop: For RF contact fingers and connectors on the resonator, distrust thin gold flash; specify thick gold or use bare copper with lacquer instead.

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

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

Tabletop: Any silver-plated RF joints in the shop atmosphere (or near vacuum-pump exhaust) need protection or periodic cleaning, or kV-level circulating currents will heat them.

This last problem has been investigated fully by Benson who recommends chemical or electrolytic polishing to produce a smooth surface and lower losses.

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

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

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

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

Tabletop: A directional coupler plus fast drive-cut on high reflected power is the single best defense when the cyclotron dee arcs or drifts off resonance mid-run.

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

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

Tabletop: Directly applicable to a homebrew 9 MHz LDMOS deck: thermal-tracking bias prevents runaway, and DC-free transformers avoid core saturation at high drain current.

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

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

Tabletop: A dee resonator is a narrowband, sometimes-detuned load; build feedback in from day one rather than after the first blown transistor.

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

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

Tabletop: At 100-500 W a copper spreader under the LDMOS pallet is cheap insurance against the die-temperature excursions that killed the reference machine's earlier MOSFET amps.

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

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

Tabletop: At 9 MHz the 27 MHz third harmonic can excite spurious dee-resonator modes and detune the match; filter it between amp and matching network.

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

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

Tabletop: The dee is a high-Q load that reflects everything off-resonance; an absorptive diplexer gives the LDMOS a resistive termination at harmonics and protects against the mismatch failures the builder has already had.

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

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

Tabletop: When copying an LDMOS pallet layout, reproduce the output-transformer connection geometry exactly; millimeter changes shift the match at hundreds of watts.

The distortion is satisfactorily low with a dummy DEE of 3/8-inch thickness.

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

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

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

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

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

Graphite is coming into wide use for cones, arc bodies, and also for D feelers or accelerating electrodes; it operates at high temperatures with a minimum of sputtering or evaporation.

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

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

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

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

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

40 of 52 contaminated sites broke down, while only 1 of 16 uncontaminated sites broke down at or below the maximum field

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Four machinable ceramic strips, each roughly 2.53 cm long, 0.77 cm wide and 0.18 cm thick, hold the two dees together at the appropriate separation gap of 0.635 cm.

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

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

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

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

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

The screw holes need to be vented so that they do not trap air or water and slowly outgas when the dee is placed in the vacuum chamber.

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

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

the RF voltage on the dee is typically between 1 and 2 kV, far greater than the 1-3 V DC placed across the filament. Thus, the filament and wires must be adequately insulated from the dee

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

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

Ceramic spacers hold the Dee and Dummy Dee apart with a gap of 0.635 cm. The entire Dee electrode assembly is supported by three KF-16 electrical feedthroughs through ports at 120 degrees from each other.

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

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

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

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

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

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

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

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

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

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

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

Fast pumping is required and it is desirable to use oil rather than mercury diffusion pumps as mercury seems to promote autoelectronic discharges from the electrodes.

Oliphant & Rutherford, Experiments on the Transmutation of Elements by Protons (1933) — p. 259-260

Tabletop: Moot for pump choice today, but the underlying rule stands: condensable metal vapors on HV electrodes trigger field emission; keep electrode surfaces free of conductive films.

the maximum current is produced from a discharge running at about 20,000 volts... the current collected by the Faraday cylinder F into which it can penetrate is of the order of 1 milliampere with 20 milliamperes in the discharge.

Oliphant & Rutherford, Experiments on the Transmutation of Elements by Protons (1933) — p. 260-261

Tabletop: Sets the historical proton-conversion baseline: expect percent-level proton yield from a gas discharge and budget discharge power accordingly.

The space between the two steel tubes is too small for a discharge to build up there and it concentrates naturally on the hole in the cathode.

Oliphant & Rutherford, Experiments on the Transmutation of Elements by Protons (1933) — p. 260-261

Tabletop: The 'gap smaller than the dark space' principle is how the builder can force their source discharge to localize at the extraction aperture rather than wander.

At first this beam consists very largely of molecular ions, but after running for some time it changes over and becomes nearly all protons

Oliphant & Rutherford, Experiments on the Transmutation of Elements by Protons (1933) — p. 261-262, 269

Tabletop: Critical for p-B11: an unconditioned source delivers H2+ that behaves as half-energy protons, silently killing the expected alpha yield at fixed magnetic rigidity.

admitting hydrogen till it was possible to run a discharge at about 20-60 kilovolts... on pumping out the hydrogen it is usually found that the tube is quite hard and stable up to 200,000 volts.

Oliphant & Rutherford, Experiments on the Transmutation of Elements by Protons (1933) — p. 265

Tabletop: A concrete glow-discharge conditioning schedule the builder can scale for dee and extraction electrodes that must hold voltage without sparking.

one should be suspicious of the ion source if the measured beam current is very low in the region close to the ion source, i.e. the regime of large turn spacing

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

Tabletop: A triage rule for the reference machine's low-current debugging: measure current at small radius first; if it's already low there, more RF power won't fix it - the source will.

arc current, 3 amp; arc voltage drop, 100 volts; electron beam from exit hole, 2 amp; gas flow, 2 cm3/min at atmospheric pressure. The resonant ion beam pulled from such a source ... might be about 0.5 ma.

Livingston & Blewett, Particle Accelerators (1962) — p. 175-178

Tabletop: These operating points scale down gracefully; the key architecture point - a differentially pumped cavity at ~1e-2 torr feeding a chamber at 1e-5 - applies at any size.

The heating power is either dc or high-frequency ac (~100 kc) to avoid damage from vibration in the magnetic field at low frequencies. Cathode life is ... materially shortened by traces of oxygen.

Livingston & Blewett, Particle Accelerators (1962) — p. 177-178

Tabletop: A 60 Hz-heated filament in a 0.59 T field literally shakes itself apart; DC heating and clean hydrogen are cheap reliability.

With no gas flow, chamber pressures of better than 1 x 10-6 mm Hg are obtained. With the deuterium gas flow from the ion source, the operating pressure is about 2 x 10-5 mm Hg.

Livingston & Blewett, Particle Accelerators (1962) — p. 198

Tabletop: The builder should expect an order-of-magnitude pressure rise when hydrogen flows; low-2e-5 territory while running is normal and workable, not a leak.

The filament is heated to incandescence by a high-frequency a-c power supply. The high-frequency is used to minimize self-destructive magnetic effects in the spiral filament.

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

Tabletop: Concrete fix for a failure mode the builder will hit at 0.6-1.7 T with a hairpin/spiral filament: filament life is a chronic tabletop problem.

Operating Data of Penning Ion Sources: Arc voltage 0.3-1.3 / 1-5 kV; Ignition volt. 3-5 kV; Gas pressure 1-10 Pa; Gas consumption 0.2 sccm.

Wolf (ed.), Handbook of Ion Sources (1995) — p. 101

Tabletop: The reference machine's MFC should be sized and calibrated around the 0.1-1 sccm range, and the arc supply must tolerate a several-kV open-circuit ignition transient before folding back to run voltage.

Stainless steel is an excellent material up to about 1000 C... It forms low-melting alloys with tantalum and molybdenum above 900 C... Tungsten... has the highest melting point of about 3400 C and is best suited for filaments.

Wolf (ed.), Handbook of Ion Sources (1995) — p. 355

Tabletop: Do not clamp Ta filament legs directly in stainless fixtures near the hot zone; use Mo or graphite intermediate parts in the next machine's chimney.

Boron nitride is an excellent material for most applications for temperatures up to 1200 C... It outgasses badly and tends to absorb water, which can destroy the parts when heated too fast.

Wolf (ed.), Handbook of Ion Sources (1995) — p. 356

Tabletop: BN filament insulators in a home source must be pre-baked and brought up to arc power slowly the first time after air exposure, or they crack and gas up the chamber.

In more practical units, this equation can be rewritten: j[mA/cm2] = 1.72 * sqrt(q*/u) * phi[kV]^(3/2) / d[mm]^2.

Wolf (ed.), Handbook of Ion Sources (1995) — p. 376-377

Tabletop: Confirms the reference machine's nA beams are nowhere near space-charge limits; if extraction is weak the problem is geometry/plasma matching, not the Child-Langmuir ceiling.

The assumption of a certain aspect ratio (aperture radius to electrode separation). A good aspect ratio is on the order of S = 0.5.

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

Tabletop: For the puller gap in a next machine: make the source-slit half-width about half the slit-to-puller distance, then tune arc density (not geometry) until the beam is parallel.

The increase of the saturation current with temperature is very strong; a 10% change in temperature corresponds to a 10-fold increase of 20% to a 100-fold increase.

Wolf (ed.), Handbook of Ion Sources (1995) — p. 38-39

Tabletop: The reference machine's hydrogen filament source lives or dies on filament temperature stability; a constant-current supply with fine adjustment is worth more than raw power.

Most of the power put into a filament is radiated and very little is lost through the ends. Most high-temperature metals show similar radiation behavior (~20 W/cm2 at 2000 K).

Wolf (ed.), Handbook of Ion Sources (1995) — p. 39

Tabletop: A few cm^2 of hot filament dumps tens of watts into the reference machine's source body; the hood/chimney around the filament needs a conductive heat path to the pole or water cooling.

The increase of temperature for higher electron output is limited by the increasing evaporation of cathode material, which decreases the cathode lifetime. Tables 1.2 and 1.3 give the respective data for W and Ta.

Wolf (ed.), Handbook of Ion Sources (1995) — p. 41-42

Tabletop: For a next machine, a fatter filament run cooler at ~0.1-1 A/cm^2 buys weeks of run time instead of days; treat used Ta hairpins as brittle after hydrogen exposure.

Gas efficiency: >50% for hydrogen and higher for other gases.

Wolf (ed.), Handbook of Ion Sources (1995) — p. 57, 69, 110

Tabletop: At 0.2 sccm feed and 50% efficiency only ~0.1 sccm of H2 leaks into the chamber; doubling source gas efficiency is worth as much as doubling pump speed for keeping the beam path at low pressure.

The arc current is 1 to 3 A and the arc voltage just 40 to 70 V... The lifetime of the source is given by the lifetime of the filament, which is between 10 and 100 h... Changing the polarity of the filament... improves cathode lifetime.

Wolf (ed.), Handbook of Ion Sources (1995) — p. 73

Tabletop: For a next machine: a thick rod cathode instead of thin wire is the cheapest lifetime upgrade, plus a DPDT reversing switch on the heater and an arc-hours log.

