Design Guide

The mean radius of curvature of the path is 10 cm., and the pole pieces are about 4 cm. wide and are separated by a 1-cm. gap. The electromagnet used will produce a field of 18,000 gauss between these pole-pieces. 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

Editorial note, tabletop extrapolation: In a cyclotron the machine itself is the analyzer, but an external species check on a next machine's beamline follows the same method: compute the magnetic rigidity of each species at the beam energy, choose bend radius and field to separate them, and let a defining slit pass one - the source's geometry is a worked example at its stated beam, not proportions to copy.

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

Editorial note, tabletop extrapolation: For 8-in poles at 5.9 kG with the reference machine's 1.42-in gap, the flat field ends near R = 3.2 in, predicting ~110 keV - below what the machine demonstrates, because its cup collects further out, in the fringe. Read the formula as the energy the UNIFORM field alone buys; a wider pole or smaller gap moves that number 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

Editorial note, tabletop extrapolation: Map n(r) on the 8-in poles; any region where the field rises with radius (n < 0) is axially defocusing, and the longer the beam spends there the less of it survives - shim such regions out rather than reasoning about how much defocusing is tolerable.

Cited in: Beam Dynamics: An Interactive Laboratory

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

Editorial note, tabletop extrapolation: The reference machine is the small, few-turn case the quote names, and the census machines converged on the same few-percent smooth droop (dg-702). Aim for a smooth 3-4%-class fall-off shaped against the machine's own n(r) requirement (dg-003), with the number as the historical anchor rather than the spec.

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

Editorial note, tabletop extrapolation: One documented profile, useful as a shape target rather than a scaling law: fringe onset and width depend on gap-to-pole ratio, edge shape and shims, so map n(r) on the actual 8-in poles (FEMM, then measurement) and place extraction where the MEASURED n has climbed toward ~0.4 - before the n = 1 radial-stability edge.

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 and calls for the best machine practice. The structure of a few heavy blocks with machined faces in contact is quite rigid and requires very few bolts; alignment can be maintained by dowel pins or keys.

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: At 5.9 kG straight cylindrical poles are fine on the reference machine; taper starts paying when the LOCAL flux in the pole approaches the steel's knee - a FEMM check, not a gap-field threshold. The source's worked case is the calibration: an 18 kG gap wanted a base about 24% larger in diameter.

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

Editorial note, tabletop extrapolation: On 8-in poles the historical ratio suggests a ~1-inch-class gap as a starting point - at tabletop scale the RF structure, chamber walls and fringe-vs-radius scaling often force it larger, so treat the ratio as the iron-economy pull in a trade the other subsystems get votes in (dg-163). Every extra gap costs amp-turns (power ~ g^2) 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

Editorial note, tabletop extrapolation: A modern current-regulated supply can meet this - verify ripple AND thermal drift on the actual unit: 0.1% of 5.9 kG is 6 G, a shift of the same order as deliberate shim corrections, so supply drift competes with the shim budget (and with RF detuning) for the resonance.

with a magnitude of decrease out to this point of about 2 per cent of the central field. Although this field shape can be achieved by machining of the surfaces of the pole faces, it is usually obtained by inserting a flat pyramidal stack of thin iron shims in shimming gaps outside the pole-face plates. ... 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

Editorial note, tabletop extrapolation: MIT's stack is historical calibration, not a recipe - shim response does not scale geometrically with pole size or gap. For the reference machine, set the droop target from the focusing requirement, then determine disk diameters and count by field mapping or magnetostatic modeling, iterating; the graded flat-pyramid form is the transferable part.

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. Also, a set of shims which are correct at high fields will be too strong and produce a defocusing minimum in the plot at lower fields.

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

Editorial note, tabletop extrapolation: An edge ring can extend the reference machine's usable radius, but size it empirically: start conservative, map the radial field at every operating current (the lower-field defocusing minimum is the trap), and trim iteratively - MIT's 3/4 x 1/4 in section is their optimum on 42-in poles, not a scaling template.

The figure of merit used to describe azimuthal uniformity is the maximum per cent variation around a circle of constant radius, and the most critical region is near the exit-slit location. ... Most operators agree that a variation of less than 0.1 to 0.2 per cent is desirable in large cyclotrons. ... After careful correction by use of sector-shaped and wedge-shaped shims, the errors were reduced to less than 0.1 per cent for all radii out to the exit slit.

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

Editorial note, tabletop extrapolation: 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.

A special search coil can be used to observe the median plane in the radially decreasing field, using two opposed identical coils equally spaced about the center and with the axis precisely aligned normal to the pole surfaces. At MIT 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

Editorial note, tabletop extrapolation: The beam follows the magnetic plane, not the machined one; with separate top/bottom coil circuits (or a properly rated shunt across one layer, as MIT used for a dished plane) the builder can steer it back to mid-gap - size any shunt for its current and dissipation first.

The experience at MIT is typical. After several years of empirical shimming, with continual difficulties in maintaining high-intensity operation, a careful program of measurement and correction was carried out as indicated in the illustrations above. 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

Editorial note, tabletop extrapolation: The single strongest process lesson for a next machine: map first, shim from data - a systematic field map costs far less time than open-ended beam-chasing, and measurement-based correction is what ended MIT's years of cut-and-try.

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

Editorial note, tabletop extrapolation: Read azimuthal maps by their harmonic content, as a first diagnosis rather than a chart: a dominant first harmonic says check tilt and centering first (it can also be a genuine dipole asymmetry of iron, coil or yoke, or nearby hardware); higher harmonics point at localised defects, sector features, extraction hardware or the measurement itself. Confirm a suspected cause by re-mapping after the mechanical correction, then trial shims taped on before permanent installation. [Note revised 2026-08-23: earlier note presented the harmonic reading as one-to-one.]

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

Editorial note, tabletop extrapolation: At the reference machine's 5.9 kG the ideal formula is a good first estimate (~1.7e4 ampere-turns across its 3.6 cm gap) before iron reluctance and leakage add their share - FEMM closes that gap. Field headroom is cheap while the iron stays unsaturated and expensive after; where the knee sits is a property of the specific circuit, not a universal 10 kG line.

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

Editorial note, tabletop extrapolation: With its 1.42-in gap on 8-in poles the builder loses ~0.85 in of radius to fringing; shrinking the gap or adding ring shims recovers usable radius.

Cited in: Cyclotron Magnet Design

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: 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. A similar shape will result if the coils are not located symmetrically or if there is a shorted turn. ... At MIT such a 'dished' median plane was corrected by connecting an external resistor in parallel with one of the coil layers, which reduced the current in this layer and in this case had the effect of flattening the median plane.

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

Editorial note, tabletop extrapolation: Rebar in the floor or a nearby steel bench can dish an H-frame tabletop field; remove or symmetrize nearby steel first where practical, then trim electrically (a rated shunt across one accessible layer, as MIT did) 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

Editorial note, tabletop extrapolation: 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. Model the actual gain in FEMM rather than assuming 1/g.

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

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

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

Cited in: Cyclotron Magnet Design

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

Editorial note, tabletop extrapolation: 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 ... The tapered pole shape and 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

Editorial note, tabletop extrapolation: A concrete, machinable geometry pattern for concentrating flux into an 8-10 inch pole face - but transfer the method, not the numbers: taper, shoulder and shim dimensions depend on gap, saturation and yoke geometry, so model (FEMM) or map the field and set them iteratively.

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

Editorial note, tabletop extrapolation: Sets the scale of the jump from the reference machine's 0.59 T solid-tubing magnet toward a 1.5-1.7 T machine: at multi-kilowatt dissipation, hollow conductor with water flow is the usual regime (dg-092). The exact power for a next machine depends on its actual gap, field and copper budget - the magnet-power calculator sizes it, this precedent scales it.

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

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

Editorial note, tabletop extrapolation: The closest historical analogue to a next machine's target: same pole diameter as the reference machine, and the ~3x field buys the ~10x energy (E ~ B^2*r^2 at fixed radius). The ~10x dee voltage buys turn count, phase margin and beam survival at that field - not the energy ceiling itself.

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

Editorial note, tabletop extrapolation: A concrete precedent for a home magnet supply: a few parts in 1e4 is achievable with a shunt, op-amp and pass bank. What a given machine NEEDS follows from its turn count and phase budget (dg-273); this figure is the documented professional practice, not the requirement.

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

Editorial note, tabletop extrapolation: The division of labor transfers: an NMR reading in a homogeneous region calibrates the mapping probe; a good calibrated Hall probe can carry the absolute job too if its spec covers the need. Either way the last word is the beam - resonance depends on the orbit-averaged field, harmonic and phase history, so set f from the map and trim on beam rather than expecting any point reading to set it exactly. (A DIY NMR gaussmeter is a classic amateur build; qualify its actual accuracy before trusting it.)

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

Editorial note, tabletop extrapolation: Derive the reference machine's own tolerance rather than copying the number: with dB/B ~ -dg/g for a gap-dominated circuit, the field error the orbit budget allows sets the gap tolerance - the source's fraction (0.005/22 ~ 0.02%) applied to a 2-in gap would mean ~0.0005 in, so pick the acceptable field error first and verify by mapping.

Magnetic shimming consists of internal Rose rings and external stepped shims. The internal rings are fastened to both the top and bottom lids and are radially located at 26 inches and extend outward to 30 inches. The rings are 1/4 inch thick and 2 inches wide. External top and bottom shimming consists of a pyramid of twelve discs, each 1/16 inch thick and of the following radii: 2 of 20 inches; 2 of 16 inches; 2 of 10 inches; 2 of 6 inches; 2 of 4 inches; and 2 of 3 inches. The largest disc is located in contact with the lid.

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: A concrete spec to hand a supplier: 1010/1018-class low-carbon steel serves for a next machine's yoke stock; for pole tips avoid high-carbon or unknown scrap - and remember silicon and processing also move the curve, which is what measuring your own stock settles (dg-1330).

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

Editorial note, tabletop extrapolation: A ready sizing pattern for a next machine's H-frame: make every return-path section 25-33% larger in area than the pole face (33% if the goal is a genuine 25% density reduction), and check the narrowest section - that is the one that saturates first (dg-037).

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

Editorial note, tabletop extrapolation: The taper's size does not transfer: the gradient it produces depends on gap, pole radius, saturation and yoke geometry. Choose a target field index n = -(r/B)dB/dr for the reference machine, get the contour from magnetostatic modeling (FEMM), and finalize by field mapping and shimming - the source's 0.02 in is one machine's value, not a starting spec.

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: One machine's by-design droop as a sanity anchor: a few percent total is the common class (dg-702's census clustering). What YOUR field may droop is set by the phase-slip budget and the n(r) requirement - verify with Poisson/FEMM against those, not against 5%.

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

Editorial note, tabletop extrapolation: The same sizing equation the reference machine's magnet obeys (its 538 turns are that build's own number, not this source's). The gap-only formula is the floor; the source's ~15% surplus is a realistic allowance for what it omits, and FEMM confirms the actual requirement (dg-016).

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

Editorial note, tabletop extrapolation: The binding quantity is local flux density in the iron (narrowest yoke section, pole roots), not the gap field: at 0.59 T in the gap the reference machine is far from saturation everywhere, but a next machine pushing the gap past ~1.5 T must check each cross-section of the return path against its own steel's saturation curve - saturation onset is gradual and alloy-dependent, not a hard wall at 1.7 T.

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

Editorial note, tabletop extrapolation: If a next machine uses NdFeB anywhere (source magnets, the PM cyclotron study), the permeance method sizes gap flux without FEA - trusted for totals and not point fields, per the source's own one-circuit comparison (2% total-flux vs 30% local). Check the final design in FEA regardless.

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 ... When the horseshoe-like structure has no tapered pole pieces as in Fig. 7, most of the external permeance is in the gap, and cladding raises the gap field from 0.5 T to only 0.8 T.

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

Editorial note, tabletop extrapolation: Mostly a curiosity at cyclotron-gap geometry - the source's own no-taper horseshoe shows the gain collapsing (0.5 to 0.8 T) when the gap dominates the permeance - but valuable for compact PM ion-source or steering assemblies. The field and mass comparisons are between the source's specific example assemblies, not like-for-like scaling laws.

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: Quick feasibility screen: with Br ~ 1.3 T NdFeB, a simple open PM assembly reaches 0.6 T-class gap fields - marginal at the reference machine's field. Beyond it the answer is confinement or Halbach-class geometry, not impossibility.

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

Editorial note, tabletop extrapolation: Same lesson as Tanabe from the PM side: every quick hand method assumes unsaturated iron. Rather than trusting a universal flux ceiling, check the chosen steel's B-H curve and verify peak local flux density (pole roots, corners) with a nonlinear FEA pass - an average yoke figure can hide saturated corners.

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

Editorial note, tabletop extrapolation: Practical warning with the mechanism stated right: an alnico circuit loses strength when opening the gap drives it to a NEW lowest point on its demagnetization curve - the first excursion does the damage; repeating the same excursion mostly retraces the established minor loop - but every deeper excursion (magnet fully removed, steel tools across the gap) ratchets it further down. NdFeB's near-linear curve 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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: A worked AVF datapoint, not a scaling law: hill/valley ratio, sector count and sector angle set flutter and tunes in a geometry-dependent way, so an 8-12 inch pole set re-derives them (FEMM plus a tune calculation) rather than copying 4.6:1 and 45 degrees. What does transfer is the design order: average field as high as iron saturation allows, then focusing from the hill/valley split - iron, not coil power, is the ceiling on a PM machine.

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

Editorial note, tabletop extrapolation: One worked ratio for a first AVF pole-tip sketch: hill gap from beam-aperture needs, valley several times deeper - re-derived for the actual field contrast and the RF/pumping geometry rather than copied. A deep valley is indeed where an amateur's Dee and pumping naturally live.

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

Editorial note, tabletop extrapolation: Design in adjustability - a gap or shim you can still reduce after measuring - because model-to-measurement discrepancies at the percent scale happen in either direction (this source's ran 5% optimistic). Adjustability is cheap before assembly and expensive after.

Average magnetic field distribution adjustment process is shown in figure 4 (last measurement is 5th step). 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

Editorial note, tabletop extrapolation: Budget several map-machine-remap cycles for a next machine's pole profile; the source machine took five.

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

Editorial note, tabletop extrapolation: A PM cyclotron in an unheated garage will drift off resonance with the seasons: from the quoted coefficient, a 10 degC swing is a 0.7% field change - orders of magnitude larger than the stability regulated professional machines hold (the dg-027 machine held +/-2.4 parts in 10^4).

Note that radial oscillations for this conditions and measured field is large enough as about 3 cm, that may lead to increasing axial oscillations through the nonlinear resonance Qr-2⋅Qz. 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 ... radial oscillations now does not exceed 3 mm and axial ones does not exceed 2 mm ... 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

Editorial note, tabletop extrapolation: A ten-fold reduction in orbit wander at the source machine for the cost of a symmetry-restoring second hole. For the reference machine, treat any asymmetric central feature as a first-harmonic suspect - but measure the harmonic (field mapping or orbit calculation) and choose the compensating geometry from the data; a mirror feature is not guaranteed to cancel a given perturbation.

Cited in: Beam Dynamics: An Interactive Laboratory · Beam Quality: What It Is and What Degrades It

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

Editorial note, tabletop extrapolation: The correction term is one contributor that bends the excitation curve at high current: comparing measured B-vs-I against the lumped formula flags when the iron starts stealing amp-turns - attributing the bend among saturation, leakage and fringing then belongs to FEMM, which the lumped model cannot do.

'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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: Edge shims are how a next machine can widen its flat-field fraction without bigger poles (see dg-022 for how far short a bare flat pole falls); expect the gain to be geometry- and saturation-dependent, and verify by field mapping.

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

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

Editorial note, tabletop extrapolation: Sets the metric - not the number - by which the builder should present their own field maps: normalized deviation from the required field profile over the region the beam actually occupies. Derive the reference machine's tolerance from allowable RF phase slip and harmonic orbit displacement rather than adopting a generic figure; even a sub-MeV machine can be intolerant of a 1% error.

The 'Rogowski' roll-off: Equation: y = g/2 +(g/π) exp ((πx/g)-1); g/2 is dipole half gap; y = 0 is centre line of gap. 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

Editorial note, tabletop extrapolation: The mathematically graded version of the Cyclotron Kids' 45-degree chamfer; worth machining on a next machine's pole edges when field analysis predicts pole-edge flux density approaching the steel's saturation. (The 1.4 T in the source is the Diamond dipole's field, not a switch-on threshold.)

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: Quick check on a next machine's supply matching: stored energy in a 10-inch, 1 T, 5 cm gap magnet is about 1 kJ from the gap alone (B^2/(2*mu0) x volume; fringe fields add more), and turn 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

Editorial note, tabletop extrapolation: Supports generous H-frame cross-section on the next machine, but the return path is only one leakage source - model or map the stray field before siting ion gauges, turbo pumps and CRT-era instruments near the magnet.

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. ... a removable insert with a machined chamfer installed on the SPEAR3 prototype gradient magnet. ... The shape of the chamfer depth was determined empirically and was approximately parabolic. It was designed to reduce the integrated sextupole field.

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

Editorial note, tabletop extrapolation: 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. ... I find it easier to develop the geometry lattice using the Excel. ... =CONCATENATE(C$1,A5,C$2,B5,C$3)

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: Free tooling that runs on a PC, in the same code family the Houghton-line theses used (dg-142) - the standard amateur path to pole-profile design alongside FEMM.

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: For the symmetric H-frame cross-section, a median-plane symmetry boundary halves the modeled domain and mesh - runtime usually falls accordingly, though not by an exact factor; a quarter model needs a second valid symmetry plane (geometry AND excitation symmetric about both).

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

Editorial note, tabletop extrapolation: Home-built yokes are typically A36/1018 mild steel; the default curve is a reasonable first pass, but A36 properties vary - run sensitivity checks with plausible BH curves (or supplier/measured data) before trusting predictions near saturation.

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: Lets the builder size a next machine's amp-turns by hand before any FEA - with the ~2% read correctly: it is the yoke's MMF consumption in a well-designed magnet, not the accuracy of the estimate. Saturation, the real B-H curve, leakage and geometry can move the answer by far more than 2%, which is what the FEMM pass is for.

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: Settles the default for a next machine: a one-off DC cyclotron magnet is normally solid steel - the source's 'often used' practice - because lamination tooling only pays across a production family. Laminations re-enter if the design ramps or regulates fast enough for eddy currents to matter (dg-089).