The extraction slit is usually about 2 mm wide and about 40 mm long. Larger slits are possible, such as 90 mm, but... the current density is not uniform along the long slit.

Wolf (ed.), Handbook of Ion Sources (1995) — p. 74, 76

Tabletop: For a cyclotron chimney only the few-mm of slit facing the dee gap matters; a ~1-2 mm wide slit is the proven starting width before puller optimization.

The cold cathode PIG source with arc voltages above 1 kV and currents between 0.5 and 5 A, and the hot cathode PIG source with arc voltages below 1 kV and currents between 1 and 50 A.

Wolf (ed.), Handbook of Ion Sources (1995) — p. 81-82

Tabletop: The reference machine's cyclotron field (>0.1 T at the center) already satisfies the PIG minimum, so a next machine's internal PIG source can trade the fragile filament for a self-heated cathode running a sub-kV, multi-ampere arc.

The total extracted current of a PIG ion source is proportional to the arc current, and for extraction through the anode, about 10 to 100 (mA/cm2)/A.

Wolf (ed.), Handbook of Ion Sources (1995) — p. 82

Tabletop: With a ~1 mm^2 chimney slit, even a 1-A arc gives ~0.1-1 mA available at the slit, orders of magnitude above the reference machine's nA beams; source output will not be the bottleneck.

The arc power for cold cathode operation is limited to about 1 kW per cathode... The cold and hot cathodes are worn out when the erosion crater's depth reaches around the anode bore radius.

Wolf (ed.), Handbook of Ion Sources (1995) — p. 84-85

Tabletop: Gives a concrete inspection criterion: measure the cathode pit depth against the chimney bore each time the source is pulled, and machine spare cathode buttons in advance.

Electrons emitted from a filament and accelerated to about 1 kV heat the cathode from the rear side... The lifetime of the heated cathode exceeds that of cold or hot cathodes.

Wolf (ed.), Handbook of Ion Sources (1995) — p. 86, 101

Tabletop: A next machine's source can keep a small filament hidden behind a Ta block cathode, out of the hydrogen plasma, converting filament sputtering into slow self-sputtering of a thick block.

at normal operating pressures of 10^-4 mm Hg, between 1/2 to 2 amps at 100 to 500 volts will be required

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 6, 10

Tabletop: Directly applicable operating envelope for a simple hot-filament source at the reference machine's scale.

hydrogen may be admitted to the tank, 'opening' the valve until the tank pressure rises by another 10^-4 mm, meanwhile watching the arc current

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 6, 10

Tabletop: Directly applicable gas-flow set-point; the reference machine's parker metering valve fills the needle-valve role.

an automobile headlight filament has been used, but the breakage has been high ... perhaps .025 in. tungsten ... A .025 in. tungsten filament requires about 25 amps d.c.

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 6-7

Tabletop: Directly applicable filament sizing; the modern equivalent of the battery filter is a well-filtered DC (not raw rectified) filament supply to stop magnetically driven filament vibration.

A quarter-inch tube called a 'chimney' sits on top of the filament, which shields it from the electric field of the dee. Ionized hydrogen is drawn out of a small hole.

Baumgartner, The Cyclotron Kids' 2 MeV Proton Cyclotron — Cyclotrons 2013, WE1PB05 (2013) — p. 3

Tabletop: A proven upgrade from a bare filament for a next machine: better-defined source position, less RF loading of the plasma.

Higher frequency, lower H2 and base pressure, lower filament voltage

Yuly et al., Modifications on the Houghton College Cyclotron (2010) — p. 17-18

Tabletop: For the reference machine's current-hunting: before adding RF watts, cut chamber pressure and re-optimize filament bias - Houghton's 7x gain cost zero watts.

fusion efficiency is enhanced by transparency of at least 92 percent (Donovan). The inner grid is 99.18 percent transparent with three loops

Kovalchick, Deuterium Fusion Using Inertial Electrostatic Confinement (2012) — p. 19-20

Tabletop: The transparency bookkeeping (wire cross-section vs aperture area) is the same calculation the builder needs for any grid, mesh, or slit that their beam must pass repeatedly.

A power supply cannot differentiate between an ion reaching the cathode grid and an electron leaving it (they both appear as positive current on the ammeter).

Miley & Murali, Inertial Electrostatic Confinement (IEC) Fusion: Fundamentals and Applications (2014) — p. 135, 144

Tabletop: When the builder meters 'beam current' anywhere near a hot cathode, part of it is electrons; a high-work-function collector surface and magnetic electron suppression keep the nA readings honest.

Assuming that sagging occurs at ~1,500 K and equating the black body radiation rate to the input power... This gives 9.5 mA of ion current at 200 kV.

Miley & Murali, Inertial Electrostatic Confinement (IEC) Fusion: Fundamentals and Applications (2014) — p. 145

Tabletop: Same balance sizes any wire electrode, probe, or beam stop in the reference machine's chamber: compute AeσT^4 at the material's sag temperature and keep beam-power deposition below it.

The stainless steel wires previously used by Murali lasted for under a week depending on the power load. In contrast, with the W-25%Re alloy, the grid lasted for over 2 years.

Miley & Murali, Inertial Electrostatic Confinement (IEC) Fusion: Fundamentals and Applications (2014) — p. 145-146

Tabletop: W-Re thermocouple wire is commercially available in small quantities and is the best upgrade for any sputtered electrode in the reference machine's source: W durability with Ta-like workability.

The product of pressure and distance between the electrodes (pd) is a better parameter to characterize the discharge... The voltage is mostly in the range between 300 and 1500 V, but... the current is generally in the mA range.

Miley & Murali, Inertial Electrostatic Confinement (IEC) Fusion: Fundamentals and Applications (2014) — p. 86-88

Tabletop: When the builder scales chamber geometry or pressure for the p-B11 test cell, keep pd constant to preserve the discharge; and remember all sputtering damage happens at the cathode sheath edge.

A hysteresis effect occurs; wherein instead of retracing the path... the discharge maintains itself in the normal glow regime... at considerably lower currents... Only then does it make the transition back to the Townsend regime.

Miley & Murali, Inertial Electrostatic Confinement (IEC) Fusion: Fundamentals and Applications (2014) — p. 89-91

Tabletop: Explains why the reference machine's source may need a several-kV kick to strike but then runs at a few hundred volts, and why current-limited (ballasted) supplies are mandatory to stop glow-to-arc runaway.

The ion mean free path at 2 mTorr is ~7 cm, while at 20 mTorr it is around 0.7 cm... The striking voltage increases with decreasing pressure.

Miley & Murali, Inertial Electrostatic Confinement (IEC) Fusion: Fundamentals and Applications (2014) — p. 92, 94

Tabletop: For any glow-driven ion supply in the p-B11 experiment, pressure is the ignition control: strike at higher pressure, then throttle the MFC down to the running point.

For fixed Vs, the value of (pd) is seen to be about three times higher for both the spherical and the planar solid-cathode discharges than for the transparent grid-type cathode discharges.

Miley & Murali, Inertial Electrostatic Confinement (IEC) Fusion: Fundamentals and Applications (2014) — p. 94-96

Tabletop: If the builder builds an IEC-style p-B11 test stand, a few large openings aligned with the beam axis beat a fine mesh: fewer grid hits, higher effective transparency, longer grid life.

it might be necessary to include a filament or other source of electrons to ionize the deuterium at low pressures. This filament should be placed just outside of the outer grid system and biased slightly positive (~200 volts)

Hull, The Farnsworth/Hirsch Fusor — The Bell Jar, Vol. 6 No. 3/4 (1997) — p. 7

Tabletop: Matches the reference machine's hydrogen filament source philosophy: a modest positive bias (order 100-200 V) on/near an emitter sustains ionization at pressures where a self-sustained discharge dies.

Care must be exercised to electrically shield (insulate) the inner grid metallic support structure so that ions will not bombard that portion of the apparatus.

Hull, The Farnsworth/Hirsch Fusor — The Bell Jar, Vol. 6 No. 3/4 (1997) — p. 7

Tabletop: Same rule protects the reference machine's Faraday cup stalk and source supports: unshielded biased metal collects spurious current and sputters.

It appears that filament bias has no effect on the beam current.

Fuller, Exploring the Capabilities of the Houghton College Cyclotron — Houghton College thesis (2013) — p. 48-49

Tabletop: Saves tuning time: spend effort on dee voltage and pressure, not filament bias, when hunting current.

If there is too little gas, less ionization will occur... Too high a pressure and the ionized particles will likely interact with gas inside the dee and fall out of resonance.

Fuller, Exploring the Capabilities of the Houghton College Cyclotron — Houghton College thesis (2013) — p. 51-52

Tabletop: Gives the builder a target pressure window and the expected non-monotonic current-vs-pressure curve to map on their own machine.

To make room for a filament and to avoid another electrical discharge from the filament to the lid, a 0.3 cm deep circular depression was milled out of the bottom of the upper lid.

Haas, Characterizing the Performance of the Houghton College Cyclotron — Houghton College thesis (2009) — p. 50

Tabletop: In the reference machine's tight pole-gap geometry, check every HV-to-ground clearance near the median plane; milling relief pockets is cheaper than chasing sparks later.

The pressure in the chamber has a large effect on the beam current obtained, and typically needs to be in the range from 1e-6 to 1e-4 Torr for the cyclotron to operate.

Yuly, The Houghton College Cyclotron: a Tool for Educating Undergraduates — Cyclotrons 2013, WE1PB01 (2013) — p. 5

Tabletop: Directly sets the gas-handling operating window for the reference machine and explains a common 'no beam' failure at too-good vacuum.

the anode floats inside the cathode body, being supported only by the two stainless steel wires that protrude through the alumina tubes and out the back of the cathode body.

Rovey, Ruzic & Houlahan, Simple Penning Ion Source for Laboratory Research and Development Applications (2007) — p. 1-2

Tabletop: An amateur-grade insulated feedthrough scheme (alumina tube + Ceramabond) the builder can reuse for chimney anodes or filament leads inside the next machine.

generate a plasma discharge that yields a continuous 1 mA beam of positively charged hydrogen ions at 1 mTorr of pressure. This operating condition requires 5.4 kV and 32.4 W

Rovey, Ruzic & Houlahan, Simple Penning Ion Source for Laboratory Research and Development Applications (2007) — p. 1-3

Tabletop: A directly copyable permanent-magnet source recipe for the next machine's external or test-stand source at exactly hobby machining tolerances.

Because the 100 kOhm current-limiting resistor develops a voltage drop during source operation, the ion source voltage (anode-to-cathode voltage) is reported instead of the power supply voltage.

Rovey, Ruzic & Houlahan, Simple Penning Ion Source for Laboratory Research and Development Applications (2007) — p. 2

Tabletop: Directly applicable to the reference machine's filament/arc supply metering; logging supply volts instead of electrode volts corrupts any operating-point map.

the pressure internal to the ion source is only approximately a factor of 2 larger than the chamber pressure... source operation has also been achieved by simply backfilling the chamber.

Rovey, Ruzic & Houlahan, Simple Penning Ion Source for Laboratory Research and Development Applications (2007) — p. 2

Tabletop: The reference machine's MFC feed into the source chimney matters most when the main chamber is well-pumped; in a small chamber the distinction between injection and backfill largely disappears.

the plasma discharge ignites easily at 1 kV or less for all cases and produces a continuous positively charged ion beam.

Rovey, Ruzic & Houlahan, Simple Penning Ion Source for Laboratory Research and Development Applications (2007) — p. 2-3

Tabletop: Tens-of-uA proton output at under 1 kV anode drive is ample for the reference machine's nA-scale accelerated beam; a multi-kV arc supply is not required to start.

the source has a current utilization efficiency (ratio of target to discharge current) of 25% and requires 32.4 W of power.

Rovey, Ruzic & Houlahan, Simple Penning Ion Source for Laboratory Research and Development Applications (2007) — p. 3

Tabletop: Gives the builder a sanity check: nA-to-uA beams need only uA-to-mA class discharges; if their beam/arc ratio is far below ~20% the extraction geometry is losing beam.

at a pressure of 0.4 mTorr and 10.5 W PIG source power, a continuous 1 mA positive hydrogen ion beam has been focused onto the target and accelerator voltages up to -30 kV have been investigated.

Rovey, Ruzic & Houlahan, Simple Penning Ion Source for Laboratory Research and Development Applications (2007) — p. 3

Tabletop: Template for a bench extraction test stand to characterize the next machine's source before it goes into the magnet.

The ion source is an internal cold cathode Penning Ion Gauge (PIG) source that operates in excess of 40 hours before requiring service.

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

Tabletop: Benchmarks source lifetime for a next machine; hot filaments burn out far faster than a cold-cathode PIG at this scale.

With a gas flow rate of 2.5 cc/min of hydrogen, the pressure in the main vacuum chamber is around 4e-5 Torr.

Forringer, Phase Space Characterization of an Internal Ion Source for Cyclotrons — MSU dissertation (2004) — p. 17-29

Tabletop: A direct benchmark for the reference machine's MFC-vs-chamber-pressure curve; large deviations from ~1.5e-5 Torr per sccm (at similar pumping speed) indicate leaks or conductance problems.

The cathode anode gap was between 0.075 (1.9 mm) and 0.150 (3.8 mm), and is not a critical parameter for the source's operation.

Forringer, Phase Space Characterization of an Internal Ion Source for Cyclotrons — MSU dissertation (2004) — p. 19

Tabletop: Relaxes the reference machine's machining tolerances on the next machine's source gap and sizes the arc supply: a 3 kV current-limited unit suffices.

Water cooling for the cathode rod and the anode base are essential (some copper parts were melted when the ion source was run without proper cooling).

Forringer, Phase Space Characterization of an Internal Ion Source for Cyclotrons — MSU dissertation (2004) — p. 19-20

Tabletop: At the reference machine's much lower arc powers passive/conductive cooling may suffice, but the sanded-cathode arc-striking trick transfers directly.

Their cathode was a U-shaped tantalum filament, heated with about 400 amps... able to extract 150 mA using a puller voltage of 12kV and a source-puller gap of about 0.13 (3.3 mm).

Forringer, Phase Space Characterization of an Internal Ion Source for Cyclotrons — MSU dissertation (2004) — p. 3-4

Tabletop: Brackets the design space above the reference machine's filament source: proton output scales with arc current and slit area over 3+ orders of magnitude, so their nA needs are met with sub-ampere arcs.

The chimney with the larger slit produces a beam with a larger emittance. However, the beam is also of higher intensity.

Forringer, Phase Space Characterization of an Internal Ion Source for Cyclotrons — MSU dissertation (2004) — p. 66-69

Tabletop: Tells the builder exactly what to expect when they widen their next machine's chimney slit: current scales faster than linearly with width, emittance grows more slowly - widen until the machine acceptance is filled.

This puller was designed for the ion source test stand to hold 50 kV... The minimum source to puller gap is 0.196 (5.0 mm).

Forringer, Phase Space Characterization of an Internal Ion Source for Cyclotrons — MSU dissertation (2004) — p. 68, 75

Tabletop: Sets the reference machine's dee-tip/puller gap voltage budget: with clean electrodes, plan on order 10 kV per mm of gap and generous edge radii.

an approximately flat plasma boundary provides the best match to the experimental beams emerging from the 'slit' style chimneys... while a concave plasma boundary... for the 'hole' style chimney

Forringer, Phase Space Characterization of an Internal Ion Source for Cyclotrons — MSU dissertation (2004) — p. 73-76, 91-107

Tabletop: Decides a next machine's chimney aperture style: cut a tall narrow slit, not a drilled hole, if beam brightness and predictable optics matter.

the general trend of increasing arc current producing increased beam current as expected... there was no noticeable change in the emittance of the beam for different currents

Forringer, Phase Space Characterization of an Internal Ion Source for Cyclotrons — MSU dissertation (2004) — p. 77-78, 81

Tabletop: For the builder: cranking arc power buys current with diminishing returns but does not spoil beam quality below ~230 uA - space charge is negligible at their nA-uA scale.

hydrogen gas flow rates greater than 2.0 cc/min) no H2+ ions were observed. We were able to observe H2+ ions by lowering the gas supply to 0.5 cc/min.

Forringer, Phase Space Characterization of an Internal Ion Source for Cyclotrons — MSU dissertation (2004) — p. 79-80

Tabletop: Directly actionable on the reference machine's MFC: starving the source of gas silently changes beam species; their flow setpoint should stay above the arc-mode transition.

the plasma temperature that provides the best match for experimental beams is approximately 35,000 K (resulting in a central starting energy of 4.5 eV).

Forringer, Phase Space Characterization of an Internal Ion Source for Cyclotrons — MSU dissertation (2004) — p. 91-107

Tabletop: Gives the builder the initial-condition recipe for any first-turn orbit simulation of their next machine's central region.

Vernier knob for repeatable flow settings ... Flow Coefficient (Cv): 0.029 (Series 20) ... Stem Taper: 3 deg ... Turns to Open: 9 (+/-1)

Parker Hannifin, Series 20 & 30 Metering Valves (datasheet) — p. 1-2

Tabletop: The 3-degree-taper Series 20 spread over 9 turns gives the fine, repeatable hydrogen admission an ion source needs; log turns-open as the process setpoint.

Not recommended for positive shut-off. If bubble-tight shut-off required, the use of a Series HR Metering Valve is suggested.

Parker Hannifin, Series 20 & 30 Metering Valves (datasheet) — p. 2

Tabletop: Put an isolation valve between the gas bottle and the metering valve; forcing the tapered stem closed to seal will ruin the calibrated taper and still leak into the vacuum system.

The rate of flow required during operation is from 2 to 3 cc/min ... Electrons are accelerated from the filament into the arc chamber by a 100 to 300 volt potential, the normal arc current being 0.5 to 1.5 amperes.

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 62, 64

Tabletop: Arc V-I and few-cc/min gas flow transfer almost unchanged to a small chimney source; graphite chimney/slit parts resist sputtering far better than copper or steel.

The alignment of the ion source with the magnetic field and with the accelerating slits is critical and is carefully adjusted to obtain best performance.

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 64

Tabletop: Directly applicable: build a next machine's source mount with repeatable rotation/translation adjustment from outside vacuum; source-to-puller alignment is worth more beam than any power knob.

Arc voltage and arc current can each be varied independently ... This regulates the filament temperature and thus the arc current, which is then held constant regardless of arc voltage.

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 66

Tabletop: Directly applicable control philosophy, trivially implemented today with two small feedback supplies; a constant-current arc is what makes beam current reproducible shot to shot.

201 through 284 / 1/8 / .139 +/-.004 / .101 to .107 / .028 to .042 / 20 to 30 / .177 to .187 / .158 to .164 / .010 to .025

Parker Hannifin, O-Ring Handbook — Design Chart 4-3: O-Ring Face Seal Glands — p. 1

Tabletop: Directly hands the mill the numbers for every lid and port groove on the next machine's chamber; note the vacuum groove width is narrower than the liquid-service column.

Surface finish X: 32 for liquids, 16 for vacuum and gases. Finishes are RMS values.

Parker Hannifin, O-Ring Handbook — Design Chart 4-3: O-Ring Face Seal Glands — p. 1

Tabletop: A fly-cut or turned finish on the chamber lid seat should be specified/checked to 16 RMS; a rougher face is a common reason a 1e-6 Torr system stalls in the 1e-5s.

For External Pressure (inward pressure direction) dimension the groove by its inside diameter (Hi) and width: (H)i = Mean I.D. of O-ring

Parker Hannifin, O-Ring Handbook — Design Chart 4-3: O-Ring Face Seal Glands — p. 1

Tabletop: For an evacuated chamber atmospheric pressure pushes the ring inward, so the groove ID (not OD) is the controlled dimension when laying out the lid groove.

A good rule of thumb is to provide a pumping speed of at least 1 liter/sec at 10-5 mm Hg per liter of volume ... 15 to 20 min is considered a good design figure.

Livingston & Blewett, Particle Accelerators (1962) — p. 197-198

Tabletop: For a ~30-50 liter tabletop chamber the SI100 (~100+ l/s class) comfortably beats the 1 l/s-per-liter rule - margin that matters because source gas load dominates.

A double-gasket seal is frequently used with a pump-out connection to the space between gaskets. This arrangement makes it possible to test the seal for vacuum-tightness quickly and with certainty.

Livingston & Blewett, Particle Accelerators (1962) — p. 200

Tabletop: Worth adopting on a next machine's main lid: a guard-vacuum groove turns the worst leak hunt into a valve twist.

increasing the squeeze reduced the leak rate dramatically... at 50% squeeze the beneficial effect of the grease was not detectable.

Parker Hannifin, O-Ring Vacuum Sealing, Catalog 5705B (1998) — p. 3-4

Tabletop: Justifies cutting a next machine's grooves at the deep end of the squeeze range (25-30%) rather than greasing the rings harder; grease is a crutch for light squeeze.