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

Editorial note, tabletop extrapolation: Practical purchasing rule: buy a next machine's pole and yoke stock as one lot from one heat where possible - and treat mixed-source top/bottom iron as a candidate cause if the median plane comes out asymmetric (a dg-138-class symptom).

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

Editorial note, tabletop extrapolation: The reference machine's magnet exceeds several of these thresholds, so the source's guarding rule applies: a sheet-metal or polycarbonate coil cover including the hot cooling fittings. Guarding is one layer only - protective earthing, overcurrent protection, and stored-energy discharge are separate requirements this rule does not cover.

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

Editorial note, tabletop extrapolation: For protons from ~150 keV to 1 MeV, gamma is about 1.00016-1.00107. Relate the reference machine's measured phase slip to a local orbital-frequency error first, then use the formula for the required field correction, and get shim thickness from simulation or measured shim sensitivity - relativistic effects are small at these energies but not automatically subdominant to mechanical field errors.

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

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: Frames the central tradeoff for a next machine: shrinking the gap raises B at fixed ampere-turns while the iron stays unsaturated (dg-021's measured case shows the ideal 1/g is an upper bound) - and everything (dee aperture, ion source, probes) must still fit and pump through the smaller gap.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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

Editorial note, tabletop extrapolation: A magnet that works but leaves no port for the probe or the pump is a classic amateur trap - exactly what this five-item checklist exists to prevent; run it 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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: If a next machine goes AVF to escape the weak-focusing energy ceiling, IBA's documented choices are a starting point, not proven tabletop values: k between 0.5 (best RF room) and 0.67 (compactness), and a modest vertical-tune target like their nu_z = 0.2 - each re-derived for the actual geometry, since a 60-degree hill only gives k = 0.67 in their sector periodicity, and sector count and valley usage carry their own trades.

calculation results and measurements differ less than 3 percent

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

Editorial note, tabletop extrapolation: The reference machine's Poisson/FEMM workflow is the professional one. Treat ~3% as the achievable-agreement benchmark rather than a diagnostic razor: a larger mismatch means something is wrong - model geometry or BH data, but equally possibly Hall-probe calibration, positioning, excitation error, or remanence - so check the measurement chain alongside the model before rebuilding either.

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

Editorial note, tabletop extrapolation: A useful upper bar from beamline practice. A weak-focusing cyclotron deliberately wants a controlled radial gradient, and its azimuthal tolerance is a different quantity: specify it as Fourier-harmonic limits (especially the first harmonic) derived from orbit-error analysis, using 0.01% only as a sense of what precision magnets achieve.

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

Editorial note, tabletop extrapolation: Explains why the pole gap exceeds the chamber's internal height by several millimetres once walls and margins stack - sum the budget's terms in a consistent full-gap or half-gap convention rather than quoting a round figure, since mixing conventions double-counts the allowances.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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

Editorial note, tabletop extrapolation: First-cut sizing for a next machine: at a 2 cm gap and 1.0 T, ~8000 A-turns per pole sets conductor and current-density scale before any FEMM run - the floor that FEMM then corrects for fringe and saturation.

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

Editorial note, tabletop extrapolation: The single most useful yoke-sizing rule for an H-frame homebuilt magnet: pick return-leg area with margin beyond flux/1.5 T - equality puts the iron AT the 1.5 T line, not under it - and verify the narrowest return section in FEMM, because that section sets the circuit's behavior.

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: Tells you the inductance scale and therefore how fast a bench supply can ramp the magnet and how big the flyback/dump protection must be (dg-218) - computing the protection against the worst-case inductance across the operating range, not the single linear figure.

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: Free operational fix for run-to-run field shifts in a home cyclotron: resonance is set by B, so reproducibility matters directly - how much field error the beam tolerates depends on RF voltage, turn count and acceptance, so measure it rather than assume. If true zero field is needed, degauss with diminishing alternating cycles instead of trusting zero current.

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: The reference machine's 538-turn solid copper tubing coils sit in the air-cooled regime; unless they qualify as small and thin enough to shed heat (the source's 2 A/mm^2 case), the quoted limit for enclosed coils is 1 A/mm^2 - going higher means 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

Editorial note, tabletop extrapolation: Hard numbers for a home chilled-water loop as DESIGN limits, not damage cliffs: hold velocity under ~5 m/s (erosion and vibration risk grow beyond it), coil surfaces under 60 C (insulation aging accelerates with temperature), and note the arithmetic - a 30 C inlet plus 30 C rise means up to 60 C outlet water, consistent with the surface limit but tight in a hot garage: derate for your ambient.

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

Editorial note, tabletop extrapolation: 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 - provided every input is converted to the source's units first: a bar-for-pascal slip in the pressure drop moves the bore answer far more than the recipe's real margin.

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

Editorial note, tabletop extrapolation: One-line check of the reference machine's 538 turns: at 0.59 T and its gap the formula predicts the required current within a couple percent if the H-frame iron is unsaturated. A measured efficiency well below the formula's ~98% says the model is missing something - saturation, leakage, a parasitic joint gap, or a wrong effective-gap value - and FEMM sorts out which.

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

Editorial note, tabletop extrapolation: 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... The right hand figure illustrates a wider coil with approximately the same area and a higher reluctance path and a lower transverse field due to both the wider coil slot and the tapered pole edge. ... a radius at the pole corner, reducing this magnetic flux stress concentration. ... The results of the listed improvements in the two dimensional design are magnets whose field remains uniform and whose excitation remains linear over a wider range of excitation.

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

Editorial note, tabletop extrapolation: Cheap insurance for the next machine's pole design: a root taper and corner radius cost one lathe operation and help keep the field shape constant over a wider excitation range.

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

Editorial note, tabletop extrapolation: Tells the builder where usable field really stops on an 8-inch pole: the fringe extends about one half-gap BEYOND the steel edge before dying away, while the flat, usable region ends somewhat inside the pole radius as the falloff begins. Map B(r) (FEMM, then Hall probe) to place the maximum stable orbit; the h rule sizes how much radial real estate the fringe transition consumes.

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. ... solid steel pieces, machined with the two dimensional pole contour, were bolted onto the pole ends. These pieces were removed, machined with the required distribution of the chamfer depth determined by the described iterative process and replaced. After replacement, the distribution of the field integral was measured. The final chamfer shape was achieved after two iterations.

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

Editorial note, tabletop extrapolation: If the next machine's pole edge is chamfered or radiused to soften the field falloff for extraction - a different geometry and objective than a dipole end chamfer, so model or map it for the cyclotron case - use bolt-on machinable end pieces so the shape can be iterated the way SPEAR3 did.

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 and causing them to transition earlier to horizontal lines. This increases the fraction of the aperture with uniform field distribution. The smooth bumps also reduce the crowding of the flow and flux lines near the pole corner, reducing the saturation of the iron in this region.

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: Direct guidance for a next machine's pole-tip upgrade at the 8-12 inch scale, as a measured comparison among these candidates rather than a ban: radial-sector AVF machines exist, but making one work takes sector-angle and profile design these candidates did not carry. Also warns that narrow spiral vanes saturate at large radius - the measured field fell below simulation there.

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

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

T304 stainless steel 5/16-8 double lead (2 start) thread with 0.25-inch pitch ... Astrosyn Type 23KM-K213-P7V stepper motors that advance 1.8 degrees per step. A ramp-up and ramp down of velocity prevents skipping. Since the load on the x-y stage is low, the stepper motors are only required to run at 25% their rated operating maximum current. 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

Editorial note, tabletop extrapolation: A stage resolving 1/800 inch (0.03 mm) is more than enough for an 8-12 inch pole and is buildable from surplus stepper/leadscrew parts; verify actual positioning repeatability (the source checked theirs with a dial indicator) and pick the map grid from the field structure, not from the step size.

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

Editorial note, tabletop extrapolation: Directly applicable method: any DIY gaussmeter-plus-stepper mapper should measure its OWN settling behavior - step the dwell in 0.5 s increments along the steepest gradient and adopt the first value where successive profiles agree within the stationary noise. Rutgers' 2-3 s is their apparatus's answer; an uncalibrated mapper risks a systematic error of unknown size, which is the reason to run the calibration, not a guaranteed 1%.

To calibrate the Hall probe's position against the magnet's mechanical center we have employed five field bumps that are formed by iron needles excited by small copper coils which are precisely located around the cyclotron magnet pole tips. ... it was necessary for our field-bump calibration to be performed with the primary cyclotron magnet de-energized. After a full 2-D scan was completed; peaks, corresponding to the needles' centers are found by fitting a Gaussian, figure 6, to the measured field bump. Four needles were used to scale both dimensions; the fifth needle was used to break the symmetry, removing orientation ambiguities. Use of the lower field (<100 Gauss) bumps necessitates two scans ... A post-measurement analysis of the two returned a distance of 2.500 inches while mechanical measurement found the distance to be 2.500.

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

Editorial note, tabletop extrapolation: Trivially cheap (iron nails plus a few turns of magnet wire) and it ties the field map to the magnet's mechanical center - extend that to chamber-center registration only by surveying the needle positions against the chamber geometry.

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

Editorial note, tabletop extrapolation: Cheap insurance: an afternoon of cycling the homemade stage qualifies its endpoint repeatability under those conditions - also spot-check intermediate positions, the other axis, and repeatability across the session before trusting the maps; the indicator's resolution bounds what the test can see, not the stage's true error.

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: Sets the practical scale of the iron-magnet approach for a next machine: above the saturation region, further field comes almost entirely from added ampere-turns at air-core rates - which is why higher-field machines move to superconducting coils. Below about 1.5 T the iron does most of the work.

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

Editorial note, tabletop extrapolation: Numerically the builder's own worked example: 538 turns at ~30 A across the reference machine's 1.42-in (3.6 cm) gap predicts ~0.56 T from the ideal gap formula - an upper bound, because real iron reluctance and leakage only subtract from it. The measured shortfall from ideal maps those losses; FEMM attributes them.

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

Editorial note, tabletop extrapolation: Rule of thumb for a next machine's layout: expect roughly one gap-height of field transition at the pole edge - how much of it is actually unusable depends on the field tolerance, so map it (dg-098) - and shield any deflector with a grounded septum as designed practice.

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

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

Editorial note, tabletop extrapolation: If a next machine ever extracts a beam, angling the magnet exit edge can focus the diverging beam without any extra magnet - check the sign convention for the actual bend geometry and verify the full extracted-beamline optics rather than trusting the thin-lens number.

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: The master sizing formula: the reference machine's 0.582 T at r ~ 0.10 m gives ~163 keV, which is its best demonstrated run; 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

Editorial note, tabletop extrapolation: The reference machine's flat-pole H-frame gets its weak focusing from natural radial falloff - but a flat pole is nearly uniform over much of its radius and falls mainly near the edge, so map n(r) rather than assuming it: the design task is confirming where n is usefully positive, then controlling how fast it rises.

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

Editorial note, tabletop extrapolation: The B^2 energy leverage argues for raising a next machine's field before enlarging poles: doubling B quadruples energy at fixed radius. The 1/B^3 mass saving holds only while the whole magnet scales geometrically - gap included - and the iron's own saturation (dg-096) caps how far the argument runs.

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

Editorial note, tabletop extrapolation: 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. Legality rides on emissions containment rather than the band label (dg-1373's verification), and the match must still be designed for the dee's actual impedance (dg-287).

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

Editorial note, tabletop extrapolation: Exactly the reference machine's problem class and size: machine a gentle crown or stepped 'lump' into the 8-inch poles (or shim equivalently), aiming for the few-percent center-to-edge fall-off of the source's worked case - and verify the result against the mapped n(r) (dg-003, dg-561) rather than the geometric recipe, since the actual profile depends on gap and permeability.

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

Editorial note, tabletop extrapolation: Directly applicable fabrication pattern for contoured pole caps that still bolt on - and a geometric design check to run: verify the theoretical contour leaves enough thickness at the mounting screws before committing, since a steep profile can thin the screw land below usability.

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

Editorial note, tabletop extrapolation: Frames the next machine's decision the way the source does: 8-inch-class poles sit in the educational range, and light-element reaction goals argue for the 12-15 inch class. Pole diameter is a proxy - field and species matter as much - and small does not mean neutron-incapable: deuteron operation makes neutrons at any energy via D(d,n)3He, which is a hazard question before it is a capability one (see the safety rules).

Ampere-Turns = 2.02 x gauss x inches gap

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

Editorial note, tabletop extrapolation: Directly applicable: 5900 G across a 2-inch gap needs ~24,000 ampere-turns as the ideal floor, with iron reluctance and leakage added on top (dg-016, dg-036). Leakage multiplies the FLUX the iron must carry - that sizes the yoke - not the gap MMF this formula computes.

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: Directly applicable - with the right variable: the binding number is the LOCAL flux density in the narrowest iron section, which leakage, joints and corners push above the gap figure (dg-037). The reference machine's 5.9 kG gap field leaves apparent margin; how much field a next machine can add before the iron dominates is a FEMM answer, not a factor read from the gap value.

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: Directly applicable to a next machine's H-frame: coil space often pushes the frame toward compliance anyway - check it explicitly whenever the frame is shortened, rather than assuming the coils did the enforcing.

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

Editorial note, tabletop extrapolation: Directly applicable: for 8-inch (50 in^2) cores, provide at least ~63 in^2 of total yoke steel around the flux return - and still check the narrowest local section, corner and joint (dg-037, dg-132): the area margin lowers AVERAGE density, while local constrictions can saturate first regardless.

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

Editorial note, tabletop extrapolation: Directly applicable: any unintended air gap adds straight onto the magnetic circuit's gap budget - 0.003 in against a 1.5-in main gap is 0.2%, small but real; the same error across tight pole-cap joints is proportionally worse. Machine flush because it is cheap at build time and unfixable after assembly.

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

Editorial note, tabletop extrapolation: Directly applicable chamber architecture for a small machine; every millimeter of chamber wall inside the gap costs ampere-turns.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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

Editorial note, tabletop extrapolation: The central trade for a next machine: each millimetre of gap saved is field (at fixed ampere-turns), and energy scales as B^2 (at fixed radius and species) - but only within the unsaturated, gap-dominated regime, and only after dee-voltage clearance, pumping and field quality have had their say. Verify the saturation and fringe terms in FEMM before banking the gain. [Note revised 2026-08-23: an earlier text called the gain 'for free'; the chamber redesign it costs is the quote's own point.]

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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

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

Editorial note, tabletop extrapolation: The reference machine's 0.59 T resonates at ~9.0 MHz; a next machine's field choice fixes the synchronous frequency via this 15.23 MHz/T constant (fundamental-harmonic protons). The tank tuning range then follows from the chosen inductance - the source's capacitance column is specific to theirs.

Increased cross section reduces flux through yoke to 1.2T

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

Editorial note, tabletop extrapolation: Area-ratio thinking for welding a next machine's frame from surplus plate: size the yoke so its flux density lands comfortably below the knee of the ACTUAL steel's BH curve - surplus plate is rarely certified, so measure or assume conservatively - and check per-limb: flux splits between return limbs, and the narrowest section, corner or weld is what saturates first, not the gross ratio.

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

Editorial note, tabletop extrapolation: The documented amateur approach at the reference machine's scale - Cyclotron Kids here, with the pole-shaping rules (dg-119, dg-152) carrying the design math: put the field index into the pole profile deliberately, designed in the field code before cutting steel, 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

Editorial note, tabletop extrapolation: An existence-proof account at exactly the reference machine's energy class: modest dee voltage (1-2 kVpp), 1e-5 torr, and a machined pole profile - not heroic RF or UHV - are what the article describes sufficing below ~300 keV.

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

Editorial note, tabletop extrapolation: A good commissioning move for a next machine when the RF stays matched at fixed frequency; whether B is the easy knob depends on the magnet - supply limits, inductance, hysteresis and settling time can make slow, repeatable B sweeps the hard part.

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

Editorial note, tabletop extrapolation: One necessary check for weak-focusing pole shaping on a 100 keV-1 MeV tabletop machine, and computable from a measured B(r) curve - necessary, not sufficient: axial focusing margin (n > 0), radial stability (n < 1), phase slip, aperture and orbit clearance all still have to be verified against the actual B(r). Where the contour cannot be pushed out to the final radius (dg-152), the design question becomes how few turns the beam spends near it, not whether the machine can work at all.

Cited in: Beam Dynamics: An Interactive Laboratory

Shimming involves the insertion of thin iron sheets (typically 0.25 inches or less) between the pole faces and the vacuum chamber. ... the magnetic field changes too quickly near the edge of the shim. This is a result of making the shim too thick. ... In retrospect it appears that these shims were far too thick and created too dramatic of a change in magnetic field. While shims could still be used with the Houghton cyclotron, the thin shims these calculations suggest would be challenging to make

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

Editorial note, tabletop extrapolation: Warns the builder off the obvious first shimming attempt; the useful shims are thinner than are convenient to fabricate and hold in place - model, or test progressively thinner shims against, the actual gap geometry.

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

Editorial note, tabletop extrapolation: For a shimming attempt on the reference machine's 8-inch poles the plottable acceptance test is n(r) from the measured B(r), by finite differences, kept inside its stable range over the whole used radius - not a straight-line fit to B(r). A field profile that passes that test still has to be checked for isochronism and phase slip (dg-1328), the n = 0.2 contour (dg-136, dg-152) and radial stability; "no orbit code needed" was an overreach, though a simple n(r) plot does reject a bad shim before any tracking is run.

Cited in: Beam Dynamics: An Interactive Laboratory

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

Editorial note, tabletop extrapolation: A concrete trap when adding iron or coils near the center of an 8-inch pole: check the sign of dB/dr over the whole usable orbit range, not just at the edge - the 5 cm crossover and the -0.1 index are that geometry's numbers, not general thresholds.

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

Editorial note, tabletop extrapolation: Saves a next machine's builder from spending months on one class of trim-coil fix inside a small gap (they also steal gap height) - but this is one modelled geometry: evaluate any other trim-coil design from its full B(r) map and orbit dynamics.

replace the current aluminum chamber lids with magnetic stainless steel lids with radius 2.2 cm larger than the Dee ... 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. ... The maximum magnetic field of the unmodified design is B = 1.27 T and is B = 1.77 T for the lid design. This is because the pole gap of the unmodified design is 3.9 cm while the lid design has a pole gap of 2.54 cm. ... B = 1.77 T corresponds to a Dee frequency of 27.0 MHz and a maximum kinetic energy of 0.91 MeV for protons. ... n=0.2 occurred at r=5.9 cm for the unmodified and at r=8.3 cm for the lid.