L = .7FDPQ(1-S)2 where: L = Approximate leak rate of the seal, std. cc/sec.

Parker Hannifin, O-Ring Vacuum Sealing, Catalog 5705B (1998) — p. 5

Tabletop: Lets the builder compute the permeation floor of their 10-inch Viton lid seal and check whether O-ring permeation, not leaks, sets their ultimate pressure.

care being taken to insure that there are no machine or tool marks perpendicular to the seal... The ideal surface finish for any vacuum seal flange has a circular lay

Parker Hannifin, O-Ring Vacuum Sealing, Catalog 5705B (1998) — p. 5

Tabletop: Face the lid seat on a lathe (concentric lay) rather than fly-cutting or hand-sanding radially; never sand a groove crosswise to remove a blemish.

Vacuum Level: Approximately 1 x 10-6 torr ... Butyl .18 ... Nitrile 1.06 ... Nitrile 3.45 ... Fluorocarbon .07

Parker Hannifin, O-Ring Vacuum Sealing, Catalog 5705B (1998) — p. 6

Tabletop: At exactly the reference machine's operating pressure: cheap Buna-N rings will slowly deposit oily film on feedthrough insulators and dee stems; Viton's 0.1%-class loss is why it is worth the money.

Butyl 6.5 @ 77F ... Fluorocarbon 12.7 @ 77F ... Silicone 238.0 @ 77F

Parker Hannifin, O-Ring Vacuum Sealing, Catalog 5705B (1998) — p. 7

Tabletop: Confirms Viton is a sound choice at 1e-6 Torr; if helium leak checking becomes routine, remember He walks through silicone and fluorosilicone.

Alpha resolution measurements should be made with a detector source spacing equal to 1.5 to 2 times the detector diameter and under good vacuum (< 100 microns HG or 10 Pa).

Canberra, PIPS Detector Instruction Sheet (2012) — p. 1

Tabletop: For his ~8 mm active-diameter PIPS, that is 12-16 mm standoff; closer spacing degrades resolution through wide-angle entrance-window losses.

This maximum value called the 'critical forepressure,' ranges from 25-75 Pa (0.2-0.6 Torr)... The critical forepressure should never be exceeded.

O'Hanlon, A User's Guide to Vacuum Technology, 3rd ed. (2003) — p. 232-233

Tabletop: Size and maintain the SI100's backing pump so the foreline stays well under ~0.2 Torr even during beam-gas loads; a tired rotary pump silently pushes the foreline over the cliff and dumps oil vapor into the chamber.

The outgassing rate of unbaked, uncleaned stainless steel is of order 10-5 Pa-m/s after 10 h of pumping... reduced by a factor of 10-100... to be suitable for high vacuum

O'Hanlon, A User's Guide to Vacuum Technology, 3rd ed. (2003) — p. 308

Tabletop: Multiply the next machine's internal area by 1e-5 Pa-m/s and divide by delivered pumping speed to predict the 10-hour base pressure before drilling a single hole.

O-rings are typically compressed 15-20% of their diameter... the general criterion for high vacuum sealing to be a minimum initial contact pressure of 13 kg/cm2

O'Hanlon, A User's Guide to Vacuum Technology, 3rd ed. (2003) — p. 337-338

Tabletop: The 2.7 kg/cm figure sizes the lid bolting: a 10-inch-circumference seal needs on the order of 200+ kg of clamping just for the ring, before atmospheric load helps.

An unbaked Viton O-ring will have an initial outgassing rate of 10-3 Pa-m/s... After a 4-h bake at 150C and 12 h of pumping, this value is reduced to 4x10-7 Pa-m/s.

O'Hanlon, A User's Guide to Vacuum Technology, 3rd ed. (2003) — p. 340

Tabletop: Pre-baking the Viton rings in a small vacuum oven before assembly is one of the cheapest order-of-magnitude improvements available to a diffusion-pumped 1e-6 Torr system.

Grease is not needed to make a static seal between an elastomer and a metal surface. It will cause pressure bursts as trapped gas pockets are released.

O'Hanlon, A User's Guide to Vacuum Technology, 3rd ed. (2003) — p. 340

Tabletop: Counters the amateur habit of greasing everything; on a clean 16 RMS seat with proper squeeze, dry Viton seals better and cleaner.

one should not rough a chamber with an oil-sealed mechanical pump below a pressure of circa 10-15 Pa (100-150 mTorr), otherwise oil backstreaming would contaminate the chamber... the '100-mTorr rule' is valid [for small systems]

O'Hanlon, A User's Guide to Vacuum Technology, 3rd ed. (2003) — p. 379-381

Tabletop: The reference machine's chamber is exactly the 'prototypical small system': valve over to the SI100 at ~100 mTorr, don't let the rotary pump grind down to 10 mTorr first.

External leak checking with helium should begin at the top of the chamber; only a small helium flow rate is necessary... Welds and seals are the most common leak sites

O'Hanlon, A User's Guide to Vacuum Technology, 3rd ed. (2003) — p. 467-470

Tabletop: Helium rises - spraying from the bottom up floods every joint at once and destroys localization on a chamber with many ports.

A molecular leak causes a linear increase in pressure with time. Outgassing causes the pressure to rise to a steady-state value

O'Hanlon, A User's Guide to Vacuum Technology, 3rd ed. (2003) — p. 468-469

Tabletop: First diagnostic to run whenever a next machine won't reach base pressure - it needs only the existing gauge and a stopwatch, and decides whether to reach for the helium bottle or the bakeout tape.

The permeation time is about 20 min for a typical Viton O-ring... First, do not attempt to leak check the system during baking.

O'Hanlon, A User's Guide to Vacuum Technology, 3rd ed. (2003) — p. 469-470

Tabletop: On an all-Viton chamber, spray briefly and wait; a slowly rising He signal minutes after spraying is gasket permeation, not a leak at the last joint sprayed.

Air leaks are discerned by the presence of oxygen at m/z = 32... Outgassing and water line leaks each can produce a large peak at m/z = 18, but they can be distinguished by the rate of rise.

O'Hanlon, A User's Guide to Vacuum Technology, 3rd ed. (2003) — p. 471

Tabletop: A used RGA head is arguably the single best diagnostic upgrade for a next machine - one spectrum replaces a day of guessing.

the molecular conductance per unit area of any structure in molecular flow has a maximum value [11.6 L/(s-cm2) for air at 22C]

O'Hanlon, A User's Guide to Vacuum Technology, 3rd ed. (2003) — p. 48-50

Tabletop: Sets the ceiling on what the SI100 can actually pump through the chamber port: a 4-inch (81 cm2) opening passes at most ~940 L/s, and a baffled elbow far less - size the pump port as large and short as possible.

Room temperature outgassing data for most gases sorbed on metals, including water vapor, show the outgassing rate to vary inversely with time, at least for the first 10 h

O'Hanlon, A User's Guide to Vacuum Technology, 3rd ed. (2003) — p. 80-81

Tabletop: Explains why the chamber keeps improving overnight without any leak being fixed, and why comparing pump-down curves is only fair at equal elapsed times.

Rule of thumb - one monolayer consists of ~1e15 molecules (atoms) per cm2

Bertolini, Accelerator Vacuum and Mechanical Engineering — USPAS course, UCRL-MI-201847 (2004) — p. 42-43

Tabletop: Explains why pump-down history and surface cleanliness dominate over chamber volume: the reference machine's chamber volume empties in seconds, the walls take days.

Real Leaks: external, constant flow, constant pressure rise. Virtual Leaks: internal, decreasing flow, decreasing pressure rise.

Bertolini, Accelerator Vacuum and Mechanical Engineering — USPAS course, UCRL-MI-201847 (2004) — p. 429-433

Tabletop: The decreasing-vs-constant slope distinction also flags virtual leaks from unvented hardware, which a helium sprayer can never find from outside.

Vacuum rated to 1 x 10-8 Torr (better suited to 1 x 10-6 Torr). Temperature rating is dependent on which elastomer o-ring is used (usually 150C)

Bertolini, Accelerator Vacuum and Mechanical Engineering — USPAS course, UCRL-MI-201847 (2004) — p. 443-446

Tabletop: Matches the reference machine's observed 1e-6 range with Viton - it is the natural floor of an all-elastomer system; a CF port or two on a next machine (gauge, RGA) buys headroom cheaply.

Avoid phrases like; leak tight, vacuum tight, good to 10-8 Torr, good for ultrahigh vacuum, etc.

Bertolini, Accelerator Vacuum and Mechanical Engineering — USPAS course, UCRL-MI-201847 (2004) — p. 456-464

Tabletop: When farming out a next machine's welds or buying used hardware, write the acceptance spec as a number (e.g. no single leak >1e-9 atm-cc/s He) - 'vacuum tight' is unenforceable.

Stainless Steel (unpolished) 266 [1 hr] 20 [4 hrs]... Mild Steel, slightly rusty 58,520 199 (mBar-l/sec-cm2 x 10-10)

Bertolini, Accelerator Vacuum and Mechanical Engineering — USPAS course, UCRL-MI-201847 (2004) — p. 49

Tabletop: The 200x penalty for rusty mild steel is the argument for keeping any exposed magnet pole faces inside the chamber plated, painted with vacuum-compatible coating, or clad in stainless.

Mechanical Cleaning; Degreasing or Solvent Cleaning; Detergent Cleaning; Chemical Etch; Electrolytic Polishing; High Pressure Spray; Bake-out

Bertolini, Accelerator Vacuum and Mechanical Engineering — USPAS course, UCRL-MI-201847 (2004) — p. 497-513

Tabletop: Scaled down: acetone wipe, hot detergent wash, DI rinse, N2 or oven dry, gloves-only handling afterward gets most of the professional benefit for chamber internals.

A virtual leak is a volume of trapped atmospheric gas that leaks into the vacuum vessel through holes or cracks that do not go all the way through the vessel wall. [Examples:] Unvented Screw, Two Welds in Series, Unvented Double O-rings

Bertolini, Accelerator Vacuum and Mechanical Engineering — USPAS course, UCRL-MI-201847 (2004) — p. 59-63

Tabletop: Every internal socket-head screw in the next machine (dee supports, ion source mounts) needs a vent hole, a slotted thread, or a vented washer; a slot machined in the O-ring groove floor serves the same purpose.

Face-type o-ring seals are recommended. Use as heavy a squeeze as possible... Two o-rings in series can drastically reduce permeation.

Bertolini, Accelerator Vacuum and Mechanical Engineering — USPAS course, UCRL-MI-201847 (2004) — p. 71-74

Tabletop: If a next machine targets below ~5e-7 Torr with elastomers, a double O-ring lid groove pumped by the existing roughing pump (guard at ~15 mTorr) removes the permeation floor for the cost of one extra groove and a hose barb.

An acceptable vacuum would allow for a mean free path an order of magnitude larger than the expected flight distance.

Dewan, Design and Construction of a Cyclotron Capable of Accelerating Protons to 2 MeV — MIT thesis (2007) — p. 9-11

Tabletop: The quantitative vacuum spec for a next machine: total path length ~ (final energy)/(energy per turn) x orbit circumference; halving dee voltage doubles path length and tightens the pressure requirement proportionally.

Seam welds are continuous, with welding only on the atmosphere side. The internal braces are stagger welded to keep virtual leaks at a minimum.

Ramler & Parker, The Argonne 60-Inch Cyclotron — ANL-5907 (1959) — p. 7

Tabletop: Standard practice worth enforcing on any welded chamber or fitting on a next machine: no vacuum-side seal welds, no closed pockets.

the frequency with which starbursts appeared at particle sites, I have concluded that particles cause breakdown

Werner, Probing and Modeling Voltage Breakdown in Vacuum — Cornell dissertation (2004) — p. 46, 78

Tabletop: When a next machine sparks, a loupe inspection for starbursts/craters tells the builder exactly where the field problem is instead of guessing from outside the chamber.

if there are contaminant particles, then they, and not the substrate material, determine the breakdown voltage.

Werner, Probing and Modeling Voltage Breakdown in Vacuum — Cornell dissertation (2004) — p. 84

Tabletop: The builder can keep aluminum dees rather than exotic electrodes: cleaning and conditioning matter, native oxide does not.

Both sites reached 95 MV/m at 100 C with no evidence of field emission ... At room temperature (22 C), field emission began near 40 MV/m, and breakdown occurred around 90 MV/m

Werner, Probing and Modeling Voltage Breakdown in Vacuum — Cornell dissertation (2004) — p. 96

Tabletop: A gentle heat-lamp or heater-tape bake of the dee assembly before HV runs should measurably raise the reference machine's sparking threshold.

a preliminary vacuum of about 10^-5 mm hg should be attained; during 'bakeout' pressure should not exceed ~10^-3 mm. Operation as a cyclotron can be attempted with a pressure of 10^-4 mm or less

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 6

Tabletop: Directly applicable pressure targets; matches the regime the builder already operates in and sets the next machine's spec.

preliminary washing of the parts in CCl4 is recommended to remove organic matter

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

Tabletop: Directly applicable (use modern solvents, not CCl4); degrease every part of a next machine that sees vacuum.

a 3 inch diameter tube in the corner can extend directly downwards to a vacuum pump underneath. This design choice maximizes vacuum conductance.

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

Tabletop: Pumping a gas-fed cyclotron is conductance-limited; a next machine should place the pump under the chamber with the largest, straightest duct possible.

Steel supporting rods allow thin top and bottom plates to minimize thickness

Baumgartner & Heuer, The Cyclotron Kids 14-Inch Accelerator (2010) — p. 6-7

Tabletop: Every millimeter of lid steel is a millimeter of magnet gap; internal posts (placed outside the beam plane) let the builder close the next machine's gap without a lid that dishes under vacuum.

You can hasten the process by running the fusor to degas the inner surfaces. This sends the pressure upward, but after a few minutes it starts to drop

Hull, The Farnsworth/Hirsch Fusor — The Bell Jar, Vol. 6 No. 3/4 (1997) — p. 5-6

Tabletop: Same conditioning applies to the reference machine's chimney and dee surfaces: schedule a beam-on bake-in run and expect pressure excursions before stable operation.

To fully clean the system of residual gases, an initial base pressure of around 1e-6 Torr is necessary. A leak valve is then used to backfill the chamber with deuterium to a pressure in the range of 1 to 10 microns.

Hull, The Farnsworth/Hirsch Fusor — The Bell Jar, Vol. 6 No. 3/4 (1997) — p. 6

Tabletop: The base-pressure-then-backfill discipline is exactly the reference machine's MFC workflow; a 100:1 ratio of operating to base pressure keeps beam-gas composition dominated by the feed gas.

an Innovac R220 diffusion pump and Kurt J Lesker TNR6XA150QF cold trap are used, which can lower the pressure to about 1e-4 Pa (1e-6 torr)

Loucks, Initial Results from the Houghton College Cyclotron — Houghton College thesis (2007) — p. 41-43

Tabletop: Matches the reference machine's scale exactly: 1e-6 torr base bled up with hydrogen for the source is the working point of every successful machine in this peer group.

A 2.54 cm thick ring with an outer radius of 9.9 cm and an inner radius of 8.5 cm was milled from 6061 T6 aluminium ... Ports were made in the chamber wall using ten KF-16 flanges, which were secured using Hysol Loctite 1C vacuum epoxy

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

Tabletop: A complete, copyable chamber spec for an 8-inch-pole machine, including the epoxy-in-flange trick that avoids welding.

continuous square rubber gaskets located in grooves in the faceplates of sufficient cross section to accommodate the entire gasket under pressure. The resulting metal-to-metal contact ... has proved very satisfactory.

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 41

Tabletop: Directly applicable to a next machine's chamber lids and faceplates; grooved captive gaskets beat flat sheet gaskets for repeatable sealing and alignment.

a steady stream of dry air injected into the outlet side of the pump cylinder could eliminate the need for a refrigerated vapor trap ... dry air is used in the tank in order to minimize the amount of moisture

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 44

Tabletop: Directly applicable: vent the next machine's chamber with dry nitrogen or desiccated air, never room air, and water-vapor pumpdown time drops dramatically.

the ion gauge is not turned on until the tank pressure is less than 0.5 microns ... the wall of the manifold provides the tube filament with some protection from the magnetic field

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 45

Tabletop: Directly applicable gauge practice near a stray-field-rich H-frame magnet.

far more rugged than the triode ion gauge and sensitive to small changes in pressure; but it is probably not as accurate in reading absolute pressure.

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 46

Tabletop: Directly applicable: a cheap Penning head is the right always-on interlock and gas-flow monitor for a next machine, with the ion gauge kept for absolute readings.

Rate of rise on tank assembly 0.00015 microns/sec

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 46

Tabletop: Scale by volume: an equally tight ~30 L chamber on a next machine would show ~4e-5 torr/s; measure rate-of-rise after every re-seal as the standard leak health metric.

Employing a seal squeeze of up to 40% inhibits media flow through the seal... because of the decreased groove depth, increased groove width is essential.

Apple Rubber Products, Seal Design Guide — p. 84

Tabletop: Endorses going beyond Parker's 30% on critical static vacuum joints if the groove is widened to take the displaced volume; 'postcuring' is the vendor name for the pre-bake O'Hanlon recommends.

As we tighten the rest of the bolts the joint is further compressed, and the previously tightened bolts tend to relax and lose some of their preload. In some cases, this can virtually eliminate our bolt tension.

Fastenal, Technical Reference Guide, Rev. 9 (2005) — p. 26

Tabletop: On the next machine's lid, a single-pass tightening leaves the first-torqued sector under-clamped and is a classic cause of an O-ring leak that 'moves' with each reassembly.

when an extra-shallow gland is desired in order to increase the squeeze, it must be made wide enough to accomodate the full O-ring volume.

Parker Hannifin, O-Ring Vacuum Sealing, Catalog 5705B (1998) — p. 1-2

Tabletop: If a next machine's grooves are cut for 30% squeeze, groove cross-section area must still exceed ring cross-section area - check fill before cutting.

Radius R is CRITICAL. Insufficient radius will potentially cause damage to the O-ring during installation, while excessive radius may contribute to extrusion.

Parker Hannifin, O-Ring Vacuum Sealing, Catalog 5705B (1998) — p. 10

Tabletop: Worth it for a hinged or frequently-removed lid where the ring falls out during assembly; otherwise plain rectangular face grooves are cheaper and more tolerant.

after the welding, the bottom plate contracted so much that it bent the whole frame out of shape... seal the bottom plate against the frame using a flat Viton ring.

Baumgartner, The Cyclotron Kids' 2 MeV Proton Cyclotron — Cyclotrons 2013, WE1PB05 (2013) — p. 2-3

Tabletop: A fabrication trap the builder can skip entirely: o-ring/flat-gasket both lids, weld nothing flat and thin.

This stretch should be between 1%-5% with 2% as the ideal in most applications. A stretch greater than 5% is not recommended.

Apple Rubber Products, Seal Design Guide — p. 11

Tabletop: When picking the AS-568 size for a non-standard groove (dee-stem feedthrough, viewport), size so the ring sits at ~2% stretch rather than swimming or straining.

The maximum volume of the O-ring should never surpass the minimum volume of the gland... the O-ring volume does not exceed 95% of the gland void.

Apple Rubber Products, Seal Design Guide — p. 14-16

Tabletop: Check fill arithmetic including worst-case ring tolerance before machining; Viton heated by RF or magnet proximity expands ~16e-5/C and needs that free volume.

a finish of 32 micro-inches RMS is preferred... Static seal cross sections are generally compressed from 10% to 40%, whereas dynamic seals are from 10% to only 30%.

Apple Rubber Products, Seal Design Guide — p. 19, 61

Tabletop: For a rotating or sliding shaft feedthrough (target manipulator), back off to <=30% squeeze and a 16-32 RMS shaft finish, or friction will shred the ring.

Do not use a lubricant composed of the same material as the O-ring because 'like' will dissolve 'like.' For example, a silicone lubricant should not be used with a silicone O-ring.

Apple Rubber Products, Seal Design Guide — p. 20, 109

Tabletop: Silicone vacuum grease on Viton is fine; silicone grease on a silicone ring (or hydrocarbon grease on Buna-N) slowly destroys it.

In order to use a standard round O-ring, the inside corner radius of the groove should not be less than three times (3X) the O-ring cross-section diameter.

Apple Rubber Products, Seal Design Guide — p. 84

Tabletop: Directly applicable to a racetrack or rectangular lid/port on a next machine: a 1/8 in. cord ring needs >=3/8 in. corner radii or it will bunch and leak at the corners.

A typical figure, used in the MIT cyclotron, is a dR of 0.15R. The deflector gap is usually tapered ... Spacings as small as 1/8 in. can be used at the entry slit, opening to 1/2 in. or greater at the exit.