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

Editorial note, tabletop extrapolation: Cheap in materials and potentially the highest-leverage change of this class, but the numbers are one thesis's model of one geometry: model your own lid as part of the magnetic circuit, verify the full B(r) and n(r), confirm the chosen stainless grade is actually ferromagnetic and vacuum/structurally suitable, and recompute energy from the usable orbit radius.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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

Editorial note, tabletop extrapolation: Low-cost simulation path for a hobbyist - Superfish is free, SIMION is paid but widespread, and FEMM plus the playbook's Python tracker is the all-free equivalent; 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

Editorial note, tabletop extrapolation: Predicts the current-vs-radius profile the builder should measure. If a next machine loses beam before full radius, diagnose first - map B(r) and n(r) and identify the loss mechanism - then shim, and re-verify field and transmitted current; a shim can worsen the index if misshaped.

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

Editorial note, tabletop extrapolation: 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 at fixed radius), while near pole saturation the iron stops helping and pole diameter becomes the effective lever.

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

Editorial note, tabletop extrapolation: Source-specific weak-focusing guidance, and not a target to shim toward: 0 < n < 1 is the stability condition, but the empirical 0-to-1 ramp is Loucks' description of one machine's profile, not an instruction to drive n as high as possible. n = 0.2 is the Walkinshaw coupling resonance (dg-136, dg-152, dg-563, dg-694), and in a many-turn classical cyclotron it can constrain the usable orbit long before n approaches 1. Map B(r) with a Hall probe, compute n(r) by finite differences, and shape the profile with that contour in mind. [Note added 2026-08-22: the resonance cross-reference was missing; read in isolation the rule invited shimming toward n = 1.]

Cited in: Beam Dynamics: An Interactive Laboratory

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: 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; average over theta before differencing, and tighten the spacing where the gradient changes fast.

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

Editorial note, tabletop extrapolation: A purchasable-magnet benchmark almost exactly at the reference machine's scale. The 0.8 gpm is a flow figure, not a chiller spec: size the chiller from coil dissipation and allowable temperature rise (P = flow x heat capacity x dT - the magnet-power calculator's territory), with the flow number as the plumbing constraint it is.

12 inch diameter poles pieces forming a 4-inch gap to which upper and lower pole tips up to 1-inch thick can be easily attached and removed. ... all capable of producing a maximum central axial field, Bz(r=0), of 1.2 Tesla ... a single 5-inch radius DEE with a 0.9 inch vertical aperture and a matching dummy DEE. The Radio Frequency (RF) supply is tunable from 2 to 30 MHz with adjustable power up to 1.5 kW ... capable of achieving a peak DEE voltages on the order of 10 kV ... the 2-inch tall, 13-inch diameter cyclotron vacuum chamber's operating pressure of 1E-5 Torr.

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

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

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

Editorial note, tabletop extrapolation: Probably the single best architecture decision the builder can copy: swap-on tips let a next machine iterate field profiles cheaply - with the caveat that a sector-tip (AVF) conversion is still re-checked against return-path saturation and coil clearances (dg-045).

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

Editorial note, tabletop extrapolation: Cheap beam-height trim for a next machine: two supplies, or a properly rated current-trim circuit on one coil, instead of re-machining anything - verify the result with a field or beam measurement, since unequal excitation perturbs the midplane symmetry it exploits.

Cited in: Beam Dynamics: An Interactive Laboratory

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

Editorial note, tabletop extrapolation: 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.

Cited in: Beam Dynamics: An Interactive Laboratory

We have built a set of poletips designed to intentionally drive a destructive axial resonance; we refer to these as the 'bad' weak focusing poles tips. 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. Since the n=0.2 is a difference resonance the axial peak-to-peak amplitude is bounded by the initial radial offset. A displacement of the chamber's center of about 3mm with respect to the magnet center was necessary to seed the resonant axial blow up

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

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

Cited in: Beam Dynamics: An Interactive Laboratory

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

Editorial note, tabletop extrapolation: If a next machine gets sector pole tips (allowing a rising average field), these two lines are the first-order SCREEN - in the source's conventions: check the sign convention for k and the flutter definition before substituting (dg-156's lesson) - with resonance avoidance and then tracking completing the design.

Cited in: Beam Dynamics: An Interactive Laboratory

A 30 AWG wire loop, with a circumference of 71 mm, was energized with a current of 2.5 amps and placed in the magnet gap. ... 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

Editorial note, tabletop extrapolation: A cheap field-quality diagnostic, but run it as an engineered experiment, not a party trick: current-limit and isolate the supply, insulate and restrain the leads, set up de-energized, check the wire's temperature rise at the chosen current, and mind magnetic forces and pinch points around a 0.5-1 T gap.

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

Editorial note, tabletop extrapolation: 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.

Cited in: Beam Dynamics: An Interactive Laboratory

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

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

Editorial note, tabletop extrapolation: Explains when the extra machining pain of spiral tips pays: when flutter is small and orbits quasi-circular - the quoted regime, where 'spiral compulsory'. Whether an 8-12 inch N = 4 design wants spiral or more hill/valley contrast is a computed comparison (the (1+2tan^2 xi) factor against achievable flutter), not a default.

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: Explains the positive field index (n > 0 in the site's n = -(r/B)dB/dr convention) that a flat-pole tabletop magnet already has from its natural falloff - 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

Editorial note, tabletop extrapolation: Settles the shim-vs-trim-coil question for a small warm magnet the way the Houghton thesis found empirically: iron wins for the main profile. A weak trim coil can still earn a place for fine, reversible adjustment where the gap budget allows one.

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

Editorial note, tabletop extrapolation: A menu of things the builder can machine on 8-inch pole tips, drawn from practice on real cyclotrons; movable flaps in particular give post-build adjustability. Unordered and geometry-dependent - model (FEMM) and map before machining any of them.

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: 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.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: The arithmetic to go from a required <B> to hill/valley fields and sector angle - first-order and reusable at any scale, with fringe and gradient effects refining it in the field code.

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

Editorial note, tabletop extrapolation: Gives a numeric focusing target to design toward instead of 'as much focusing as possible'. On a classical weak-focusing machine at the reference machine's energies, nu_z = 0.2 means n = 0.04 - modest and achievable from pole-face falloff. The caveat belongs to AVF designs: there the isochronous average field RISES with radius (vertically defocusing on its own), and the flutter/spiral term must supply the whole tune, which is exactly why the source treats nu_z as a choice that determines the spiral angle.

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

Editorial note, tabletop extrapolation: The core sizing identity for a home magnet, in its regime (unsaturated iron, h the total effective gap): field follows ampere-turns over gap, and bigger poles alone buy nothing. Shaving the gap buys field at the price of chamber, dee and beam clearance (dg-163's trade) - cheap, not free.

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: Lets a hobbyist study an AVF pole set's average field and yoke sizing in free 2-D codes (POISSON/FEMM) before committing to a 3-D solver; the azimuthal flutter and edge focusing that make an AVF machine work need the 3-D model or measurement.

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: The fractional pattern transfers, not the inches: a smooth, monotonic few-percent center-to-edge fall-off with azimuthal ripple shimmed to the few-per-mille level is what the 86-inch exemplifies. The right numbers for an 8-inch pole come from its own n(r) stability requirement (dg-003, dg-119), not from this machine's profile.

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. ... It is possible then to make minor changes in the shims and to take a complete set of field measurements in a few hours. ... After the contour shims were installed, field measurements indicated that the flux in an area of 3 to 4 square feet was ... higher than in the rest of the tank at corresponding radii. Approximately 0.020 in. of material from each pole over the area opposite the high field region was removed in about two hours with a portable grinder.

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 35, 116

Editorial note, tabletop extrapolation: Directly applicable method: leave gap allowance for machined shim rings/plates so a next machine's field shaping is a measurement-and-remachining loop, not a magnet rebuild - and note ORNL fixed a residual local error by grinding the pole, so plan for both add and remove operations.

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. The coils consist of 65 turns of #6 wire wound on each pole piece. A dc power supply provides up to 75 amperes

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

Editorial note, tabletop extrapolation: Cheap and direct for a next machine: an auxiliary winding on the poles gives a vertical-centering knob instead of mechanical re-shimming - size its ampere-turns from the field asymmetry the orbit calculation asks for (the 86-inch used up to ~4900 A-turns; a small machine needs proportionately less, but compute it), with a reversible supply and thermal check.

Cited in: Beam Dynamics: An Interactive Laboratory

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

Editorial note, tabletop extrapolation: Map the reference machine's H-frame fringe field with a Hall probe and site the LDMOS amplifier, its magnetics and instrumentation by each component's OWN field tolerance - 60 G is the historical machine's siting outcome, not an immunity standard. Copper lining screens RF and electric fields, not the DC fringe; DC-sensitive items need distance or a high-permeability shield.

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: Direct transfer of the tolerancing practice: face-grind a next machine's pole and yoke mating surfaces and check with a dial indicator. Do not transfer the load ratio: at ORIC's scale the magnetic load dwarfed the vacuum load, but magnetic pressure is B^2/(2*mu0) - at 0.5 T about one atmosphere - so on a tabletop machine the two loads are comparable and the structure must carry both.

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

Editorial note, tabletop extrapolation: Directly applicable: 1010/1018-class steel is the right iron for a next machine. On yoke sizing, the documented corridor runs from ORIC's 1:1 (pole BASE to yoke) to the +25-33% (pole FACE to return path) of dg-032 - the compared sections differ between sources, so pick one convention, apply it consistently, and check the narrowest section (dg-037).

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

Editorial note, tabletop extrapolation: Inverted for the builder: their whole magnet is model-sized, so a dense XY Hall-probe map - grid pitch chosen from the field structure you need to resolve - is the equivalent discipline, with an error budget drawn up for YOUR instrument chain (Hall calibration, angular alignment, temperature drift, positioning, current regulation) the way ORIC drew up theirs.

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

Editorial note, tabletop extrapolation: Directly applicable to a next machine's shimming: regulate and MONITOR magnet current during a map (in a linear magnet, current error maps ~1:1 into field error, so the regulation must beat the field goal, not just approach it), index the probe mechanically, and write the error budget with its combination rule before trusting shim-sized differences.

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

Editorial note, tabletop extrapolation: The coupled optimization transfers: pick a next machine's dee voltage and magnet gap together, since dee clearance ultimately costs ampere-turns and field.

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: If a next machine's coils run hot, more copper is a fix on equal footing with more cooling: doubling conductor volume halves dissipation at the same ampere-turns - paid for in coil size, weight and winding-window space.

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

Editorial note, tabletop extrapolation: Potting the reference machine's coils stops the slow insulation abrasion that coil hum causes. The >100 V/mil figure is the source's historical material datum, not an allowable design stress: size insulation from maximum turn-to-turn and coil-to-ground voltage with margin for voids, transients, creepage and temperature - the quote itself reserves voltage-to-ground duty for mica - and prove the finished coil with a hipot test rather than resting on the coupon number.

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

Editorial note, tabletop extrapolation: Two portable METHODS, not specs: monitor conductivity and pH on any hollow-conductor DI loop, and stabilize dee-water temperature if a next machine water-cools the dee (the RF tune walks with dee temperature). Set the actual limits from conductor material, voltage to ground, and measured RF drift, not from ANL's numbers.

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

Editorial note, tabletop extrapolation: For a next machine dissipating 1-5 kW, real margin over normal load is what makes long runs boring - ANL carried about 3x; pick your own factor from duty cycle, ambient conditions and fouling allowance rather than copying the ratio.

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: A conductor rating like this is conditional on the cooling that produced it - wall thickness, bore, flow, inlet temperature - so treat it as one documented data point for hollow-conductor coils, not a transferable ampacity. Rate a next machine's conductor from its own cooling calculation; the coil-geometry and magnet-power calculators cover the resistive side.

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

Editorial note, tabletop extrapolation: A rebuild of the reference machine's 538 turns as potted double-pancakes with a cooling manifold is an attractive concept - as a design study: pancake count, potting, parallel water paths and repairability are engineering choices needing their own magnetic, hydraulic and thermal analyses, not properties the source's uniformity comparison confers.

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

Editorial note, tabletop extrapolation: Set a next machine's potted-coil design point from the resin system's rated thermal class and a modeled or measured hotspot with margin for cooling failure - not from another magnet's numbers. Note 61 C at ordinary ambient is already a 36-41 C rise, looser than Tanabe's ~30 C-rise guidance 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

Editorial note, tabletop extrapolation: The reference machine's 538 turns were set by its supply; for a next machine, pick the surplus supply first and wind N = NI_required/I_supply - then check voltage compliance, inductance (and its dump-path consequences, dg-218) and cooling before committing.

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

Editorial note, tabletop extrapolation: An orientation point, not a coil rating: magnet coils differ from distribution cables in bundling, enclosure and heat path. The coil-specific limits are dg-092's - voluminous enclosed coils are held to 1 A/mm^2, and water cooling is what opens the range upward.

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

Editorial note, tabletop extrapolation: For a home machine the source's trade often runs toward the low end: hand-wound coils and metered power favor the ~4 A/mm^2 economic optimum, and the reference machine's tubing coil runs lower still. Window space and magnet size push the other way - which is why the canonical 10 exists - so do the two-line cost comparison for your own copper and power prices.

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

Editorial note, tabletop extrapolation: The straight-passage core of hydraulic sizing for any hollow-conductor or tubing-wound coil - add bends, fittings and manifold (minor) losses on top, and confirm with a flow test; the formula alone is the floor, not the whole recipe.

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: The cited source's upper design guideline when sizing pump and passage diameter for a hollow-conductor coil; onset of vibration and erosion also depends on bend severity, passage geometry, material and water chemistry, so use a lower limit where conductor-manufacturer guidance or testing warrants.

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: When choosing hollow conductor for a next machine, weigh bore against copper cross-section (a bigger hole raises electrical resistance) and flow-test each pancake before potting - the fabricated bore, not the drawing, sets the pressure drop.

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

Editorial note, tabletop extrapolation: 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.

The procedure consists of starting with a low voltage pulse (~ 10 Volts/turn) and increasing the voltage until one reaches 200 Volts/turn or 2 kV maximum and observing the waveform. ... 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. ... After potting, the coil should undergo a hipot test. ... Specifications normally call for raising the voltage in the coil to twice the operating voltage plus one kV. The maximum drainage current is usually set at 2 mAmps/kV.

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

Editorial note, tabletop extrapolation: A pulse source, capacitor and scope let the builder screen the next machine's coils before they are trapped under the yoke - run the impulse test during fabrication, before the coil goes on the core, and photograph the low- and high-voltage waveforms as the baseline. Both tests put hazardous voltage on the coil: use rated, current-limited test gear, discharge and ground between steps, and keep others clear.

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

Editorial note, tabletop extrapolation: A bucket-and-stopwatch flow test at operating pressure is the real spec for the reference machine's 538-turn tubing coil (many turns; check its bend radii against the passage size). Record water temperature - viscosity matters most if any branch runs laminar - and measure each parallel branch separately, since a total-flow test hides an imbalance.

Water hoses should be at least one meter long and use nonconducting material to prevent current leakage from the magnet. The water “in” fittings should be smaller than the water “out” fittings ... If a flow interlock (orifice plate) is used, it should be attached to the return manifold.

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

Editorial note, tabletop extrapolation: The reference machine's water-cooled copper-tubing coil sits at supply potential; a meter of non-conducting hose per lead limits leakage current, and an interlock on the return detects a blocked circuit - cheap practices worth copying at home scale. They reduce specific risks; they are not shock protection as a whole, which still rests on earthing and supply-side protective devices.

The normal set-point of Klixons is about 89 C. It will generally reset at about 70 C ... One thermal interlock is installed on each water circuit ... All the interlocks on one magnet are connected in series. ... The Klixon is preferably mounted on the water return lead of the coil ... always mounted on the current carrying portion of the conductor ... mounted to a block hard-soldered to the conductor.

Tanabe, Iron Dominated Electromagnets, Lecture 9: Coil Fabrication, Testing and Electrical Safety (2005) — p. 5-7

Editorial note, tabletop extrapolation: A thermal snap-switch soldered to the coil exit tube, wired in series with the supply enable, is cheap, high-value protection against cooking a winding on a lost-water event - alongside the flow interlock (dg-202), not instead of it. Set-point and switch rating are the designer's to verify against the winding's own insulation limit.

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

Editorial note, tabletop extrapolation: Sets expectations for how much winding window the insulation eats on a hand-wound 538-turn coil - then compute the actual packing factor from the chosen conductor's finished insulated dimensions and the real winding layout, since fill depends on shape, pattern and voids, not on insulation thickness alone.

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

Editorial note, tabletop extrapolation: For bending round copper tubing on a homemade coil the analogous risks are ovalization and bore pinch: use tube-specific minimum-bend-radius and ovality limits (diameter, wall, temper and tooling all matter), inspect or flow-test the formed passage, and watch the insulation at the bends.

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: Explains why splitting a big coil into 2 or 4 hydraulic circuits lets a garage chiller pump do the job - under the model's conditions: total flow and total conductor length fixed, circuits dividing both equally; then pressure drop falls as the cube of the circuit count. Confirm the friction regime still holds after the split.

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

Editorial note, tabletop extrapolation: If a next machine uses water-cooled coils at supply potential, ordinary tap water misses all three quoted limits. A deionizing cartridge loop is the standard way to hold resistivity, but the spec is three-dimensional - oxygen and pH need their own control - and the source pairs the water spec with filters near the magnet.

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

Editorial note, tabletop extrapolation: For the reference machine's circuit: any leg - bus, jumper, lead - running above ~1.5 A/mm^2 without an engineered cooling path will run warm, so size leads generously. Above the line the options are any real cooling: water, forced air, conductive sinking, or intermittent duty with temperature monitoring (dg-220).

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

Editorial note, tabletop extrapolation: Lets the builder size a next machine's coil cross-section on one sheet of paper: gross winding area ~ NI/(j*f) = NI/5 mm^2 for water-cooled copper - a first pass the thermal calculation then confirms, and the 10 A/mm^2 presumes genuine water cooling (dg-092's geometry conditions).

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: Directly applicable thermal sizing for coils matching the quoted conditions - close-wound, naturally air-cooled: 750 A/in^2 continuous, 1000 intermittent. A different winding style (open spacing, forced air, tubing with internal flow) carries different limits - dg-092's geometry table is the map.

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: A cheap construction to reach for when a next machine's pancake coils run hot: 1/16-inch copper donut plates with soldered edge tubing between pancakes. The 1300 A/in^2 is the historical design target for that geometry, not a number to adopt - recompute I^2R, water flow and temperature rise, the thermal path through the insulation, and solder and tube reliability, then measure winding temperature in operation. [Note revised 2026-08-23: earlier note called it a directly applicable upgrade that 'nearly doubles' allowable 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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: Directly applicable: any magnet coil whose stored energy exceeds a few joules needs a dump path across the winding - freewheel diode, varistor, or resistor - rated for the coil's stored energy, peak current and clamp voltage. Without one, opening the circuit at current can arc the switchgear.

the Dee may be oscillated with voltage amplitudes of up to approximately 3000V relative to the grounded Dummy Dee. The Dee capacitance is approximately 76 pF. The secondary coil inductance of 0.87 uH or more in parallel with the Dee capacitance yields a resonance as high at 19.5 MHz, which is the maximum cyclotron frequency corresponding to 411 keV protons in the maximum magnetic field of 1.28 T. ... These inductors are 1/4 inch copper tubing, wound coaxially, with the 6 cm diameter primary coil outside the 4 cm diameter secondary coil. The inductance of the primary coil can be changed by replacing the coil with one having a different number of turns, several of which have been constructed

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

Editorial note, tabletop extrapolation: Concrete worked values at the same scale, but measure your own machine's total capacitance (dee + stray + coil) and size the coil from L = 1/((2*pi*f)^2 * C_total); the swappable-primary approach lets you retune coupling without rebuilding the tank. The 411 keV is that machine's figure at its own field and extraction radius.

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 ... the maximum life of the magnet coil insulation, which the manufacturer estimates will vary with temperature as follows: [table: 79 C, 8-40 years; 87 C, 4-20 years; ... 130 C maximum allowable]

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

Editorial note, tabletop extrapolation: 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. The 130 C figure is this manufacturer's rating for this insulation - a next machine's ceiling is its own insulation's thermal class.

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

Editorial note, tabletop extrapolation: Applies to the homemade dee-tank coil: assess its RF loss and temperature under the intended loaded-Q and coupling conditions (resonator circulating current depends on Q and coupling, not on the DC feed), and give it forced air if it runs hot.

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

Editorial note, tabletop extrapolation: Reject nickel-plated hardware anywhere RF current flows in the resonator, coil, or ground-return path unless the overplate is verified thick and continuous - or validate by measuring loss and temperature.

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

Editorial note, tabletop extrapolation: Buy the tank-coil tubing as electrolytic/electrical-grade (C10100/C11000) copper with certified conductivity, not generic plumbing tube - worth roughly 6-23% lower RF surface resistance depending on where the plumbing tube fell in its range.

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

Editorial note, tabletop extrapolation: Do not budget the resonant step-up on textbook thousands: measure or model the loaded Q of the actual resonator under representative coupling (loaded Q sits well below the coil's unloaded Q), then size the amplifier for 5-13 kV dees from that measurement.

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

Editorial note, tabletop extrapolation: For the cited Q-meter method, treat the reading as a lower bound and keep leads and fixture capacitance minimal. A VNA measurement is a different animal: state whether loaded or unloaded Q is being extracted, calibrate and de-embed the fixture, and include the distributed capacitance in the fit - VNA errors can bias either direction.

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

Editorial note, tabletop extrapolation: At 9 MHz a 3-4 inch diameter tank coil in the charted geometries reads Q over 1000. At fixed frequency and capacitance the dee voltage scales as sqrt(P*Q) - doubling Q at the same drive buys about 40% more voltage, not double - so treat Q gains as helpful, and verify with the loaded Q actually measured.

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

Editorial note, tabletop extrapolation: For a 9 MHz matching/tank inductor, space the turns so the wire fills 45-70% of the pitch - close-winding bare tubing costs Q (proximity effect is the standard explanation, beyond this source's scope) - and check any stock coil against the ratio before trusting its rated Q.

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

Editorial note, tabletop extrapolation: Make the resonator coil short and fat (length a bit under half its diameter), not the long skinny solenoid that fits most easily in a corner - and not a pancake either: below the optimum Q collapses quickly.

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

Editorial note, tabletop extrapolation: 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

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

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

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

Editorial note, tabletop extrapolation: The sizing equation for the reference machine's LDMOS upgrade - with P as the power actually DELIVERED to the tank: at a good match forward power approximates it; otherwise net out the reflected fraction first. Doubling dee voltage costs 4x power, so 1.3 kV to 5-13 kV needs a 15-100x power increase unless L/C or Rs improves (dg-239's knobs).

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

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

Editorial note, tabletop extrapolation: When predicting a next machine's dee voltage, include every RF current path - chamber return, stem, feedthroughs, contacts - and prefer copper returns where possible; then measure the assembled tank's Q and infer Rs from it rather than assume a multiplier. [Note revised 2026-08-23: earlier note told the builder to 'expect ~1 ohm scale Rs', a number that belongs to Rutgers' geometry.]

after a power level of 200 watts, the measured voltage of the P6015 probe departed from the trend and dropped below the expected value. It is as if an additional resistance is introduced. The behavior was similar to that of a high-resistance break-down ... while the P6015 probe's value deviated from the trend, the induced voltage on the chamber's capacitively coupled pickup continued to followed the trend which was consistent with the theoretical model ... 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

Editorial note, tabletop extrapolation: The measurement chain for the LDMOS upgrade, rebuilt on the reference machine's own hardware: calibrate its pickup against an independently validated dee-voltage measurement over an overlapping safe range, confirm linearity and unchanged tuning, and never transfer the 3710 ratio or the power breakpoints between machines.

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: A bench L-C meter trick for characterizing the coupling loop: measure series-aiding and series-opposing, difference is 4M. The M a matched loop NEEDS follows from M = sqrt(R_tank*Z_source)/omega with the tank's measured series resistance and the source impedance at the operating frequency - compute it for the actual tank rather than expecting a stock tens-of-nH answer.

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: A benchmark to scale, not a floor: for the reference machine's ~9 MHz tank, skin-effect scaling of the same coil suggests Q0 ~ sqrt(9/15)*920 ~ 700-class; a measured Q0 far below the scaled expectation is the excess-loss flag (bad joints, steel in the return path) worth hunting.

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

Editorial note, tabletop extrapolation: Good news for coupler design: don't agonize over loop position vs tap point - but on a new tank, after nulling reflected power, verify dee voltage and coupler temperature once per geometry before treating settings as equivalent; a nominal match can hide coupler or cable loss.

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

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

Editorial note, tabletop extrapolation: For a next machine, shrinking dee-to-liner capacitance (larger dee-to-lid spacing) and a bigger low-loss coil raise dee voltage before amplifier watts do - bought, not free: more L usually brings more conductor and more Rs, and dee-to-lid spacing spends the magnet-gap budget (dg-163). Optimize the L/C-versus-Rs package together, then buy watts.

inductance of 1.1uHy, capacitance of 78.1pF, and the estimated AC resistance of 50mOhm ... Preliminary tests with the new generator show that the cyclotron chamber is capable of withstanding 2000 watts of input power. The tank, tank housing, cyclotron chamber and DEE stem become very warm. It is not necessary to operate at 2000 watts, as shown above 1000 watts produces a peak-to-peak DEE voltage of approximately 15kV.

Koeth, Theoretical Calculations and Measurements of the DEE Voltage in the Rutgers 12 Inch Cyclotron (2005) — p. 2, 8

Editorial note, tabletop extrapolation: Scales the reference machine's plan only under ideal sqrt-power scaling at unchanged loaded shunt impedance: 500 W -> ~10.6 kVp-p, comfortably in the 5-13 kV target - but measure the actual dee voltage with a calibrated pickup; thermal management of stem and coil becomes the real issue.

the 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

Editorial note, tabletop extrapolation: For nA-level collection near a ~9 MHz dee, treat the choke as one element of a verified filter: choose it from measured impedance and self-resonant-frequency data at the RF frequency, keep whatever shielding the noise floor turns out to demand, and validate by running RF with no beam - displacement currents into an unshielded tip can dwarf the beam signal.

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: Make the source mount adjustable in both directions and tune position for beam, not for geometric center. Size the travel from RF-field and orbit modelling for the actual dee geometry - the large machines needed over 2 inches; what a tabletop machine needs is its own calculation, and generous commissioning range is cheap.

Cited in: Beam Dynamics: An Interactive Laboratory

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: At ~1.3 kV and ~150 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. ... The limit can be raised by designing for greater clearance between D's and chamber lids and by providing round, smooth contours and clean, polished surfaces.

Livingston & Blewett, Particle Accelerators (1962) — p. 175, 189

Editorial note, tabletop extrapolation: At 1.3 kV the reference machine has large margin against this failure mode. For a next machine at several kV, treat MIT's ~56 kV/in at breakdown as one calibration point, not an allowable: analyze peak surface fields, round and polish, assemble clean, and expect to condition (see dg-253) - no universal safe kV/in exists for vacuum gaps.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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. ... In some cyclotrons the D's have been shaped to conform roughly to such a beam envelope, having wide inner vertical aperture in the central region and tapering to a narrower width at the outer edge.

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

Editorial note, tabletop extrapolation: At tens of RF watts the builder likely needs no water, but check rather than assume: what matters is local RF current density and the thermal path, not total power. Dee thermal drift detunes the resonator - keep dee structures stiff and thermally anchored, and watch tuning drift as power rises.

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

Editorial note, tabletop extrapolation: Hood or collimate the reference machine's source with the exposed column ADJUSTABLE, starting near a third of the aperture height, and optimize against extracted beam and dee voltage together - the historical ratios locate the starting point; the machine's own optimum may sit elsewhere.

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

Editorial note, tabletop extrapolation: If a next machine goes two-dee push-pull, watch for the push-push mode (no dee-to-dee voltage, oscillator happily locked); a single-dee-plus-dummy design sidesteps that mode entirely - one reason small machines favor 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

Editorial note, tabletop extrapolation: The reference machine's dee operates in the range where these discharge phenomena live: the ~100 V-class multipactor band is crossed at every start, and blue-glow gas discharge appears when pressure and surfaces allow. Surface conditioning, low pressure, and drive that can snap up fast are the standard escapes - and whether a given stall is multipactor or gas discharge is diagnosed, not assumed (dg-1273).

Cited in: The Vacuum Budget of a Cyclotron

A technique frequently used to adjust or trim the relative resonant frequencies of the two D-line circuits is to use one or more trimmer capacitors which can be adjusted by remote control under full power operation. Such a variable capacitance can be provided by a movable plate on the side wall of the chamber facing one edge of the D. It must have excellent electrical contact to the walls for the radiofrequency currents and a range of motion sufficient to tune over about 1 per cent in frequency. The availability of such a tuning device makes it possible to adjust relative D voltage as desired for optimum operation.

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

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

It is common experience, however, that no amount of smoothing or polishing will eliminate the necessity of some high-voltage conditioning under vacuum. Clean laboratory techniques in preparing a chamber for reassembly after opening are essential; dust should be controlled and all grease removed (even fingerprints), and under no circumstances should steel wool or coarse abrasives be used in cleaning. The oscillator circuit must be capable of driving the cyclotron through these varied conditions of sparking and discharge, without the necessity of tuning or of manual resetting of overload relays.

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

Editorial note, tabletop extrapolation: After every chamber opening, ramp dee voltage gradually with vacuum and arc-rate monitoring until sparking subsides before expecting stable beam; how long that takes is the machine's answer, not a fixed budget.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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

Editorial note, tabletop extrapolation: The same logic favors a drive that follows the dee on the reference machine: self-excited, or a PLL tracking the resonator - similar in spirit though not identical in dynamics, since a PLL adds its own loop behavior. Either way, 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. ... Most natural or artificial rubbers have unacceptable vapor pressures and also deteriorate when used with lubricating greases. Neoprene is free of these faults and is widely used in cyclotrons.

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

Editorial note, tabletop extrapolation: The copper-foil RF bridge over elastomer joints prevents mysterious Q loss and local heating and transfers directly. For the gasket itself, a modern machine should size grooves from the O-ring manufacturer's vacuum-service squeeze and gland-fill tables - the historical 1.5x ratio is the era's flat-gasket practice, not an O-ring spec.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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

Editorial note, tabletop extrapolation: A concrete tuning rule for the builder: do not tune RF to the central field alone - place it inside the quoted window and find the best point empirically by beam current; the phase-history reasoning is the theory behind the knob, not a substitute for turning it.

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

Editorial note, tabletop extrapolation: Explains failed runs where beam dies at small radius, and quantifies how little phase budget a mistuned machine has - for the actual machine, integrate the slip turn by turn from the measured B(r) and dee voltage rather than using 12 turns as a threshold.

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

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

Editorial note, tabletop extrapolation: The reference machine already does this, and it stays attractive for a next machine - one HV feedthrough fewer, the chamber as return electrode - unless push-pull two-dee RF is wanted for higher energy gain per turn. A common choice among documented small machines, not a rule.

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

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

Editorial note, tabletop extrapolation: A documented dee geometry near the reference machine's scale - note it exceeds an 8-inch pole, so it fits 10-inch-class machines as-is: scale the proportions, not the dimensions. Dee cooling need tracks the dissipated RF power and construction, not a fixed kilowatt line: compute it from the RF budget (dg-313) and watch dee temperature during commissioning.

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

Editorial note, tabletop extrapolation: Sets expectations if a next machine attempts a deflector: capturing a third of the circulating beam was a mature machine's result, so plan around numbers of that order - and account for where the rest goes (septum heating, sputtering, and at higher energies activation), rather than booking the loss as free.

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

Editorial note, tabletop extrapolation: Direct rule for source-to-puller spacing - clean DC gaps are the law's home turf: a few-kV gap needs sub-mm minimum, with real margin because sputtered metal films spoil the 'clean surface' assumption fast. For dee-to-ground RF clearances use it only as a lower-bound sanity check: edges, insulators, RF conditioning and enhancement move the practical limit (dg-353, dg-662).

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

Editorial note, tabletop extrapolation: When insulating the reference machine's extraction or dee leads, design from certified data for the actual material, thickness, frequency and environment - a bulk breakdown number is a test-condition figure, not a working rating. Grade the field at edges, design creepage and surface flashover paths separately, and qualify the finished assembly under vacuum with a conservative withstand test.

Compared to T or Pi networks, the L network uses only one combination of inductance and capacitance. This simplifies the microcontroller tuning algorithm. The disadvantage is that one L network cannot match all possible load impedances. Figure 3 shows two L network types with complimentary matching ranges on the Smith Chart. The IMS uses an RF switch to select one of the two L networks, allowing a wider matching range.

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

Editorial note, tabletop extrapolation: If the builder automates their dee match at 9 MHz, a stepper-driven L-network is the simplest topology for the search algorithm; verify the two configurations' combined range covers the tank's actual impedance excursions (a Smith-chart sweep or simulation) before committing.

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

Editorial note, tabletop extrapolation: For the reference machine's 100-500 W upgrade: a homebrew 30 dB coupler plus AD8307 board works with a calibrated pad (10 dB or more) between them; include coupler tolerance and mismatch peaks in the level budget, and calibrate the chain end to end.

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

Editorial note, tabletop extrapolation: A cheap coupler build bracketing the reference machine's 9 MHz band - built from the source's full schematic, not the one-line summary: the shield treatment and grounding are what make the directivity, so replicate them exactly, then bench-test directivity, insertion loss and core heating at 9 MHz through the intended power and mismatch range before trusting it.

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

Editorial note, tabletop extrapolation: Do not chase - or trust - SWR readings within the bridge's directivity band: near-1.0 does not prove a good match any more than 1.08 proves a bad one. Characterize the actual homebrew bridge's directivity first; then readings inside its band are 'unresolved', not data.

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

Editorial note, tabletop extrapolation: A Bird 43 (owned or borrowed) transfers power calibration to permanently installed cheap sensors - within the installed element's frequency range, power range and its own accuracy spec, so record which element was used. Take the AD8307's slope and intercept from its datasheet and the actual unit's measured response, not nominal folklore.

actuates stepper motors to alternately adjust a variable capacitor and a variable inductor to reduce VSWR to less than 1.5:1 ... The antenna tuner system can match loads of up to 26:1 initial VSWR within a frequency range of 3.5 MHz to 30 MHz.

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

Editorial note, tabletop extrapolation: Coordinate-descent on C then L is not guaranteed to converge on an interacting high-Q load - test it against the dee resonator before trusting it - and set the LDMOS amplifier's reflected-power shutdown from that device's own specification, not from the 1.5:1 convention.

fo = qBo/2pi mi = (1.52x10^7) Bo(tesla)/A

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: At sub-MeV this limit is distant - by this formula a 10 kV dee puts the proton ceiling near 7 MeV - 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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: For the builder: 1 MeV at 2 kV per gap (2 gaps) is ~250 turns with final-orbit spacing ~0.25 mm at r = 12 cm - which is 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

Editorial note, tabletop extrapolation: At 1 MeV the instantaneous slip is only ~0.4 deg/turn, but slip accumulates over every turn, so what that buys depends on volts per turn: a machine gaining a few kV per turn spends thousands of turns getting to 1 MeV and can run out of phase well below the textbook ceiling. The design check is the summed slip across all turns against the +/-90 deg window, not the per-turn number.

The second DEE has been faked using the image of the real DEE on a grounded conductor ... By twisting the inductor, we can change the inductance to match our inductance requirements.

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

Editorial note, tabletop extrapolation: This is the reference machine's exact topology, in use on a comparable documented machine; the deformable-inductor trim is a simple tuning mechanism worth copying on a next machine.

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

Editorial note, tabletop extrapolation: A benchmark, not an expectation: measure the reference machine's own unloaded AND loaded Q, compare against a loss model to decide whether joints are costing Q, and judge retuning needs from measured thermal drift against the loaded bandwidth - Q alone predicts neither the drift rate nor the need for active tuning.

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

Editorial note, tabletop extrapolation: A gas-fed cyclotron chamber often sits in exactly this transition decade, so the spark limit can move with operating pressure: measure holdoff with the actual gas flowing at operating pressure as well as at base vacuum, and interlock conservatively - which direction the limit moves depends on where the geometry sits relative to the Paschen minimum.

Cited in: The Vacuum Budget of a Cyclotron

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

Editorial note, tabletop extrapolation: Directly applicable startup ritual at the reference machine's 1.3 kV dee level - ramp in short bursts with current-limited RF, arc detection and pressure monitoring. The report reads failure to reach its endpoint as organic contamination (grease, oil, rubber) in the tank; leaks and ordinary outgassing can mimic it, so inspect or run an RGA before blaming contamination.