Livingston & Blewett, Particle Accelerators (1962) — p. 180-181

Tabletop: Scaled to 160 keV the same geometry needs only ~500-900 V on the deflector - an easy supply; keep the entry slit no wider than the turn separation.

304L SS, most commonly used in vacuum, a little more expensive... Joint design is critical from vacuum, metallurgical and distortion standpoints. Cleanliness is essential.

Bertolini, Accelerator Vacuum and Mechanical Engineering — USPAS course, UCRL-MI-201847 (2004) — p. 355-360

Tabletop: For a next machine's chamber welds specify 304L filler and pipe where possible; carbide precipitation in plain 304 welds is a known source of micro-leak porosity.

a lid with radius 10 centimeters and thickness of 3.5 millimeters would undergo less than 1 mm of deflection when covering a chamber with internal pressure of 1e-3 Torr

Dewan, Design and Construction of a Cyclotron Capable of Accelerating Protons to 2 MeV — MIT thesis (2007) — p. 12

Tabletop: Gives the builder the actual formula for trading a next machine's lid thickness against magnet gap - a few mm of 7075 plate suffices at 8-12 inch chamber diameter if the edge is well supported.

all cyclotron components must be made of magnetically transparent materials such as aluminum, copper, or brass

Dewan, Design and Construction of a Cyclotron Capable of Accelerating Protons to 2 MeV — MIT thesis (2007) — p. 9

Tabletop: Standard but easily violated rule: screws, feedthrough bodies, and detector hardware inside the reference machine's gap should be checked with a hand magnet before installation.

the VTO box and obround are mounted on a motor-driven carriage which operates on a rail system. This permits the removal of the dee heads... to facilitate maintenance.

Ramler & Parker, The Argonne 60-Inch Cyclotron — ANL-5907 (1959) — p. 6-7

Tabletop: At tabletop scale this means: chamber slides out of the gap, dee removable through a lid, pump cart disconnectable - the difference between a research tool and a sealed monument.

It is seen that particles are detected at about 70 kv. and the numbers increase more rapidly with increase of bombarding energy than with the lithium film.

Oliphant & Rutherford, Experiments on the Transmutation of Elements by Protons (1933) — p. 266-270

Tabletop: Proof that p-B11 alphas are observable far below the 675 keV resonance if the builder integrates tens of uA-hours with large solid angle - and that their alphas stop in under 5 cm of air (vacuum path to PIPS required).

the ion revolution turn spacing near r = 4 inches, in a B-field of 1.0T will be just 0.04 inches, which is smaller than the 0.06 inch RF shield of the tip

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

Tabletop: At the reference machine's ~1.3 kV dee voltage turn spacing is even smaller, so a bare, grooved copper collector (no thick shield) is essential or the probe reads zero while beam exists.

The limit at the entry is set by the dr between successive turns at this radius ... it is desirable to have adjustable controls on deflector spacing and location which can be trimmed empirically.

Livingston & Blewett, Particle Accelerators (1962) — p. 181-183

Tabletop: With 2.6 kV/turn on 160 keV, the reference machine's turn spacing at extraction is ~1.6% of R (~1.3 mm at 3.2 in) - build the septum mount with mm-scale radial adjustment.

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 ua.

Livingston & Blewett, Particle Accelerators (1962) — p. 182

Tabletop: Judge a next machine first on internal-probe current at full radius; a 4:1 ratio between internal and extracted beam is historically normal, not a failure.

the septum is formed of two strips of tungsten, 0.020 in. thick and 12 in. long and with the edges spaced 1/8 in. apart. Each strip is silver-soldered to a copper bar bent to the correct curvature.

Livingston & Blewett, Particle Accelerators (1962) — p. 184

Tabletop: At the reference machine's microamp/keV beam power the thermal problem vanishes, but the slotted-septum geometry still maximizes transmitted current into the channel.

once the particle has been accelerated to 10 MeV the mass has been changed by about 1%, which has a frequency shift of 1%.

King, A Preliminary Design for a Small Permanent Magnet Cyclotron — Houghton College thesis (2002) — p. 12, 21

Tabletop: Reassurance with numbers: at the reference machine's 100 keV-1 MeV scale, relativistic detuning is ~0.01-0.1% and can be ignored in a next machine's design.

The separation for non-relativistic ions is dR = (R/2) (2qVo sin phi_s/T)... Eq. (15.3) implies that dR = 0.44 cm.

Humphries, Principles of Charged Particle Acceleration (1986) — p. 527

Tabletop: Lets the builder compute whether their probe or a future septum can distinguish final turns: at 150 keV, R~9 cm and 5 kV/turn gives dR ~ 3 mm - workable.

0.15 0.91 +/- 0.015... 0.65 218.42 +/- 0.55

Spraker et al., The 11B(p,α)8Be → α+α and the 11B(α,α)11B Reactions at Energies Below 5.4 MeV (2012) — p. 360

Tabletop: The master rate table for the reference machine's PIPS count-rate prediction across their entire 150-675 keV window; it quantifies exactly what reaching the resonance is worth.

Vd = 32.531 kV

Ponter, Beam Energy Measurements with a New HV Deflection System and Ion Source Upgrades on the Rutgers 12-Inch Cyclotron (2010) — p. 6

Tabletop: Gives the builder the extraction-voltage scale for a next machine: deflector kV requirements scale linearly with beam energy, so a ~100 keV beam needs only ~7 kV in the same geometry.

H2+/9 H+/7 H+/5 H+/3 H+ H2+

Yuly et al., Modifications on the Houghton College Cyclotron (2010) — p. 15-18

Tabletop: Prevents misidentifying beam in the reference machine's B-field sweeps: a peak at one-third the expected field is the same ion on the 3rd harmonic, not a new species.

At -25 kV, 8 mA, and 16 mtorr, neutron levels were 60 cpm. This measurement confirmed that nuclear fusion was achieved.

Kovalchick, Deuterium Fusion Using Inertial Electrostatic Confinement (2012) — p. 45-46

Tabletop: Same lesson as p-B11 cross-section curves: yield is exponential-ish in particle energy, so for the builder every extra 10% beam energy buys far more counts than 10% more current.

It was limited to low level output by its 22kv internal supply. 103 n/sec... a 33 kilovolt supply. 105 n/sec... currently produces in excess of 600,000 neutrons per second

Hull, Fusor: An Easy to Construct Fusion Reactor Based on Inertial Electrostatic Confinement (2009) — p. 36-39

Tabletop: Reinforces the energy-over-current rule for the builder: sub-Coulomb-barrier reaction rates reward every extra keV exponentially.

If many ions in the beam fall out of phase before reaching maximum Dee radius, the beam current will drop suddenly to near zero beyond whatever radius the ions tend to reach

Morrow, Focusing in the Houghton College Cyclotron — Houghton College thesis (2015) — p. 28, 57

Tabletop: Diagnostic rule: a sharp cutoff in the radial current profile means phase slip, not wall collisions - which points at field shape/Dee voltage rather than focusing.

for a fixed frequency f, resonances will occur for lower magnetic fields, e.g. B/3 and B/5, corresponding to an odd multiple of a lower frequency

Yuly, The Houghton College Cyclotron: a Tool for Educating Undergraduates — Cyclotrons 2013, WE1PB01 (2013) — p. 4-5

Tabletop: Practical commissioning technique: the builder can confirm they are accelerating protons (not H2+ or contaminants) with only a magnet current sweep and an electrometer.

Frame-by-frame analysis... revealed that ions nominally populate 40 degrees of the 360 degree RF cycle in our cyclotron.

Koeth, Undergraduate Education with the Rutgers 12-Inch Cyclotron (2015) — p. 9

Tabletop: Sets expectations for pulsed diagnostics and duty-factor arithmetic on any measurement the builder makes with fast instrumentation.

The stray magnetic field over T effectively prevents the escape of secondary electrons, so that the current measured is the true ion current.

Oliphant & Rutherford, Experiments on the Transmutation of Elements by Protons (1933) — p. 262

Tabletop: The reference machine's Faraday cup inside the cyclotron fringe field gets free secondary-electron suppression; outside the field it needs an explicit suppressor bias or magnet.

a mica window W, 1 cm in diameter and supported on a grid which subtends the smallest possible area... The solid angle obtained in this way is approximately 0.7.

Oliphant & Rutherford, Experiments on the Transmutation of Elements by Protons (1933) — p. 262-265

Tabletop: The close-geometry, calibrate-with-a-known-alpha-source method is exactly how the builder should commission their PIPS geometry before hunting p-B11 alphas.

One technique has been to measure the width of the region of induced radioactivity on the leading edge of probes inserted to different radial locations.

Livingston & Blewett, Particle Accelerators (1962) — p. 174-167

Tabletop: A radial probe (the reference machine's shielded Faraday cup on a linear feedthrough) is the workhorse diagnostic; falling current at some radius localizes where field shape loses the beam.

The frequency for resonance can be measured and reduced to magnetic field through the relation B = (234.82 +/- 0.13)f where B is in gauss and f is in megacycles per second.

Livingston & Blewett, Particle Accelerators (1962) — p. 286-287

Tabletop: 5.9 kG corresponds to 25.1 MHz proton NMR; the machine's own resonance (f, e/m) also gives the average field to ~0.5%, a free sanity check.

Pulser line width should be about 5 keV (FWHM) narrower than Alpha Resolution ... the noise level which is approximately 3 times the pulser line width (FWHM).

Canberra, PIPS Detector Instruction Sheet (2012) — p. 1-3

Tabletop: A pulser check separates electronics noise (grounding, RF pickup from the 9 MHz drive) from true detector degradation without risking source contamination.

A retarding grid attached to the front of the Faraday cup will eliminate loss of secondary electrons... The grid will be at some negative potential.

King, A Preliminary Design for a Small Permanent Magnet Cyclotron — Houghton College thesis (2002) — p. 24

Tabletop: Slightly better-engineered alternative to the 9 V cup bias; easy to add to the reference machine's beam probe.

either one rocked back and forth until a current peak is indicated on the target probe. The probe may be pushed in closer to the center to facilitate locating this resonance.

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

Tabletop: Directly applicable commissioning procedure; starting the search at small radius relaxes the resonance tolerance enormously.

the authenticity of the beam should be checked by the sharpness of resonance as a function of r.f. tuning and magnet current, as well as by its sensitivity to hydrogen gas pressure

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

Tabletop: Directly applicable; a 'beam' that stays constant while you detune B or RF is ion leakage to the probe, not orbiting protons.