Cited in: The Vacuum Budget of a Cyclotron

the 'single-dee' construction; this has many advantages ... Better ion focussing can be obtained by installing a 'dummy' grounded dee edge symmetric to the insulated dee, but this is a refinement

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 8

Editorial note, tabletop extrapolation: Exactly the reference machine's architecture. The dummy-dee edge is the source's named refinement for better ion focusing - a natural next-machine upgrade once the basic machine works, which is the sequencing the source itself implies ('but this is a refinement').

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: Directly applicable to the reference machine's amplifier: wide copper sheet or strap grounds and a short feed run, with magnetically SENSITIVE parts kept out of the fringe field - the tube in the quote; in modern gear whatever actually cares (fans, ferrites, meters - dg-670's shield-or-relocate).

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

Editorial note, tabletop extrapolation: Directly applicable: the reference machine's beam-current, bias and gauge lines all deserve feedthrough RC/choke filtering at 9 MHz - with 'adequate' proven by measurement: an RF sniff at the meter terminals with the transmitter running.

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

Editorial note, tabletop extrapolation: Directly applicable home-lab safety baseline for the HV systems of a next machine - covers interlocked, hooks in reach, and the full discharge discipline around them (dg-522).

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

Editorial note, tabletop extrapolation: Directly relevant to any thin-lid chamber on a next machine squeezed into a small magnet gap: design the lids to a calculated stiffness (the lid-deflection calculator) from the start. Internal posts clear of the beam spiral and the RF high-field region are one remedy; thicker or dished lids and external ribs are others, and each needs its own deflection, buckling, venting and weld checks. [Note revised 2026-08-23: earlier note planned posts as the remedy.]

Cited in: Cyclotron Vacuum Chamber Design and Sealing

Having only one dee rather than two doubles the voltage requirement, but reduces the cost and complexity of having two RF feedthroughs in the vacuum chamber.

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

Editorial note, tabletop extrapolation: Supports the single-dee choice for a next machine unless attainable dee voltage, insulation or the coupling scheme becomes the binding constraint.

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

Editorial note, tabletop extrapolation: For any HV feed on a next machine (deflector, source bias): keep cable runs short. Stored cable energy is delivered into an arc in the first instant, faster than any supply limiter acts - it adds to what the supply and other capacitances feed the fault, it does not replace them. Series resistance at the load (dg-286) limits the follow-on current.

We've encased the resistor in a grounded shield, and the coax shields go through 68 Ohm, 2 watt resistors ... 150 Meg HV resistor ... HV Vacuum Feed Through is now inside an acrylic tube covered with copper mesh.

Ponter, Beam Energy Measurements with a New HV Deflection System and Ion Source Upgrades on the Rutgers 12-Inch Cyclotron (2010) — p. 44-52

Editorial note, tabletop extrapolation: A staged-resistance pattern for electrostatic HV feeds (deflector, PIG source bias) whose load draws no standing current: series megohms limit arc current at the price of regulation under load, so it does not transfer to circuits that must deliver current. Even with this shielding the arcs stopped only after the cable-energy fix (dg-285) - 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

Editorial note, tabletop extrapolation: Essentially the reference machine's current architecture. A ham antenna tuner can match a dee-shaped load in this frequency range - but its voltage ceiling is construction- and tuning-dependent: expect the ~kV class rather than the 5-13 kV a dedicated resonator supports (the LDMOS upgrade path), and MEASURE the dee voltage (dg-quoted methods in the dee-coupling deep dive) instead of inferring it from the tuner's rating.

3.55 MHz 1700 Vpp (26 W) ... 3.48 MHz 800 V (10 W)

Yuly et al., Modifications on the Houghton College Cyclotron (2010) — p. 17-19

Editorial note, tabletop extrapolation: A benchmark for the order of magnitude the reference machine's autotuner path reaches (its ~1.3 kV from a 5 W amplifier is in the same band), not a curve to read values off: state the voltage convention, tuning and loading before comparing, and do not infer a plateau from two points.

No peaks for magnetic fields larger than H2+ at 0.5 T -> 35 keV; 44 orbits at 800 Vpp

Yuly et al., Modifications on the Houghton College Cyclotron (2010) — p. 21

Editorial note, tabletop extrapolation: Quantifies why the reference machine's dee-voltage upgrade matters: at 1.3 kV their protons need ~hundreds of turns to reach interesting energies, and ~44 turns was already the survival ceiling at Houghton's pressures.

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: Anchors the power budget with one measured point: 2 kW bought 8.4 kV peak on that 12-inch tank. Scaling to the reference machine's planned LDMOS runs through ITS shunt impedance (dg-313's formula with measured Q and C): at comparable impedance, 500 W supports roughly 1/2 the voltage (P ~ V^2), a ~4 kV class - measure, then budget.

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

Editorial note, tabletop extrapolation: A free end-to-end CONSISTENCY check for the builder: the power at which beam vanishes ties the trajectory model, the dee-voltage estimate and the RF chain together at one point. It is a cross-check, not a probe-independent voltage measurement - source emission, phase, pressure and detector sensitivity all sit inside the observed threshold - so use it alongside a calibrated pickup, not instead of one.

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

Editorial note, tabletop extrapolation: At 100-500 W expect real warm-up drift and MEASURE it: the measured drift against the loaded bandwidth decides whether hand-touchup, a slow motor loop, or nothing is needed. The cyclotron constraint is the point - the RF must stay synchronous with qB/(2 pi m), so the resonator follows the beam frequency, not the other way round.

Beam Inferred DEE Voltage ... In the 1st half revolution E(r) = (qB^2/2m) r^2 = 1/2 Vp-p

Koeth et al., The Rutgers 12-Inch Cyclotron for Students (2010) — p. 33

Editorial note, tabletop extrapolation: The builder can cross-check a dee-voltage estimate by measuring where the first half-turn lands - the beam is the most honest voltmeter - provided the landing radius is converted to orbit radius using the actual source-to-probe geometry, and the ion is assumed to cross near peak phase (real phases read low).

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

Editorial note, tabletop extrapolation: Bring the reference machine's dee and extraction voltages up gradually on first pump-down, watching for micro-discharge pulses. Conditioning raised the measured threshold in the source's account; the gain is not permanent capital - re-condition after venting rather than assuming the old ceiling still holds.

They found that at a critical angle of 31.5 deg, the surface charge was zero; this angle was independent of the applied voltage. The surface charges were positive at smaller angles, but negative at larger ones. ... Fryszman and colleagues found that by screening the section of the insulation surface near the cathode or covering this section with a semiconducting layer, the breakdown voltage was raised by a factor of approximately 2.5. ... Roughening the surface of the insulator in a region adjacent to the cathode increased the breakdown voltage by about 40 %. Roughening the surface adjacent to the anode had little effect.

Miley & Murali, Inertial Electrostatic Confinement (IEC) Fusion: Fundamentals and Applications (2014) — p. 113-114

Editorial note, tabletop extrapolation: For the next machine's source stalk - a DC cathode-junction context like the studies' - cone the insulator toward the negative electrode and consider recessing the triple junction behind a screen. The factors come from separate experiments and are not multiplicative, and a dee-stem RF feedthrough alternates polarity every half cycle: there, treat all of this as qualitative guidance to be tested, not booked margin.

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

Editorial note, tabletop extrapolation: The source's fixture works out to 2-4.5 kV/mm of creepage - a first sanity check for an extraction stalk, not a design allowable: flashover depends on triple-junction geometry, finish, contamination and conditioning, and does not scale linearly with length (the source's own longer insulators held less per mm). Size real hardware by test, with margin.

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

Editorial note, tabletop extrapolation: The classic failure of home-built HV feedthroughs: a loose PTFE sleeve over a rod arcs in the annular air film. Fill the gap - potting or liquid dielectric - so no gas layer sits in series with the solid. Evacuating the annulus removes the Paschen path but leaves field-emission breakdown and surface flashover, so vacuum is not a substitute for filling.

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. ... In order to keep stress at Z below that at X in Fig. 4.15, the radius of curvature at Z should not be less than the radius of the inner cylinder.

Miley & Murali, Inertial Electrostatic Confinement (IEC) Fusion: Fundamentals and Applications (2014) — p. 117, 122-124

Editorial note, tabletop extrapolation: Preliminary ideal-coax sizing for the reference machine's HV stalk: a grounded 25-mm-bore port gives a ~9.2-mm center conductor at the 1/e optimum - then check the complete feedthrough (ends, dielectric interfaces, triple junctions) electrostatically, 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. ... The electrode is surrounded by a coaxial aluminum tube, which in turn is shadowed by a coaxial large diameter, aluminum tube. ... The stalk is a conical-shaped insulator facing toward the cathode grid that is expected to block the ions passing through the cathode grid. ... The corrugated surface is intended to lengthen surface current path lengths, preventing premature surface breakdown.

Miley & Murali, Inertial Electrostatic Confinement (IEC) Fusion: Fundamentals and Applications (2014) — p. 87, 105, 109

Editorial note, tabletop extrapolation: In the reference machine's small chamber everything sees the source; a washer-stack or skirt shielding the feedthrough ceramic from the chimney slit is the same shadow-shield idea and should lengthen time between cleanings - validate on the actual geometry, since much of the sputtered flux travels as neutral atoms and simple line-of-sight shielding is the right first-order defense.

The axial component of the magnetic field can be decreased at larger radii in order to increase the radial (focusing) component, provided the ions only have a few revolutions left once they reach this portion of the field.

Morrow, Focusing in the Houghton College Cyclotron — Houghton College thesis (2015) — p. 27-28

Editorial note, tabletop extrapolation: One candidate for the reference machine's next big win: at ~150 keV on a low Dee voltage the turn count is large, and cutting it relaxes both the phase budget and gas-scattering exposure. Whether Dee voltage or field shaping pays more on a given machine is a diagnosis - measure what actually limits the beam first; the quote's own condition is narrower: late-radius focusing tricks need few turns remaining.

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

Editorial note, tabletop extrapolation: Essential for interpreting the reference machine's magnet scans: a peak at one-third field is likely a subharmonic, not a mystery species. H2+ vs H+ assignments need more than one matching peak - or an independent species diagnostic - since different q/m patterns can overlap.

It can be seen that in general, an increase in dee voltage results in a higher beam current.

Fuller, Exploring the Capabilities of the Houghton College Cyclotron — Houghton College thesis (2013) — p. 49-50

Editorial note, tabletop extrapolation: For a fill-gas machine, dee volts are a strong current knob - the measured trend here: fewer turns, less path, fewer collisions. Whether they are THE binding knob depends on what limits the machine that day: source output, pressure, phase acceptance and detuning all compete (dg-359, dg-525). Measure before spending.

the 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 ... The data points represent the voltage gain between the RF amplifier and the dee. The voltage gain will be a maximum at the resonant frequency. For this plot, f0=3.55MHz.

Haas, Characterizing the Performance of the Houghton College Cyclotron — Houghton College thesis (2009) — p. 63-64

Editorial note, tabletop extrapolation: A simple, scope-only resonance-finding recipe after any mechanical change to a next machine's dee or stem: coarse-to-fine, with the fine step sized to the resonance linewidth rather than copied - and use a rated or noncontact voltage pickup on the dee side.

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

Editorial note, tabletop extrapolation: Quantifies the architecture choice: the reference machine's antenna-tuner match delivers kV-class dee voltage at low measured Q, and multi-kV wants a high-Q tank coil. The caveat travels: a low measured LOADED Q reflects the whole coupled system, matching-network losses included - so measure Q on the actual assembly and compare loaded with loaded when weighing the upgrade.

the resonant frequency occurred at f0=3.55 MHz ... Its results were f0=3.63 MHz at a SWR of 1.4:1 ... 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. 64-65

Editorial note, tabletop extrapolation: When cross-checking NanoVNA SWR sweeps against powered probe measurements, probe loading is the first hypothesis for a small frequency disagreement - confirm it (adding the probe should lower the frequency, repeatably) before ruling out coupling, calibration-plane or mechanical causes; Houghton's 2 percent is their number, not a generic tolerance.

By comparing the CT2591 HV probe with the pickup probe, a scaling factor can be determined ... It was determined that the real voltage was roughly 11,300 times the pickup voltage. The frequency of the RF system will affect the values recorded by the pickup probe. For this reason, the probe had to be recalibrated every time the frequency was adjusted. The results given here were for a frequency of 3.55 MHz. ... A linear fit was performed and indicated that the real voltage was roughly 11,300 times the pickup voltage at an RF frequency of 3.55 MHz.

Haas, Characterizing the Performance of the Houghton College Cyclotron — Houghton College thesis (2009) — p. 65-66

Editorial note, tabletop extrapolation: The pickup scale factor is frequency-dependent - the builder must recalibrate their pickup whenever they retune, not assume one constant.

First, the RF system was tuned to a resonant frequency of 3.55 MHz while the filament was set to 2.0 A and floated at -100 V relative to the chamber. At these settings, a SWR of 1:1 and forward power of 15.43 W were measured. ... there is a resonance peak with a magnitude of 1.5 pA at around 0.23 T. ... Collection took place at a radius of roughly 5.95 cm corresponding to proton energies of 9.2 keV.

Haas, Characterizing the Performance of the Houghton College Cyclotron — Houghton College thesis (2009) — p. 69

Editorial note, tabletop extrapolation: Reassurance for commissioning a next machine: hunt for first beam at tens of watts with a clean match before scaling power - on the cited machine, detection sensitivity rather than RF power was the limiting factor at first beam.

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

Editorial note, tabletop extrapolation: At the reference machine's ~150 keV the relativistic shift is small (gamma-1 ~ 0.02%), but phase slip accumulates over the whole turn count, so low volts-per-turn can still spend the +/-90 deg budget well below the textbook ceiling (dg-273's summed-slip check). 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

Editorial note, tabletop extrapolation: A replaceable-filament pattern worth copying next to a live dee: bias the filament, and RF-bypass every lead at the feedthrough - but size the bypass for the actual RF impedance and current, and use capacitors rated for the DC bias plus transients rather than copying 1 nF.

the Dee may be oscillated with voltage amplitudes of up to approximately 3000V relative to the grounded Dummy Dee ... For normal operation, 10-40 W of RF power are required

Yuly, The Houghton College Cyclotron: a Tool for Educating Undergraduates — Cyclotrons 2013, WE1PB01 (2013) — p. 3-4

Editorial note, tabletop extrapolation: Tells the builder that Dee voltage is a tank-Q problem, not a brute-force power problem: a modest amplifier into a good resonator beats a big amplifier into a lossy one - and dg-313's formula computes the actual watts-per-kV pairing for any target.

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

Editorial note, tabletop extrapolation: The reference machine's 9 MHz benefits from the modern form of the same effect: HF amateur-radio technique and parts are abundant below ~30 MHz. Today's sweet spots follow ham bands and ISM frequencies rather than a 15 MHz line; the transferable point is choosing field and frequency where the RF art is cheap.

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

Editorial note, tabletop extrapolation: Formula transfers once the conventions are fixed: at 9 MHz, ~50 pF and unloaded Q ~ 1000, 5 kV peak dee-to-ground dissipates ~35 W in the resonator - tens of watts, the FLOOR an amplifier must clear with margin for coupling loss, detuning and arcs. Double the voltage, four times the power.

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: Test discipline for a next machine's dee-voltage conditioning: rate the machine at the level it holds quietly under a defined acceptance protocol (duty cycle, thermal soak, vacuum stability, RF interlocks), not at the level it touches momentarily.

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

Editorial note, tabletop extrapolation: The order of magnitude transfers as expectation-setting: most RF power goes to resonator and ion-loading losses, so size a next machine's RF from resonator dissipation (dg-313), not from 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

Editorial note, tabletop extrapolation: Scaled down: any sliding or bolted joint in the reference machine's dee-stem/coil path should be a broad, clean, firmly clamped contact - poor joints are a common and avoidable Q killer in small resonators; whether plating or water cooling is warranted follows from contact loss and temperature, not from the 86-inch's spec.

Since the dees are insulated to operate at a dc bias, ... two-inch rubber hose about seven feet long are used to insulate the dees and to connect to the inlet and outlet headers at the extension wall. ... 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. 55, 59

Editorial note, tabletop extrapolation: 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 hose is not automatically insulation: the water column conducts, so check coolant conductivity and path length for leakage current, the choke's impedance and self-resonance at the RF frequency, and creepage and pressure rating.

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

Editorial note, tabletop extrapolation: Modular paralleled supplies (or PA pallets) with individual protection can give a home machine graceful degradation - but that takes design, not just fuses: current sharing or ORing, backfeed isolation, DC-rated load-break disconnects, fault coordination, and a written de-energization procedure before anyone touches a unit. Never hot-swap hardware that wasn't designed and tested for it.

Oscillator starting difficulties due to 'ion loading' are avoided by the use of insulated negatively-biased dees.

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 7, 47

Editorial note, tabletop extrapolation: Directly applicable if a next machine's RF start-up stutters or the dee glows at low voltage: insulate the dee for DC and feed a negative bias through an RF choke. The same lever also bears on multipactor (dg-324), which lives in the same low-voltage start regime. The source records the method; the bias magnitude is found on the machine.

The selected value of 100 kv peak voltage requires about 1.5-in. clearance from dee-to-liner ... Since the magnetic gap is so precious ... this minimum value is taken for design.

Livingston & Howard (eds.), The Oak Ridge Relativistic Isochronous Cyclotron — ORNL-2648, OSTI 4275955 (1958) — p. 100

Editorial note, tabletop extrapolation: The reference machine's 1.3 kV is electrically trivial by this calibration - its clearances are set by beam aperture and mechanical tolerance. For a 20-50 kV dee on a next machine, set clearance from electrostatic analysis of the actual geometry (edges, finish, conditioning, pressure regime), not by scaling kV/cm linearly.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

the maximum voltage gain/dee is Vd = 2*V0 sin(theta/2); for particles rotating on subharmonics of the dee frequency the angular width of the dee is n*theta to the particle

Livingston & Howard (eds.), The Oak Ridge Relativistic Isochronous Cyclotron — ORNL-2648, OSTI 4275955 (1958) — p. 100

Editorial note, tabletop extrapolation: Directly applicable when trimming a next machine's dee for probe or source clearance: keep the dee close to 180 degrees or compute the sin(N*theta/2) penalty for the harmonic in use. Fundamental-mode trims are gentle - 15 degrees off costs about 1% at N = 1 - but the same trim costs more at higher harmonics.

The high dee voltage required in cyclotrons can be achieved for practical driving power only by using a high-Q resonant circuit.