The six-inch cyclotron has indicated a 7 microampere beam, at a frequency corresponding to about 800 kv protons.

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

Tabletop: Directly comparable scale; microamp-level internal beam is a realistic expectation for a next machine and the choke-protected probe is the right pickup.

a convenient target substance would be LiF which, when bombarded with protons, will emit gammas from Li ... The target may be prepared by simply fusing a small amount of LiF onto a small stainless steel block

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

Tabletop: Partially applicable: the p-Li gamma resonance needs ~440 keV, above the reference machine's 160 keV; a next machine reaching 0.5 MeV could use exactly this LiF-on-probe gamma check with their gamma detector.

At these energies beam intensities varied from 0.5 to 10 nA on target and beam resolution varied from approximately 60 to 70 keV.

Spraker et al., The 11B(p,α)8Be → α+α and the 11B(α,α)11B Reactions at Energies Below 5.4 MeV (2012) — p. 359

Tabletop: The single most encouraging number in the batch: professional low-energy p-B11 data were taken at exactly the reference machine's nA beam scale.

simulations show that out of the three emitted a-particles, on average 2.1 a-particles contribute to this peak at the 0.675 MeV resonance

Spraker et al., The 11B(p,α)8Be → α+α and the 11B(α,α)11B Reactions at Energies Below 5.4 MeV (2012) — p. 359-360

Tabletop: When the builder converts PIPS counts to a 'cross section' they must divide by ~2 alphas per reaction - or better, publish counts-per-luminosity as this paper does.

The relative solid angles for each detector were measured using low energy Rutherford scattering on gold as well as a known 241Am source.

Spraker et al., The 11B(p,α)8Be → α+α and the 11B(α,α)11B Reactions at Energies Below 5.4 MeV (2012) — p. 360

Tabletop: The builder already owns the pieces: their Faraday cup/Keithley 617 integrates charge, and an Am-241 check source calibrates PIPS solid angle and energy scale.

energy at far left: T=.5087 MeV ... dT=13.3 keV ... Theory: dT/2=12.73 keV

Ponter, Beam Energy Measurements with a New HV Deflection System and Ion Source Upgrades on the Rutgers 12-Inch Cyclotron (2010) — p. 35-40

Tabletop: Shows a phosphor screen plus this one formula suffices for energy-spread measurement at student-machine scale - no magnetic spectrometer needed.

The location of the ammeter in the circuit keeps it essentially at ground potential... Do not omit the 10 meg bleeder resistor.

Hull, The Farnsworth/Hirsch Fusor — The Bell Jar, Vol. 6 No. 3/4 (1997) — p. 8

Tabletop: The ground-leg metering trick is how the builder can safely log arc and extraction currents on the next machine without floating instruments at kV.

The beam current measured was lower with the addition of the voltage bias... the bias reduces the emission of secondary electrons, resulting in a more accurate measurement.

Fuller, Exploring the Capabilities of the Houghton College Cyclotron — Houghton College thesis (2013) — p. 55-56

Tabletop: A one-component fix for honest current numbers on any Faraday-cup measurement the builder makes.

A +9 V bias can be applied to the target using a battery to reduce the effect of secondary electrons on beam current measurements ... secondary electrons are created in significant numbers on the target.

Yuly, The Houghton College Cyclotron: a Tool for Educating Undergraduates — Cyclotrons 2013, WE1PB01 (2013) — p. 4-5

Tabletop: One battery fixes a systematic error in the main diagnostic the builder has; also gives a way to separate true beam from secondaries.

The highest proton energy obtained so far is about 160 keV, with a 3 pA peak near the correct magnetic field of 796 mT for 12.1 MHz.

Yuly, The Houghton College Cyclotron: a Tool for Educating Undergraduates — Cyclotrons 2013, WE1PB01 (2013) — p. 5

Tabletop: Calibrates expectations exactly at the reference machine's operating point (~160 keV) and names the three things that gate the next factor of 2-3: magnet current, cooling, RF frequency.

operating steadily for some time with 500 ua of 23 Mev protons on a 6 by 10 inch water-cooled aluminum target of the grazing-incidence type

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

Tabletop: Overkill at the reference machine's ~mW beam power, but the geometry trick transfers if a next machine ever puts tens of watts on a probe tip: tilt the target.

By having only three faces any one face is completely shielded from the material sputtered from that which is in the beam

Oliphant & Rutherford, Experiments on the Transmutation of Elements by Protons (1933) — p. 262

Tabletop: A boron target plus a blank plus a calibration face on one rotatable holder would let the builder switch targets and measure background without venting.

it is a good idea to evacuate the chamber for 10 to 15 minutes before applying bias. This will remove excess surface moisture ... It is recommended to wait 30 seconds to stabilise the detector.

Canberra, PIPS Detector Instruction Sheet (2012) — p. 1

Tabletop: Interlock the PIPS bias supply to chamber vacuum in the beam-diagnostics routine; biasing a humid detector raises leakage and can damage the junction.

use a cotton ball dampened with a good quality isopropyl alcohol; Do not use methyl alcohol ... put under vacuum for 15 minutes or heat to 50 C for an hour to remove residual moisture before applying bias.

Canberra, PIPS Detector Instruction Sheet (2012) — p. 1

Tabletop: The ~500-angstrom implanted window scratches easily; in a chamber with pump oil and target debris this is the only sanctioned cleaning procedure.

Remember that leakage current doubles for about 5 C rise in temperature and take this into account when you compare your measurement to that of the factory.

Canberra, PIPS Detector Instruction Sheet (2012) — p. 1-3

Tabletop: A detector near warm cyclotron hardware can legitimately read several times 10 nA; only a rise beyond the temperature-corrected value indicates radiation damage or contamination.

Recommended bias voltage +130 Volts ... Full depletion bias voltage +110 Volts ... Maximum bias voltage +150 Volts

Canberra, PIPS Detector Instruction Sheet (2012) — p. 2-3

Tabletop: The reference machine's two detectors (S/N 98343/98344) have only 20 V of headroom above recommended bias; a supply glitch to 150+ V risks breakdown, so use a current-limited, capped supply.

(10 ... 300 um thick): 100ps-30ns. Thick (~cm) Si or Ge detector: 1-10us

Spieler, Semiconductor Detectors Part 2 — SLUO Lectures on Detector Techniques, Lecture 7 (1998) — p. 2

Tabletop: The reference machine's PIPS collects alpha charge in nanoseconds; they can choose shaping time purely for noise optimum without worrying about ballistic deficit.

S/N cannot be improved by feedback. This result is generally valid, i.e. it also holds for active integrators (charge-sensitive amplifiers).

Spieler, Semiconductor Detectors Part 2 — SLUO Lectures on Detector Techniques, Lecture 7 (1998) — p. 24

Tabletop: For the builder: mount the preamp on the vacuum feedthrough, not at the far end of a coax run - every pF of cable directly worsens alpha energy resolution.

Detector capacitance may vary within a system or change with bias voltage (partially depleted semiconductor diode)... Amplifier output directly determined by signal charge, insensitive to detector capacitance

Spieler, Semiconductor Detectors Part 2 — SLUO Lectures on Detector Techniques, Lecture 7 (1998) — p. 3-8

Tabletop: Confirms the standard PIPS chain for the p-B11 experiment: a charge-sensitive preamp at the feedthrough, never a plain voltage amp on the diode.

en2 = 12 tau IB + 6e5 tau/RP + 3.6e4 vn2 C2/tau [rms electrons]

Spieler, Semiconductor Detectors Part 2 — SLUO Lectures on Detector Techniques, Lecture 7 (1998) — p. 42

Tabletop: Lets the builder compute expected keV-scale resolution of their PIPS chain from datasheet numbers before buying a shaping amplifier, and re-optimize tau if leakage rises.

a 1 MeV neutron transfers about 60 to 70 keV to the Si recoil atom, which in turn displaces roughly 1000 additional atoms in a region of about 0.1 um size.

Spieler, Semiconductor Detectors Part 2 — SLUO Lectures on Detector Techniques, Lecture 7 (1998) — p. 49

Tabletop: The reference machine's PIPS detectors shrug off the cyclotron's X-ray background but must be shielded or retracted during any neutron-producing (e.g., deuterium) runs.

For 650 MeV protons alpha = 3e-17 A/cm, 1 MeV neutrons alpha = 2e-17 A/cm.

Spieler, Semiconductor Detectors Part 2 — SLUO Lectures on Detector Techniques, Lecture 7 (1998) — p. 51-52

Tabletop: The builder can track their PIPS bias current on the Keithley 617 as a built-in damage log: any secular rise flags beam or neutron exposure of the detector.

Cooling to 0 C typically reduces the reverse bias current to 1/6 of its value at room temperature.

Spieler, Semiconductor Detectors Part 2 — SLUO Lectures on Detector Techniques, Lecture 7 (1998) — p. 52

Tabletop: A Peltier or cold-finger on the PIPS mount is a cheap resolution upgrade if leakage-current shot noise ever dominates the reference machine's alpha spectra.

the common mode of disintegration is into two [alpha] particles which proceed at angles of 150 to 180 relatively to one another, the third particle receiving very little energy

Spraker et al., The 11B(p,α)8Be → α+α and the 11B(α,α)11B Reactions at Energies Below 5.4 MeV (2012) — p. 357-358

Tabletop: Two PIPS detectors in near-back-to-back coincidence would give the builder a background-crushing p-B11 signature even at very low count rates.

While the resonance at 0.675 MeV exhibits isotropy, anisotropy can be seen for the resonance at 2.64 MeV

Spraker et al., The 11B(p,α)8Be → α+α and the 11B(α,α)11B Reactions at Energies Below 5.4 MeV (2012) — p. 358-360

Tabletop: Frees the builder to place their PIPS detectors wherever geometry and shielding are best - solid angle, not angle, is what matters at their energies.

The large peak just below 1 MeV is produced by elastically scattered protons

Spraker et al., The 11B(p,α)8Be → α+α and the 11B(α,α)11B Reactions at Energies Below 5.4 MeV (2012) — p. 358-360

Tabletop: Warns the builder that their PIPS spectra will be dominated below ~1 MeV by scattered protons - set the alpha discrimination window above that, or use a thin proton-stopping foil.

the target, which was composed of 56 +/- 2 ug/cm2 of isotopically pure 11B deposited on a 9 ug/cm2 carbon backing

Spraker et al., The 11B(p,α)8Be → α+α and the 11B(α,α)11B Reactions at Energies Below 5.4 MeV (2012) — p. 360

Tabletop: Defines 'thin' for the reference machine's boron target (tens of ug/cm2) and gives two independent thickness checks they can perform with their own detectors.

D-D fusion can occur in an IEC device at voltages as little as 10 kV or less, but detectable fusion generally does not occur until voltages are at least 15 kV

Kovalchick, Deuterium Fusion Using Inertial Electrostatic Confinement (2012) — p. 18

Tabletop: Calibrates expectations for any sub-threshold nuclear signal at home: being physically above a reaction threshold is not enough; detection thresholds sit well above it.

a peak capture rate is obtained with a 3.89 cm layer of HDPE. This detection method involves positioning the HDPE as close to the neutron source as possible

Kovalchick, Deuterium Fusion Using Inertial Electrostatic Confinement (2012) — p. 23-24

Tabletop: If the builder ever cross-checks their PIPS counting with activation or a moderated tube (e.g., for D-D work), this fixes the moderator thickness to build.

The amateur is limited to the middle or D-D reaction which yields a split 50:50 reaction D+D to T + Proton, D+D to He3 + neutron

Hull, Fusor: An Easy to Construct Fusion Reactor Based on Inertial Electrostatic Confinement (2009) — p. 19-20

Tabletop: The reference machine's aneutronic p-B11 choice sidesteps even this; but if they ever runs deuterium in the cyclotron, D-D is the only license-free fusion fuel.

Fast neutron bubble detector acts as backup to electronic detection

Hull, Fusor: An Easy to Construct Fusion Reactor Based on Inertial Electrostatic Confinement (2009) — p. 43

Tabletop: Same philosophy for p-B11: pair the PIPS/electronics chain with a passive detector (e.g., CR-39 track plastic) immune to the cyclotron's RF pickup.

Thread lubrication is one of the most effective measures to lessen the potential for galling... Heat contributes significantly to thread galling.

Fastenal, Technical Reference Guide, Rev. 9 (2005) — p. 8

Tabletop: Every stainless bolt into the stainless chamber flange gets anti-seize (outside the vacuum) or silver/moly plating (inside); one galled lid bolt can strand the whole chamber.

Pitting primarily in the outline of the electrode - not directly underneath or on top.

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

Tabletop: When the builder opens the chamber after sparking, the pit geography tells them whether to fix edge radii (perimeter pits) or surface contamination (random pits).

We coated the HV electrode with Aerodag G dry lubricant, which is also conductive and has low secondary electron emission coefficient.

Ponter, Beam Energy Measurements with a New HV Deflection System and Ion Source Upgrades on the Rutgers 12-Inch Cyclotron (2010) — p. 53

Tabletop: A cheap surface treatment the builder can apply to deflector or dee edges if they hit breakdown limits near the top of their voltage range.

The grid should be made from tantalum or tungsten wire and be fusion or resistance welded.

Hull, The Farnsworth/Hirsch Fusor — The Bell Jar, Vol. 6 No. 3/4 (1997) — p. 5-8

Tabletop: Applies to the reference machine's chimney slits, puller edges, and beam stops: anything the beam or arc touches for long runs should be refractory metal with welded, not soldered, joints.

With conventional steel nut and bolt materials, a length of engagement of about one nominal diameter of the bolt is typical. A longer thread length engagement will be needed when dealing with tapped holes in soft material.

Fastenal, Technical Reference Guide, Rev. 9 (2005) — p. 14

Tabletop: Tapped holes in aluminum lids or pole pieces need 1.5-2d of thread or inserts; a stripped hole in the finished chamber is far costlier than a longer bolt.

Torque = K x d x F... F = 75% of bolt material proofload for standard bolts... even perfect input torque can give a variation of preload by as much as 25 - 30 %.

Fastenal, Technical Reference Guide, Rev. 9 (2005) — p. 25-26

Tabletop: Gives defensible torque numbers for lid bolts and magnet clamp bolts; critically, if a bolt is lubricated but torqued to the dry-K table value, preload can double and snap the bolt.

we used an installation torque of 70 ft-lbs to obtain a clamp load of 9000 lbs... By the fourth installation, we required 145 ft-lbs to reach a clamp load of 9000 lbs.

Fastenal, Technical Reference Guide, Rev. 9 (2005) — p. 30

Tabletop: Lid bolts cycled dozens of times per year drift far from any torque table; for repeatable magnet-gap or flange clamping, replace nuts periodically or control by turn-of-nut instead of torque.

The project was a long and laborious one, but the efforts were well-rewarded when the first beam was obtained three years later, in the spring of 1957.

McGuire, The Iowa State University 1.5 MeV Undergraduate Cyclotron (1961) — p. 3

Tabletop: Schedule reality check for a next machine and for any educational-accelerator product plan.

TOTAL: $128500. Who has >$125k to blow on a very modest strawman small particle accelerator?

Niell, Effective Scientific Equipment Procurement Strategies: Building on a Budget (2010) — p. 2-3

Tabletop: Calibrates the next machine's budget: every subsystem the builder does not scrounge or fabricate costs thousands new, so design decisions should follow what surplus actually offers.

Cost: Can spend no more than $400. Performance: Want to measure 40MHz sinewaves... Function: Must be in calibration, and nearly bombproof

Niell, Effective Scientific Equipment Procurement Strategies: Building on a Budget (2010) — p. 7-10

Tabletop: A disciplined method for the next machine's shopping list: define B-field, vacuum, and RF numbers first, then match each to the cheapest vendor tier whose reliability the subsystem can tolerate.

The voltage divider allowed use of a low voltage meter by tapping the divider string at a 10,000 part fraction of the total voltage drop.

Kovalchick, Deuterium Fusion Using Inertial Electrostatic Confinement (2012) — p. 18-19

Tabletop: Directly reusable for the reference machine's dee/extraction HV monitoring; a divider-plus-panel-meter is safer and more trustworthy than reading the supply front panel.

One might choose a 12 kV, 60 mA neon sign transformer and use 2 - 12 kV microwave oven diodes... Never apply full voltage immediately to the fusor!

Hull, The Farnsworth/Hirsch Fusor — The Bell Jar, Vol. 6 No. 3/4 (1997) — p. 5-8

Tabletop: A scrounger-grade current-limited HV architecture suitable for the reference machine's source-conditioning and glow-discharge cleaning supplies.

At voltages greater than 20 kV, the resulting x-rays can be hazardous.

Kovalchick, Deuterium Fusion Using Inertial Electrostatic Confinement (2012) — p. 25, 44

Tabletop: The reference machine's dee/extraction voltages are below this, but any HV conditioning or future higher-voltage upgrades cross the 18-20 kV line where viewport X-ray monitoring becomes mandatory.

Both light neutron and x-ray shielding are needed beyond this level and the planned fusor V will incorporate these upgrades.

Hull, Fusor: An Easy to Construct Fusion Reactor Based on Inertial Electrostatic Confinement (2009) — p. 39

Tabletop: Gives the builder a community-vetted numeric line for when a home nuclear device graduates from 'monitored' to 'shielded' - p-B11 alpha work stays far below it.

The axial focusing, as shown above, takes place for any positive values of the field decay exponent. Therefore, orbital stability in both directions takes place only for 0 < n < 1.

Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 18-20

Tabletop: This is the governing stability rule for the weak-focusing reference machine; the FEMM-derived B(r) should be checked for 0 < n < 1 over every acceleration radius, with n typically a few percent.

its passage without noticeable losses of particles becomes possible only due to the fact that the beam crosses it for 1-3 revolutions, and the first harmonic of the magnetic field with a large amplitude is absent

Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 37

Tabletop: In the reference machine Qr = sqrt(1-n) sits just below 1 everywhere, so the key is field symmetry: keep the first-harmonic error (pole tilt, off-center coils) to gauss level or coherent orbit distortion grows every turn.

When transferring the energy of radial betatron oscillations into axial oscillations, the amplitude of the latter turns out to be twice the amplitude of radial oscillations.

Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 39

Tabletop: Very concrete for the reference machine: if the edge-field falloff pushes n through 0.2 near the last turns, the beam blows up vertically into the dee aperture; keep n < ~0.2 until the extraction radius or cross it fast.

If the task is to obtain an average field with a value of the field decay index n close to constant for all radii, then the axial gap g can vary in accordance with the expression

Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 49

Tabletop: A one-line pole-taper recipe for the builder tool: pick n (e.g. 0.02-0.2), machine the gap to this power law, verify in FEMM.

if the field is formed such that the deviation from the isochronous one for all operating radii is no more than 5 G, then this corresponds to a deviation of the RF phase... by no more than 5 degrees

Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 50

Tabletop: A concrete shimming target: on a 0.59 T, 8-inch machine, holding the measured field to ~1e-3 of the design curve (a few gauss) keeps phase errors negligible next to the classical-cyclotron phase slip itself.

the so-called calibration coefficients are introduced to the level of the field created by the windings, which, as a rule, are not large and amount to ~1-2% of the current value

Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 50

Tabletop: Sets the expected FEMM-vs-Hall-probe discrepancy for the reference machine's magnet: 1-2% mismatch is normal (unknown B-H curves, geometry error) and should be absorbed by a per-coil scale factor in the builder tool, not chased in the mesh.

the level of the magnetic field in the center is raised to an amount of a few tens to a few hundred gauss

Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 50-51

Tabletop: Directly usable on a next machine: shim a small central cone so B falls gently from center outward, giving vertical focusing where n ~ 0 would otherwise leave the first turns unfocused.

The presence of the resonance makes it possible to use the first harmonic of the field with a small amplitude (usually a few gauss) to obtain a significant increase in radial amplitudes.

Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 64-65

Tabletop: The dR formula tells the builder exactly what turn spacing a ~kV energy gain buys at 4-inch radius (fractions of a mm), i.e. whether a septum/foil extraction is geometrically feasible for a next machine.

The practically achievable engineering current density (the ratio of the value of the ampere-turns in the winding to the cross section of the conductor) is of the order of 5 A/mm2.

Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 15-16

Tabletop: Direct sizing rule for a next machine's coil packs: total ampere-turns / 5 A/mm^2 gives the minimum copper cross-section with water cooling; air-cooled magnet wire should be derated well below this.

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

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

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

By selecting the value of the generator frequency, it is possible to achieve that the point of changing the direction of the phase motion is near -90 degrees.

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

Tabletop: Directly applicable: at 100 keV-1 MeV the reference machine is far from the ceiling, but deliberately detuning the oscillator slightly low buys extra phase headroom against an imperfect field profile.