Livingston & Howard (eds.), The Oak Ridge Relativistic Isochronous Cyclotron — ORNL-2648, OSTI 4275955 (1958) — p. 17

Editorial note, tabletop extrapolation: Directly applicable framing for the reference machine's matching network: every dB of resonator Q lost to bad joints or lossy insulators is paid in amplifier watts.

it is possible to bias the dees to prevent multipactoring, and a more complex booster oscillator circuit is required

Livingston & Howard (eds.), The Oak Ridge Relativistic Isochronous Cyclotron — ORNL-2648, OSTI 4275955 (1958) — p. 99

Editorial note, tabletop extrapolation: Directly applicable: multipactor lives in the low-voltage, MHz regime every starting tabletop dee passes through, so anticipate it - designing the dee stem so DC-bias insulation CAN be added is cheap at design time and expensive after. Whether the bias is actually needed is learned at first RF turn-on.

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

Editorial note, tabletop extrapolation: A workable pattern for a kW-class dee driver assembled from LDMOS boards - but the transistor/module manufacturer's mounting spec wins: check flange flatness, clamping force, and which interfaces want grease, pads, solder, or dry metal contact for the specific device.

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

Editorial note, tabletop extrapolation: Relevant if building a broadband solid-state dee driver: these devices carry enormous low-frequency gain, so low-end stability needs deliberate design - feedback networks of this kind are one tool, verified by stability analysis or measurement on the actual amplifier; neither the 15 nH value nor certain oscillation without it transfers between layouts.

many amplifiers use a push-pull topology that tends to attenuate the second harmonic. For those amplifiers, it is often the third harmonic that has the highest amplitude ... The classic way is with a spectrum analyzer ... you would want to have about 40 dB of attenuation between the amplifier and the measuring device. ... 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

Editorial note, tabletop extrapolation: A cyclotron dee tank is narrowband, but the rule holds: measure what the PA actually emits before designing filtering or worrying about interference from a garage machine. Take the sample through a power-rated coupler or sampler and compute the pad from actual PA power against the analyzer's rated input - at 1.4 kW (61.5 dBm) a bare 40 dB still leaves +21.5 dBm, too hot for most analyzers.

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

Editorial note, tabletop extrapolation: Relevant if the builder drives the dee with a broadband solid-state PA instead of a tube - but a harmonic diplexer does not protect the FETs from the dee's reactive load at the fundamental. That protection is matching, reflected-power shutdown and, where needed, an isolator; the diplexer only tames the harmonic terminations.

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

Editorial note, tabletop extrapolation: Schedule measurement-and-adjustment time for any homemade filter bank, dee tank or matching network as a first-class line item; which DIRECTION values move is what the measurements tell you - this author's all-upward shift was his design's particular error, not a law.

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. ... I used 500v micas but slowly but surely I am changing them to 1000v specs because they are more robust.

Buckler, Solid-State, 2-Decade, 1.25 kW Linear Amplifier — Development Notebook (2015) — p. 31-32

Editorial note, tabletop extrapolation: Cheap fault-tolerance for a homebuilt RF deck, as the source built it. Check the fault arithmetic before copying: 50 V across 20 ohm is 2.5 A and 125 W, above the resistor's continuous rating, so the part rides through brief faults only - pair it with a fuse or fast shutdown rather than treating it as continuous-duty protection. Voltage-derating the filter 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

Editorial note, tabletop extrapolation: Size the RF chain from a component-by-component loss budget (relays, filters, couplers, feedline, matching, resonator) measured or taken from datasheets - the cited 7% is one chain's number; a cyclotron drive's tax depends on what sits in its line, so derive the PA headroom rather than assigning a stock percentage.

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

Editorial note, tabletop extrapolation: Before specifying silver on the dee or coil, get the plating process's conductivity data and compare thickness to skin depth at 9 MHz; an uncharacterized jobbing-shop bright-silver finish risks raising resonator loss, while a verified high-conductivity deposit can lower it.

a layer of high conductivity copper plating at least two skin depths in thickness, at the operating frequency, then protecting this against corrosion by a very thin layer of low conductivity plating or a layer of low-loss lacquer

Fowler, Radio Frequency Performance of Electroplated Finishes — Proc. IREE Australia (1970) — p. 10

Editorial note, tabletop extrapolation: For dees, stems, and tank coils at 9 MHz: copper at least ~45 um thick plus a thin low-loss protective finish beats unspecified decorative plating; properly specified high-conductivity silver can do better still, and nickel remains excluded on permeability grounds (dg-222).

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

Editorial note, tabletop extrapolation: Assess a proposed coating by computing the multilayer surface impedance with the coating's own conductivity AND permeability against its own skin depth - the trap case is a mid-thickness medium-conductivity layer, and magnetic coatings (nickel!) cannot be cleared by nonmagnetic skin-depth arithmetic; very thin protective flashes are usually small in effect at 9 MHz, verified by that same calculation rather than assumed harmless.

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

Editorial note, tabletop extrapolation: For RF contact fingers and connectors on the resonator, distrust thin gold flash: specify a qualified contact-plating system at proven thickness. Lacquer belongs only on non-contact surfaces, and only after RF-loss and vacuum-outgassing checks - never on a current-carrying contact interface.

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

Editorial note, tabletop extrapolation: Where sulfur contamination is credible (some shop atmospheres, rubber outgassing, industrial air), protect silver-plated RF joints or periodically inspect and measure their resistance - raised contact resistance heats under the resonator's high circulating RF current.

Several reasons have been given for the decrease in conductivity below the bulk values, including: (a) the Beilby layer ... (c) the hill and dale effect ... This last problem has been investigated fully by Benson who recommends chemical or electrolytic polishing to produce a smooth surface and lower losses.

Fowler, Radio Frequency Performance of Electroplated Finishes — Proc. IREE Australia (1970) — p. 8

Editorial note, tabletop extrapolation: Polishing dee edges and stems lowers RF resistance. Smooth, clean, well-conditioned electrodes may also reduce field emission, but the breakdown voltage must be established by field analysis and testing - do not book the second benefit in advance.

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

Editorial note, tabletop extrapolation: A directional coupler with fast drive-cut on high reflected power is a strong defense when the cyclotron dee arcs or drifts off resonance mid-run - one protection among the source's set (thermal, load-failure), not a complete answer on its own.

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

Editorial note, tabletop extrapolation: Directly applicable to a homebrew 9 MHz LDMOS deck: thermal-tracking bias holds the operating point against drift, and DC-free transformers remove one saturation mechanism - still verify RF flux density and transformer temperature at full drive.

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

Editorial note, tabletop extrapolation: A dee resonator is a narrowband, sometimes-detuned load: design feedback in from day one with a stability analysis over the expected load range, and pair it with real mismatch protection - drain-current limiting and reflected-power foldback - since feedback alone is not a detuned-load defense.

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

Editorial note, tabletop extrapolation: At 100-500 W a copper spreader under the LDMOS pallet is cheap thermal margin; the reference machine's earlier MOSFET amplifiers died in service without a firm post-mortem, and die-temperature margin is the inexpensive insurance either way.

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

Editorial note, tabletop extrapolation: At 9 MHz the 27 MHz third harmonic can couple into a spurious dee-resonator mode if one lies nearby; filter between amp and matching network, sized from the measured spectrum.

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

Editorial note, tabletop extrapolation: The dee's off-resonance reflection is a fundamental-frequency problem the diplexer does not solve: give the LDMOS reflected-power foldback or shutdown and, if needed, an isolator, and characterize the dee's impedance across its detuning range. The diplexer buys clean harmonic terminations - that is all.

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

Editorial note, tabletop extrapolation: When copying an LDMOS pallet layout, preserve the cited design's output-transformer tap geometry, and if anything about it changes, remeasure the output match - the source says position is critical; how sensitive, at what power, is a measurement on the actual build.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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

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

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

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

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

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

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

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

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

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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

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

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

Cited in: The Vacuum Budget of a Cyclotron

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

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

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

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

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

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

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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

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

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

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

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

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

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

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

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

Cited in: The Vacuum Budget of a Cyclotron

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

Editorial note, tabletop extrapolation: Moot for pump choice today; the observation transfers cautiously: the source found mercury vapor SEEMED to promote field emission from HV electrodes, and condensable conductive films on electrodes are a recognized breakdown risk generally - keep electrode surfaces free of deposition, sputtered films included (dg-261's clean-surface caveat).

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

Editorial note, tabletop extrapolation: Sets the historical scale: percent-class collected current from tens of mA of glow discharge - a budgeting anchor, not a conversion efficiency; aperture acceptance, extraction and species mix all live inside that 5%, so measure your own ratio before sizing the discharge supply.

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. ... The anode is a second steel tube A, supported axially inside the cathode and separated from it by about 4 mm ... the cathode C and the steel tubes can run red-hot

Oliphant & Rutherford, Experiments on the Transmutation of Elements by Protons (1933) — p. 260-261

Editorial note, tabletop extrapolation: The 'gap smaller than the discharge can live in' principle is how a builder forces the source discharge to localize at the extraction aperture rather than wander - pick the clearance for the actual gas, pressure and voltage and verify it empirically; the 4 mm is the source's worked point.

At first this beam consists very largely of molecular ions, but after running for some time it changes over and becomes nearly all protons ... The H2+ ion may be thought of as a pair of protons travelling together with an electron. The binding energy between them is negligible compared with the kinetic energy, which for either proton is one-half the energy of the particle. Hence a given current of molecular ions represents a current of protons of twice the magnitude, but with half the energy. We would therefore expect to begin to detect disintegration particles at about twice the energy found for the protons, and that the curve would rise twice as steeply.

Oliphant & Rutherford, Experiments on the Transmutation of Elements by Protons (1933) — p. 261-262, 269

Editorial note, tabletop extrapolation: For p-B11 the point survives translation with care: a proton-tuned cyclotron does not even hold H2+ in resonance (half the cyclotron frequency), but any acceleration mode that does deliver molecular ions yields constituent protons at a half (fixed voltage) or a quarter (fixed rigidity) of the expected energy - and p-11B is exothermic with no kinematic threshold, so what collapses is the cross-section-weighted yield, not an on/off threshold.

When it was once degassed it was only necessary to run for about half an hour in the morning to get the tube into a steady state. It was found to be most easy to degas the main accelerating electrodes and tube by 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

Editorial note, tabletop extrapolation: A historical conditioning observation for electrode structures that must hold voltage - adapt, don't copy: ramp with current and stored-energy limits, remote operation, interlocks, and a measured breakdown-rate criterion, and remember DC column conditioning does not transfer one-to-one to RF dees.

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

Editorial note, tabletop extrapolation: A triage order for the reference machine's low-current debugging: measure current at small radius first; if it's already low there, put ion production and extraction at the top of the checklist - while still verifying RF capture, focusing, alignment and the probe itself, since the clue is suggestive, not exclusive.

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

Editorial note, tabletop extrapolation: The architecture point transfers at any size: a differentially pumped source cavity running much higher pressure than the chamber, fed through the exit hole (the Penning-table rules carry pressure numbers - dg-372). The single operating point is a sanity anchor for a similar source, not a spec or a promise of half a milliamp.

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. Lifetimes in service of 100 to 200 hr have been reported. The limit is due to erosion of a small area the size of the exit hole on the cathode surface, which represents the effective emitting surface.

Livingston & Blewett, Particle Accelerators (1962) — p. 177-178

Editorial note, tabletop extrapolation: A mains-frequency-heated filament in a 0.59 T field risks vibrating itself to death; 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

Editorial note, tabletop extrapolation: Expect a large pressure rise when source gas flows: on a tight system the flow-on/flow-off ratio identifies the source as the load, while a rise WITHOUT flow is the leak-or-outgassing signature. What operating pressure a machine can afford is the beam-survival calculation's answer (the vacuum calculator's orbit mode), not MIT's 2e-5.

Cited in: The Vacuum Budget of a Cyclotron

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

Editorial note, tabletop extrapolation: A real failure mode for hairpin/spiral filaments in a strong main field. DC removes the alternating force entirely (at the cost of a static deflection), so the practical choice is high-frequency AC or DC depending on filament geometry - mains-frequency AC is the option to avoid; filament life is a chronic tabletop complaint either way.

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

Editorial note, tabletop extrapolation: The reference machine's MFC should be sized and calibrated around the table's ~0.2 sccm scale, and the arc supply must tolerate a several-kV open-circuit ignition transient before folding back to run voltage - the table's ignition/run split is the reason.

Cited in: The Vacuum Budget of a Cyclotron

Copper is suited for low-temperature operation (600 C) and for cooled ion source parts. ... 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

Editorial note, tabletop extrapolation: The trap in a source chimney is any hot joint touching stainless: the source's warning is that stainless alloys with BOTH tantalum and molybdenum above 900 C, so an intermediate piece helps only if the stainless contact itself stays below the reaction range - move the joint to a demonstrably cooler region or add thermal length. And check pairs, not just single-metal limits: graphite on hot tantalum can form carbides.

Macor or glass ceramic can be easily machined, but is very brittle. It has good vacuum behavior and can be used up to about 1000 C. ... Boron nitride is an excellent material for most applications for temperatures up to 1200 C. It can be used up to 1500 C but starts to decompose and releases large quantities of nitrogen. 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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: 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.

For the cylindrically symmetric case the maximum current can be estimated from References 11 and 12 and 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

Editorial note, tabletop extrapolation: For the puller gap in a next machine, carry over the shape of the rule - aperture dimension about half the extraction gap, beam parallelism tuned by matching plasma density - but the cited numbers are for round apertures: model the actual chimney slit electrostatically or by simulation rather than substituting the slit half-width, and expect to adjust both arc density and geometry.

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

Editorial note, tabletop extrapolation: The reference machine's hydrogen filament source lives or dies on filament temperature stability, so a finely adjustable constant-current supply is worth more than raw power. Area, work function and surface condition set the baseline the temperature knob multiplies - and space-charge-limited extraction caps what raw emission increases can deliver.

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: For a next machine, a fatter filament run cooler at ~0.1-1 A/cm^2 buys far more run time - but the tables are evaporation-limited upper estimates: in a real arc source, ion bombardment, sputtering and contamination can dominate, so measure actual filament life rather than banking on the table.

Gas efficiency: >50% for hydrogen and higher for other gases.

Wolf (ed.), Handbook of Ion Sources (1995) — p. 57, 69, 110

Editorial note, tabletop extrapolation: At 0.2 sccm feed and 50% efficiency only ~0.1 sccm leaves the chimney as neutrals - but the extracted ions end their lives in the same vacuum envelope (implanted, neutralized, desorbed later), so higher gas efficiency shifts where and when the load appears more than it deletes it. It still pays: neutral leakage at the source is continuous and concentrated in the beam region, so better confinement is worth real pumping speed there even though total throughput is conserved.

Cited in: The Vacuum Budget of a Cyclotron

The arc current is 1 to 3 A and the arc voltage just 40 to 70 V. A quite massive cathode rod, usually 2 mm in diameter and made of tantalum or tungsten, is heated with about 130 A and a few volts to the right temperature. ... The erosion of the filament is not uniform, but stronger at the positive end due to electron movement and higher plasma density. Changing the polarity of the filament after some time of operation improves cathode lifetime. Heating by ac has the same effect but increases plasma instabilities and the energy spread of the extracted ions. ... The lifetime of the source is given by the lifetime of the filament, which is between 10 and 100 h

Wolf (ed.), Handbook of Ion Sources (1995) — p. 73

Editorial note, tabletop extrapolation: For a next machine: a thick rod cathode instead of thin wire is the cheap lifetime upgrade, plus an arc-hours log. Polarity reversal on a ~130 A heater that may float at source potential is not a toggle-switch job - reverse only de-energized and discharged, through buswork or contactors rated for the heater current and the source-to-ground voltage.

The extraction slit is usually about 2 mm wide and about 40 mm long. Larger slits are possible, such as 90 mm, but there are some disadvantages because the current density is not uniform along the long slit due to the bigger voltage drop along the cathode. By careful design of the anode and the magnetic field, however, it was possible to overcome this problem. ... The extraction slit is usually 40 x 2 mm but designs up to 100 x 5 mm have been realized.

Wolf (ed.), Handbook of Ion Sources (1995) — p. 74, 76

Editorial note, tabletop extrapolation: For a cyclotron chimney, the ~2 mm slit width is the historical arc-source value to start from; the slit's length and total area still matter for gas load, arc stability and beam interception, so optimise chimney length and aperture for the actual puller and dee geometry against measured beam. [Note revised 2026-08-23: earlier note said only the few millimetres facing the dee gap matter.]

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

Editorial note, tabletop extrapolation: The reference machine's center field clears the handbook's 0.1 T minimum, which makes an internal PIG a candidate - trading the fragile filament for a self-heated cathode running a sub-kV, multi-ampere arc. Suitability is more than field magnitude: geometry, cathode cooling at multi-ampere currents (dg-416) and pumping all vote; the regime table is the starting point, not the qualification.

The ion current to the anode has about the same value as to the cathodes, which means that the ion current density at the cathodes is five to ten times the density at the anode surface, and, consequently, the extracted current densities show the same relation. 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

Editorial note, tabletop extrapolation: With a ~1 mm^2 chimney slit, a 1-A arc offers ~0.1-1 mA of ideal aperture current - orders of magnitude above the reference machine's nA accelerated beams. That margin lives at the slit: capture, centering and transmission still take their share, so treat it as headroom, not proof the source can never be the bottleneck.

The arc power for cold cathode operation is limited to about 1 kW per cathode, because of the start of thermal electron emission, and depends on the cathode material and the ion source design. ... Titanium has been selected as the best compromise. If the cathodes are allowed to run hot, tantalum has been shown to be a good choice. ... The cold and hot cathodes are worn out when the erosion crater's depth reaches around the anode bore radius. The discharge becomes unstable under these conditions.

Wolf (ed.), Handbook of Ion Sources (1995) — p. 84-85

Editorial note, tabletop extrapolation: Gives a concrete inspection criterion: measure the cathode pit depth against the ANODE BORE radius (about half the bore diameter) 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

Editorial note, tabletop extrapolation: A next machine's source can hide a small filament behind a Ta-class block cathode, out of the hydrogen plasma - the filament stops being the consumable, and what erodes instead is the thick block face under PLASMA-ion sputtering (slow, by mass). The burn-down behavior, block material and electrical ratings are design choices to verify, not inherited guarantees.

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

Editorial note, tabletop extrapolation: A documented operating envelope for a simple hot-filament source at the reference machine's scale - a starting point whose actual values shift with geometry and field: commission against it, not to it.

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

Editorial note, tabletop extrapolation: Transfer the method, not the number: admit gas gradually while watching pressure and arc behavior, and find the reference machine's own setpoint with its calibrated gauge and pumping stack (its parker metering valve fills the needle-valve role). The 1e-4 mm rise is the source machine's figure - gauge species, gauge location and pumping speed make it non-portable.

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

Editorial note, tabletop extrapolation: Filament sizing starts from emission demand and temperature, with Wouters' 0.025-in / 25 A as the documented anchor rather than a universal spec. The modern equivalent of the battery is a well-filtered DC filament supply - raw rectified current drives magnetically induced filament vibration in the cyclotron field.

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

Editorial note, tabletop extrapolation: A worthwhile arrangement for a next machine: the chimney gives a defined source position and shields the filament from the dee field - the quote's stated purpose. Comparisons against a bare filament (loading, output) are the builder's to measure, not the source's claim.

3.55 MHz 1700 Vpp (26 W) H2 1.5 10-5 torr Total 4.0 10-5 torr -100 V filament ... 6.04 MHz 1700V (26 W) H2 2.2 10-6 torr Total 1.3 10-5 torr -6 V filament ... Higher frequency, lower H2 and base pressure, lower filament voltage

Yuly et al., Modifications on the Houghton College Cyclotron (2010) — p. 17-18

Editorial note, tabletop extrapolation: For the reference machine's current-hunting: before adding RF watts, cut chamber pressure and re-optimize filament bias - Houghton's gain cost zero watts - but change one variable at a time so you learn which knob actually paid.

The grid was made of .0114 cm thick tungsten wire shaped into circles chosen to be one fifth of the chamber in size. The chamber diameter was 21 cm so the grid diameter was 4.2 cm. ... fusion efficiency is enhanced by transparency of at least 92 percent (Donovan). The inner grid is 99.18 percent transparent with three loops as calculated by comparing the cross section of the total grid wire used to the surface area of the grid sphere.

Kovalchick, Deuterium Fusion Using Inertial Electrostatic Confinement (2012) — p. 19-20

Editorial note, tabletop extrapolation: The transparency bookkeeping (wire cross-section vs aperture area) is the calculation method to transfer - but a circulating cyclotron beam hits a grid or slit repeatedly and directionally, so compute projected obstruction along the actual trajectory over many turns, not the spherical-area figure.

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

Editorial note, tabletop extrapolation: When metering beam current near a hot cathode, part of the reading can be electrons. High work function helps only against thermionic emission; a Faraday cup's secondary-electron escape needs its own fix - a suppressor electrode or magnetic suppression, validated on the actual geometry.

Assuming that sagging occurs at ~1,500 K and equating the black body radiation rate to the input power ... ~76 cm2 for a 10-cm grid made of 0.08 cm diameter with 5 latitudes and 12 longitudes ... the emissivity of the material (~0.15 for stainless) ... This gives 9.5 mA of ion current at 200 kV, whereas the power supply can produce 75 mA at 200 kV.

Miley & Murali, Inertial Electrostatic Confinement (IEC) Fusion: Fundamentals and Applications (2014) — p. 145

Editorial note, tabletop extrapolation: The same balance sizes any wire electrode, probe or beam stop in the reference machine's chamber - with its assumptions on the table: uniform temperature and radiation-only cooling. Compute A*eps*sigma*(T^4 - T_amb^4) against actual intercepted beam power, and check local hot spots and conduction separately.

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. ... It is relatively cheap, has a high melting point (2,800 K), a low sputter yield, and is easy to manufacture by spot welding. To test this material, the 10-cm grid was run at various voltages in the range of 30-130 kV and with the current range of 30-180 mA for over 1,000 h

Miley & Murali, Inertial Electrostatic Confinement (IEC) Fusion: Fundamentals and Applications (2014) — p. 145-146

Editorial note, tabletop extrapolation: W-Re thermocouple wire is commercially available in small quantities - a strong candidate for any sputtered electrode in the reference machine's source, with W-class durability and far better workability than pure tungsten; fabrication, activation and sputter behavior remain application-specific, so qualify it in place.

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

Editorial note, tabletop extrapolation: When scaling chamber geometry or pressure for the p-B11 test cell, pd similarity is the right first knob - it organizes breakdown - but sustained-glow behavior also moves with gas, electrode material and area, and current density, so expect to re-tune rather than translate. Either way, sputter damage concentrates at the cathode sheath edge.

Cited in: The Vacuum Budget of a Cyclotron

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

Editorial note, tabletop extrapolation: Explains the striking-vs-running asymmetry a source can show: ignition up on the breakdown branch, then sustaining down on the glow branch at much lower voltage - the Penning table's several-kV-ignite / sub-kV-run split (dg-372) is this physics - and why current-limited (ballasted) supplies are needed to stop glow-to-arc runaway. The actual voltages move with gas, pd and geometry.

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

Editorial note, tabletop extrapolation: For any glow-driven ion supply in the p-B11 experiment, pressure is the ignition control: strike at higher pressure, then throttle the MFC to the running point - a device-specific procedure to commission, with the actual striking curve measured (Paschen-type behavior depends on pd, gas, geometry and surfaces, not the ion mfp alone).

Cited in: The Vacuum Budget of a Cyclotron

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

Editorial note, tabletop extrapolation: If building an IEC-style p-B11 test stand, grid-opening geometry is a real trade study - larger openings mean fewer grid hits and longer grid life, finer mesh means better field definition - informed by the cited 3x pd result, with the Star-mode operating claims taken from the re-read source rather than summary memory.

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

Editorial note, tabletop extrapolation: Matches the reference machine's hydrogen filament philosophy: a modest bias on an emitter sustains ionization where a self-sustained discharge dies. Wire the POTENTIAL TOPOLOGY deliberately - what accelerates the electrons is the difference between emitter and the collecting electrode, so state the reference (the source does not say 'to ground') and set the electron energy against the ionization physics, not against the chamber wall by default.

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

Editorial note, tabletop extrapolation: Same rule protects the reference machine's Faraday cup stalk and source supports: unshielded biased metal collects spurious current and sputters - and bare insulation over it charges up and distorts fields, so shield with guarded conductor, then insulate behind it.

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

Editorial note, tabletop extrapolation: Tuning-order advice, not physics: hold filament bias fixed during initial tuning and spend the effort on dee voltage and pressure - but scan bias if ionization or emission looks current-limiting, since other geometries and regimes do respond to it.

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

Editorial note, tabletop extrapolation: Map current vs pressure on your own machine, recording resonance width and source stability along with current - expect an apparatus-dependent optimum and a non-monotonic curve, and use Houghton's window as calibration context, not a target.

Cited in: The Vacuum Budget of a Cyclotron

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

Editorial note, tabletop extrapolation: 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.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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. ... [higher pressures] reduce the mean free path of the ions, and cause the resonance peaks to become broad and shift. The largest beam current recorded, shown in Figure 6, was about 0.1 uA

Yuly, The Houghton College Cyclotron: a Tool for Educating Undergraduates — Cyclotrons 2013, WE1PB01 (2013) — p. 5

Editorial note, tabletop extrapolation: Directly sets the gas-handling operating window for the reference machine and explains a common 'no beam' failure at too-good vacuum - throttle up before concluding the source is dead.

Cited in: The Vacuum Budget of a Cyclotron

Three holes are machined in the cathode body; two are used to support the anode and the third is used as a gas inlet. Alumina tubes are inserted into the two holes used for anode support, and a stainless steel tube is inserted into the gas inlet hole. Ceramic epoxy (Ceramabond) is used to mate the alumina and stainless tubes to the back of the cathode body. Stainless steel wire with 0.5 mm diameter was spot welded to the anode, and the wires were threaded through the alumina tubes in the cathode body. ... Essentially 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

Editorial note, tabletop extrapolation: An amateur-grade insulated support for a modest-voltage, low-current internal electrode - an ion-source anode and the like. Not unchanged for filament leads (0.5 mm stainless is a poor conductor for filament current) or for chamber-wall HV or current feedthroughs: use current-rated conductors and qualified vacuum/HV feedthroughs there, and test the ceramic-epoxy joint for bakeout, leakage and voltage standoff before trusting it. [Note revised 2026-08-23: earlier note extended the scheme to filament leads.]

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

Editorial note, tabletop extrapolation: A directly copyable permanent-magnet source recipe at hobby machining tolerances - copy from the paper's drawings, and treat the output as mixed hydrogen species (H+, H2+, H3+) until a bend or velocity filter resolves it (dg-001).

The ion source anode is powered by a 6 kV 200 mA Hipotronics dc power supply and a 100 kOhm, 100 W resistor is connected in-line with the power supply to current limit the discharge. ... 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

Editorial note, tabletop extrapolation: Directly applicable to the reference machine's DISCHARGE/ARC supply metering (the ballast correction belongs to the electrode circuit, not the filament heater): logging supply volts instead of electrode volts corrupts any operating-point map. Check ballast power, working-voltage and transient ratings for the actual supply.

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

Editorial note, tabletop extrapolation: Worth testing on the reference machine: in a small chamber the injection-vs-backfill distinction may shrink - but the source-to-chamber pressure ratio is set by aperture conductance, flow and pump placement, so measure it (or model the conductances) rather than assuming 2x transfers.

Cited in: The Vacuum Budget of a Cyclotron

the plasma discharge ignites easily at 1 kV or less for all cases and produces a continuous positively charged ion beam. ... For the 1 mTorr case, at 580 V, the discharge current and target current are 0.3 mA and 20.8 uA, respectively. As the ion source voltage increases to 5.4 kV, the discharge current and target current increase to 6.0 and 1.5 mA, respectively.

Rovey, Ruzic & Houlahan, Simple Penning Ion Source for Laboratory Research and Development Applications (2007) — p. 2-3

Editorial note, tabletop extrapolation: Tens of microamps of positive hydrogen ions at under 1 kV anode drive is ample raw current next to the reference machine's nA-scale accelerated beams - but it is aggregate H+/H2+/H3+ at the target: species fraction and RF capture are separate measurements before any of it is credited as proton beam.

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

Editorial note, tabletop extrapolation: A test-stand collection ratio, not a cyclotron benchmark: the reference machine's beam-to-arc ratio folds RF capture, centering and transmission on top of extraction, so a much lower ratio there does not by itself convict the extraction geometry. Use 25% as the source-side sanity scale only.

The electrode closest to the source was the suppressor and was located 2.5 cm from the cathode faceplate. A target electrode was placed 7.6 cm from the suppressor. During high-voltage operation, the suppressor and target were biased negative with respect to the ion source cathode (i.e., ground). ... 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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: Benchmarks source maintenance for a next machine: one documented internal cold-cathode PIG ran 40+ hours between servicings. Filament sources trade shorter cathode life for simpler supplies (dg-704's census practice) - lifetimes vary with design and duty on both sides of that trade.

The boron-nitride insulator, which is a tight fit, separates the high vacuum region behind the insulator (on the order of 10-5 Torr), from the lower vacuum region in the chimney and between the anodes and cathodes. ... The best vacuum achieved in the ion source test stand (with source gas supply turned off) was 8 x 10-7 Torr. 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

Editorial note, tabletop extrapolation: A single calibration point (about 1.6e-5 Torr per cc/min at that stand's pumping speed), not a slope: characterize the reference machine's own MFC-vs-chamber-pressure curve with its calibrated flow and gauges before reading deviations as leaks or conductance faults.

Cited in: The Vacuum Budget of a Cyclotron

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

Editorial note, tabletop extrapolation: Relaxes the machining tolerance on a next machine's source gap and anchors the supply class: a ~3 kV current-limited unit ran this source. Strike voltage moves with pressure, gas, field and surface condition, so provide voltage headroom (or an ignition boost) rather than assuming the same number transfers.

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

Editorial note, tabletop extrapolation: The source's warning stands as written: they melted copper running without cooling. A reference-machine-class source at much lower arc power may not need water - but that is a claim to establish by thermal estimate and a supervised first run with temperature monitoring, not by assumption. The sanded-cathode arc-striking preparation transfers directly.

Their cathode was a U-shaped tantalum filament, heated with about 400 amps ... the arc current (the total current measured between the anode and cathode of the ion source) was between 2 and 6 amps. As seen in figure 1.2 a 0.2 in2 (129 mm2) area vertical slit provided the path for ions to exit the source. With this source Livingston and Jones were 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

Editorial note, tabletop extrapolation: Brackets the design space above the reference machine's filament source as an existence proof, not a scaling law: determine the arc a nA beam actually needs by measuring extracted and captured current against arc current on the real geometry.

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

Editorial note, tabletop extrapolation: Suggests slit width is a powerful knob worth sweeping on a next machine: expect more current and more emittance from a wider slit, and stop widening when the machine acceptance is filled - but the 4.4x/1.7x ratios are that source's numbers; do your own aperture sweep and acceptance analysis before extrapolating.

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

Editorial note, tabletop extrapolation: Two measured holdoff points from one clean DC stand - anchors for a dee-tip/puller voltage budget, not a kV-per-mm allowable: vacuum holdoff is nonlinear in gap and hostage to finish, conditioning, and RF-vs-DC differences. Do what the source did: measure the actual geometry on a test stand rather than applying a scaling law.

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 ... The size of the hole in the chimney is 0.047 (1.19 mm) with a sixty degree chamfer. At 50 mA of arc current, the normalized luminosity of the beam which made it to the wire probe was 129 A/(mm2-sr), about half of that for the slit chimney with the same arc current (264 A/(mm2-sr)).

Forringer, Phase Space Characterization of an Internal Ion Source for Cyclotrons — MSU dissertation (2004) — p. 73-76, 91-107

Editorial note, tabletop extrapolation: Decides a next machine's chimney aperture style within the tested regime: cut a tall narrow slit rather than drilling a hole if beam brightness and predictable optics matter - and re-verify on the actual source, since the ranking comes from these apertures and operating points.

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

Editorial note, tabletop extrapolation: Cranking arc power buys current with diminishing returns, and in this scan it did not spoil measured emittance. Do not read that as space charge being negligible in general: generalized perveance rises steeply at low velocity, so keep space charge in extraction and first-turn models until a sensitivity check shows it is negligible at your energy and current.

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

Editorial note, tabletop extrapolation: Directly actionable on the reference machine's MFC: starving the source of gas silently changes beam species, so locate the actual arc-mode transition for the machine and keep the setpoint above it - and remember 'no H2+ detected' is not 'pure protons': H3+ and below-detection species need their own check.

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

Editorial note, tabletop extrapolation: A starting calibration for any first-turn simulation of a next machine's central region: begin near 35,000 K / 4.5 eV, then sweep the initial temperature and meniscus shape and validate against measured emittance or beam profiles - the value is a fitted effective parameter, not a universal plasma property.

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

Editorial note, tabletop extrapolation: The 3-degree taper spread over 9 turns gives the fine, repeatable hydrogen admission an ion source needs. Log turns-open as the VALVE-POSITION setpoint - repeatable flow additionally needs regulated upstream pressure and a calibration of flow (or chamber pressure) against turns under operating conditions; the vernier repeats position, not sccm.

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

Editorial note, tabletop extrapolation: Practical form for the gas panel: give the metering valve an isolation valve between it and the bottle - or specify a metering valve designed for shut-off duty, the HR-class option the sheet names. Forcing a plain tapered stem closed to seal ruins the calibrated taper and still leaks 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

Editorial note, tabletop extrapolation: Documented arc conditions for a hot-cathode chimney source. Scaling to a much smaller chimney shifts gas flow and arc balance with geometry and pumping, so treat 0.5-1.5 A / 100-300 V / a few cc/min as the class of numbers to expect and tune on the machine. The robust transfer is the material lesson: graphite chimney and 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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: A control philosophy readily implemented with two small feedback supplies; a constant-current arc removes one major drift term from shot-to-shot beam current - stable gas flow and extraction conditions are still needed for real reproducibility.

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

Editorial note, tabletop extrapolation: Hands the mill the numbers for the chamber's lids and ports - per ring size and per geometry: these are STATIC AXIAL FACE seals; a port using a different cross-section or seal configuration gets its own chart row or chart. Note the vacuum groove width column is narrower than liquid service.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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

Editorial note, tabletop extrapolation: Specify and check the chamber lid seat to 16 RMS (fly-cut or turned); a rough or cross-scratched sealing face can contribute to leakage and belongs on the leak-diagnosis checklist - as one suspect among several, not a signature of any particular pressure plateau.

Cited in: Cyclotron Vacuum Chamber Design and Sealing · The Vacuum Budget of a Cyclotron

For Internal Pressure (outward pressure direction) dimension the groove by its outside diameter (HO) and width: (HO) = Mean O.D. of O-ring ... Tolerance = Minus 1% of Mean O.D., but not more than -.060 ... For External Pressure (inward pressure direction) dimension the groove by its inside diameter (Hi) and width: (H)i = Mean I.D. of O-ring ... Tolerance = Plus 1% of Mean I.D., but not more than +.060

Parker Hannifin, O-Ring Handbook — Design Chart 4-3: O-Ring Face Seal Glands — p. 1

Editorial note, tabletop extrapolation: 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.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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

Editorial note, tabletop extrapolation: For a ~30-50 liter tabletop chamber the rule asks for 30-50 l/s DELIVERED at the chamber; the SI100's 100+ l/s class inlet rating leaves margin that the plumbing then spends - baffle, elbows and port conductance cut delivered speed (1/S_eff = 1/S + 1/C, dg-906) - so compute the delivered figure before crediting the margin. On a gas-fed machine the source load dominates either way.

Cited in: The Vacuum Budget of a Cyclotron

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

Editorial note, tabletop extrapolation: Worth adopting on a next machine's main lid: a guard-vacuum groove turns the worst leak hunt into a valve twist for TESTING; riding out a leak in service additionally needs the interspace continuously pumped with adequate speed, and only helps for leaks through the outer seal.

Cited in: Cyclotron Vacuum Chamber Design and Sealing · The Vacuum Budget of a Cyclotron

One butyl compound has been tested in face-type O-ring seals, using grooves that provide 15%, 30%, and 50% squeeze. It will be seen from the results plotted in Figure I that increasing the squeeze reduced the leak rate dramatically... at 50% squeeze the beneficial effect of the grease was not detectable. ... It is therefore recommended that dovetail or face type O-ring grooves be used whenever possible for static vacuum seals, employing a suitable vacuum grease as a sealing lubricant and surface coating in addition to a heavy squeeze on the O-ring.

Parker Hannifin, O-Ring Vacuum Sealing, Catalog 5705B (1998) — p. 3-4

Editorial note, tabletop extrapolation: Cut a next machine's grooves toward the heavy end per the source's recommendation, but set the nominal from the ring manufacturer's static-vacuum gland tables under worst-case tolerances - 50% was a test point, not a design target; gland fill, compression set and assembly damage cap real designs. Grease is a crutch for light squeeze.

Cited in: Cyclotron Vacuum Chamber Design and Sealing · The Vacuum Budget of a Cyclotron

L = .7FDPQ(1-S)2 where: L = Approximate leak rate of the seal, std. cc/sec. F = Permeability rate of the gas through the elastomer at the anticipated operating temperature. Std cc cm/cm2 sec bar ... D = Inside diameter of the O-ring, inches. P = Pressure differential across the seal, lb/in2. Q = Factor depending on the percent squeeze and whether the O-ring is lubricated or dry. (From Figure II) S = Percent squeeze on the O-ring cross section expressed as a decimal. ... This formula provides only a rough order of magnitude approximation ... For convenience, the formula contains mixed units. ... The .7 factor provides dimensional homogeneity.

Parker Hannifin, O-Ring Vacuum Sealing, Catalog 5705B (1998) — p. 5

Editorial note, tabletop extrapolation: Computes the permeation floor of the 10-inch Viton lid seal - then convert to pressure via P = Q_gas/S_eff with the actual effective pumping speed, and remember outgassing and real leaks usually dominate above the permeation floor.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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

Editorial note, tabletop extrapolation: 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.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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

Editorial note, tabletop extrapolation: At exactly the reference machine's operating pressure, nitrile's high weight loss marks it a potential outgassing concern near feedthrough insulators, optics and RF surfaces - where the lost mass actually lands was not measured, so treat the ranking as a screening result and prefer the low-loss compounds (Viton's 0.1%-class loss is the cheap insurance) rather than claiming proven film deposition.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

Butyl 6.5 @ 77F ... Fluorocarbon 12.7 @ 77F ... Silicone 238.0 @ 77F

Parker Hannifin, O-Ring Vacuum Sealing, Catalog 5705B (1998) — p. 7

Editorial note, tabletop extrapolation: Viton's placement plus its other properties is why it is the default; silicone's high permeability matters most when helium leak checking (He walks through silicone and fluorosilicone seals, confusing the sniffer) and in permeation-limited systems - compute the actual permeation gas load for the seal geometry before ruling a compound in or out, since at 1e-6 Torr with decent pumping the load is often ignorable either way.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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

Editorial note, tabletop extrapolation: For his ~8 mm active-diameter PIPS, that is 12-16 mm standoff; closer spacing degrades resolution through wide-angle entrance-window losses.

Cited in: Experiments by Energy Band

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

Editorial note, tabletop extrapolation: Size and maintain the backing pump so the foreline stays well under the pump's critical forepressure during beam-gas loads - for the SI100, take the manufacturer's figure; the quoted 0.2-0.6 Torr is the generic design range. A tired rotary pump silently pushes the foreline over the cliff and dumps oil vapor into the chamber.

Cited in: The Vacuum Budget of a Cyclotron

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

Editorial note, tabletop extrapolation: 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.

Cited in: The Vacuum Budget of a Cyclotron

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

Editorial note, tabletop extrapolation: The 2.7 kg/cm figure sizes the lid bolting: a 10-inch-circumference seal (25.4 cm) needs about 69 kg of clamping just for the ring - a 10-inch-diameter ring (79.8 cm around) needs about 216 kg - before atmospheric load helps. Size bolts and flange stiffness from the complete load and allowable-stress calculation.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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

Editorial note, tabletop extrapolation: Argues for baking the assembled system under vacuum where the components allow it. An ex-situ pre-bake in a small vacuum oven helps only to the extent air exposure before assembly is minimized, and the payoff in chamber pressure depends on whether the rings dominate the gas load - budget the gas loads before promising an order of magnitude.

Cited in: Cyclotron Vacuum Chamber Design and Sealing · The Vacuum Budget of a Cyclotron

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

Editorial note, tabletop extrapolation: Counters the amateur habit of greasing everything: on a clean, undamaged seat with proper squeeze, a dry Viton ring seals without grease's gas burden. A scratched flange is a repair item first; grease is the temporary expedient, not the standard practice.

Cited in: Cyclotron Vacuum Chamber Design and Sealing · The Vacuum Budget of a Cyclotron

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

Editorial note, tabletop extrapolation: For the reference machine: valve over to the SI100 around 100 mTorr rather than letting the rotary pump grind into the 1e-2 Torr range - after checking the SI100's own maximum inlet/crossover and foreline specs, which are the binding numbers for the diffusion-pump side.

Cited in: The Vacuum Budget of a Cyclotron

the mechanical pump should be disconnected and connected to a blank flange containing only a thermocouple gauge. ... If the pump is operating properly, sections of the foreline and roughing line can be pumped sequentially and systematically until the leaky section is isolated. ... External leak checking with helium should begin at the top of the chamber; only a small helium flow rate is necessary. ... Alcohol freezes in a small leak and allows adjacent areas to be checked without confusion. The alcohol can be removed with a heat gun. ... Welds and seals are the most common leak sites

O'Hanlon, A User's Guide to Vacuum Technology, 3rd ed. (2003) — p. 467-470

Editorial note, tabletop extrapolation: Helium rises and migrates: working top-down with small flow keeps the migrated-helium background from swamping localization on a chamber with many ports (the source suggests nitrogen-flushed plastic wrap where sites crowd together). Alcohol near energized equipment is a flammability point - sensible precautions.

A molecular leak causes a linear increase in pressure with time. Outgassing causes the pressure to rise to a steady-state value that is determined by the vapor pressures of the desorbing species.

O'Hanlon, A User's Guide to Vacuum Technology, 3rd ed. (2003) — p. 468-469

Editorial note, tabletop extrapolation: First diagnostic whenever a next machine won't reach base pressure - existing gauge plus stopwatch. A constant slope points toward the helium bottle, a rolling-over curve toward bakeout - as the leading hypothesis, not a verdict: virtual leaks also roll over, water outgassing can mimic a leak on an RGA, and a real leak departs from linearity once the pressure rises far enough.

Cited in: The Vacuum Budget of a Cyclotron

This pressure rise is due to helium permeation. The permeation time is about 20 min for a typical Viton O-ring. ... First, do not attempt to leak check the system during baking. Second, helium background from a loaded O-ring will not decrease until it has been pumped from the gaskets. A coffee break may be required before proceeding.

O'Hanlon, A User's Guide to Vacuum Technology, 3rd ed. (2003) — p. 469-470

Editorial note, tabletop extrapolation: On an all-Viton chamber, spray briefly and wait: a slowly rising, broad He signal minutes after spraying is CONSISTENT WITH gasket permeation rather than a leak at the last joint - confirm by letting the baseline recover and re-testing for a prompt, reproducible local response before moving on.

Cited in: Cyclotron Vacuum Chamber Design and Sealing · The Vacuum Budget of a Cyclotron

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

Editorial note, tabletop extrapolation: A used RGA head is arguably the single best diagnostic upgrade for a next machine - one spectrum plus a short rate-of-rise watch 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

Editorial note, tabletop extrapolation: 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.

Cited in: The Vacuum Budget of a Cyclotron

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: Explains why pump-down history and surface cleanliness dominate at high vacuum: the wall inventory dwarfs the volume inventory for ordinary chamber geometries - by a factor you compute from the actual area, volume and outgassing rate, which is also what sets whether the walls take hours or days to give up their load.

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

Editorial note, tabletop extrapolation: 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

Editorial note, tabletop extrapolation: Matches the reference machine's observed 1e-6-range vacuum with Viton seals - typical of all-elastomer systems, where permeation and outgassing usually hold operation near the recommended regime, though well-designed elastomer systems can run lower. A CF port or two on a next machine (gauge, RGA) buys bake and UHV headroom cheaply.

Cited in: Cyclotron Glossary · Cyclotron Vacuum Chamber Design and Sealing · The Vacuum Budget of a Cyclotron

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

Editorial note, tabletop extrapolation: When farming out welds or buying used hardware, write the acceptance spec as a number DERIVED from the machine's gas-load budget: Q_leak,max = S_eff x (allowable pressure contribution), split between total and single-leak allocations, with tracer gas, test pressure and calibrated detection limit stated - detector sensitivity is what the instrument can see, never itself the acceptance criterion.

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

Editorial note, tabletop extrapolation: The ~200x one-hour penalty (dropping to ~10x by four hours) for rusty mild steel is the argument for keeping exposed in-chamber pole faces from corroding at all - and for qualifying any specific remedy (plating, vacuum-rated coating, stainless cladding) on its own outgassing, adhesion and magnetic-gap costs rather than prescribing one.

Cited in: The Vacuum Budget of a Cyclotron

Mechanical Cleaning; Degreasing or Solvent Cleaning; Detergent Cleaning; Chemical Etch; Electrolytic Polishing; High Pressure Spray; Bake-out ... Remove all tape, ink, & other residues with Acetone & a clean cotton rag ... DI rinse (2 x 10^6 Ohm min. resist. @ 65oC) Air dry or dry with filtered compressed nitrogen ... Protect with lint free paper, foil, or plastic bags ... Acid pickle (50% by vol. HNO3 ... @ 25oC) 10 minutes if removing mill scale, 30 seconds to remove trace alkaline ... A 200oC bakeout is still required after glow discharge cleaning.

Bertolini, Accelerator Vacuum and Mechanical Engineering — USPAS course, UCRL-MI-201847 (2004) — p. 497-513

Editorial note, tabletop extrapolation: 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. The acid pickle stays professional - HF work needs formal controls and alloy-specific procedure, and is not part of the amateur-safe subset.

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

Editorial note, tabletop extrapolation: 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.

Cited in: Cyclotron Vacuum Chamber Design and Sealing · The Vacuum Budget of a Cyclotron

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

Editorial note, tabletop extrapolation: To push an elastomer-sealed system's floor lower on a next machine, a double O-ring lid groove with a guard vacuum from the existing roughing pump attacks the permeation term specifically - the dominant elastomer floor once outgassing is conditioned down - for the cost of one groove and a hose barb. The guard reduces pressure-driven permeation through the inner seal (DARHT's numbers are that installation's); the inner ring's own outgassing remains, so the floor drops rather than disappears.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

An acceptable vacuum would allow for a mean free path an order of magnitude larger than the expected flight distance. For protons accelerated by a 2.7 T magnetic field and a voltage difference of 1000 V between the electrodes, the expected flight distance is approximately 300 meters.

Dewan, Design and Construction of a Cyclotron Capable of Accelerating Protons to 2 MeV — MIT thesis (2007) — p. 9-11

Editorial note, tabletop extrapolation: The quantitative vacuum spec for a next machine: turns = final energy / energy-per-turn, and total path is turns times the average orbit circumference (about two-thirds of the final one for r proportional to sqrt(E)); halving dee voltage doubles the path and tightens the pressure requirement proportionally. Evaluate lambda with sigma(E) from ORNL-6086 along the orbit (the vacuum calculator's orbit mode does this); a 150 keV, 1 kV-per-dee proton machine needs ~1e-5 torr for 10% loss, not 1e-3.

Cited in: Beam Quality: What It Is and What Degrades It · The Vacuum Budget of a Cyclotron

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

Editorial note, tabletop extrapolation: On any welded chamber or fitting for a next machine the question to ask of every joint is: is there a pocket sealed on both sides, or a crevice open to vacuum? Vent it, or weld it through. Argonne's atmosphere-side seams are one way to satisfy that, not the rule itself.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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

Editorial note, tabletop extrapolation: When a next machine sparks, a loupe inspection for starbursts and craters gives the builder candidate locations for the field problem instead of guessing from outside the chamber - corroborate with particle, geometry and field checks before machining anything.

if there are contaminant particles, then they, and not the substrate material, determine the breakdown voltage. ... The Cu and Au films were about 1000 A thick; the oxide films were hundreds of angstroms thick. ... there seems to be no significant difference in breakdown voltages on niobium and copper cathodes.

Werner, Probing and Modeling Voltage Breakdown in Vacuum — Cornell dissertation (2004) — p. 84

Editorial note, tabletop extrapolation: The builder can reasonably keep aluminum dees and spend the effort on cleaning and conditioning instead of exotic electrodes - with the caveat that the tests covered Nb, Cu, Au and their oxides, not aluminum's native oxide; let the machine's own conditioning behavior confirm it.

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

Editorial note, tabletop extrapolation: Motivates a controlled experiment on the reference machine, not a guaranteed fix: try a gentle bake of the dee assembly before HV runs and measure field-emission onset and holdoff after cooldown - the cited data compare performance AT temperature and don't establish that the improvement survives cooling, or the mechanism.

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

Editorial note, tabletop extrapolation: Historically grounded milestones, and the regime the reference machine operates in. What pressure a given machine NEEDS is the charge-exchange survival calculation (dg-460; the vacuum calculator's orbit mode) - at 1e-4 torr a proton spiral loses heavily, which is why this collection's operating rules sit in 1e-5-class territory.

Cited in: The Vacuum Budget of a Cyclotron

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

Editorial note, tabletop extrapolation: Degrease everything on a next machine that sees vacuum - machining oil, fingerprints, rubber residues - with a solvent chosen per material (elastomers, coatings and trapped volumes need their own compatible process); CCl4 itself is excluded on toxicity grounds.

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

Editorial note, tabletop extrapolation: Pumping a gas-fed cyclotron is conductance-limited, so place the pump under the chamber with the largest, straightest duct possible - the term you control at layout time. What pressure results is the whole budget's answer: throughput, pump speed and conductance together (the vacuum calculator).

Steel supporting rods allow thin top and bottom plates to minimize thickness

Baumgartner & Heuer, The Cyclotron Kids 14-Inch Accelerator (2010) — p. 6-7

Editorial note, tabletop extrapolation: Every millimeter of lid steel is a millimeter of magnet gap - but posts are not free: ferromagnetic posts in or near the gap distort or shunt the field, so place them outside the useful-field region (or use nonmagnetic posts) and verify by model or map; and do the plate-stress and buckling arithmetic for full atmospheric load before trusting a thin lid.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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 ... Turning the fusor power down or off after a few minutes of on time will have the pressure plunge to new lower levels.

Hull, The Farnsworth/Hirsch Fusor — The Bell Jar, Vol. 6 No. 3/4 (1997) — p. 5-6

Editorial note, tabletop extrapolation: The same logic applies to the reference machine's chimney and dee surfaces - but translate it as controlled RF or discharge conditioning with pressure and arc interlocks, not an open-ended beam-on bake-in: beam operation adds sputtering, beam loss, and (at higher energies) activation questions a conditioning plan should assess first.

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

Editorial note, tabletop extrapolation: The base-pressure-then-backfill discipline is exactly the reference machine's MFC workflow; at the quoted fusor numbers the operating-to-base ratio is 1,000-10,000:1, which is what keeps the feed gas dominant - but composition is earned by measurement (RGA or gas-load accounting), not by a pressure ratio alone.

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

Editorial note, tabletop extrapolation: Matches the reference machine's scale exactly: 1e-6 torr base, bled up with source hydrogen, is the working point of the documented machines in this peer group (Houghton, the Rutgers 12-inch, the reference machine - the census's compare rows carry the values). The recipe is the proven one at 15 cm scale; the pressure a machine actually needs remains the survival calculation's answer (dg-460).

Cited in: The Vacuum Budget of a Cyclotron

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

Editorial note, tabletop extrapolation: A complete documented chamber design for an 8-inch-pole machine, including the epoxied-flange trick that avoids welding. Copy from the paper - then qualify your own copy: epoxy joints and lid stiffness are workmanship-dependent, so leak-check the flanges and run the lids through the lid-deflection calculator rather than inheriting the paper's result.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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

Editorial note, tabletop extrapolation: A strong pattern for a next machine's chamber lids: the metal stop limits further squeeze after closure and makes reassembly repeatable - still check gland fill and squeeze for the actual compound (groove depth sets the squeeze; a too-shallow groove over-crushes even with a metal stop), including tolerance, swell and thermal growth.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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

Editorial note, tabletop extrapolation: Two separable methods: vent the next machine's chamber with dry nitrogen or desiccated air rather than room air (admitted water vapor drops and pumpdown shortens), and treat exhaust-side purging as pump-specific - follow the pump manual, keep any inlet trap the pump needs for vapor handling or oil backstreaming, and mind oxygen deficiency when nitrogen-venting in a small space.

Cited in: The Vacuum Budget of a Cyclotron

the ion gauge is not turned on until the tank pressure is less than 0.5 microns ... In this position the conductance from the diffusion pumps around the gate valves to the ion gauge has been estimated to be approximately the same as the conductance from the diffusion pumps to the tank proper. ... 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

Editorial note, tabletop extrapolation: Directly applicable gauge practice near a stray-field-rich H-frame magnet: place the gauge to read the pressure you care about (conductance gradients bias a badly placed gauge under gas flow), and verify the shielding by comparing readings with the field on and off.

Cited in: The Vacuum Budget of a Cyclotron

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

Editorial note, tabletop extrapolation: A cheap Penning head earns its keep as a trend and gas-flow indicator, with the ion gauge kept for absolute readings. For protection interlocks use fail-safe, manufacturer-approved instrumentation - Penning cells can ignite late and drift with contamination - and commercial heads carry their own magnet: mount and shield per the head's specification rather than borrowing the cyclotron's field.

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

Editorial note, tabletop extrapolation: Measure rate-of-rise after every re-seal as the standard leak-health metric, and state the benchmark as a gas load, not a pressure rate: the ORNL figure corresponds to Q = V*dP/dt ~ 1.2e-3 torr-L/s. A ~30 L chamber would rise at ~4e-5 torr/s only if it carried that same total load - rate-of-rise includes real leaks, virtual leaks and outgassing, so 'equally tight' means equal Q, not equal construction scaled by volume. [Note revised 2026-08-23: earlier note scaled the expectation by volume alone.]

For vacuum seals, O-rings must be comprised of elastomeric materials featuring low gas permeability, low weight loss under vacuum, and good compression set characteristics. ... With outstanding low permeability to gases, Butyl is especially effective in vacuum sealing applications. ... 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

Editorial note, tabletop extrapolation: Endorses heavier-than-usual squeeze on critical static vacuum joints when the groove is widened to take the displaced volume - within the compound's own application limits. A pre-bake ('post cure' in vendor language) to drive off volatiles before service is cheap insurance on silicone and fluorocarbon compounds.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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

Editorial note, tabletop extrapolation: On the next machine's lid, single-pass tightening leaves the first-torqued sector under-clamped - a plausible contributor to O-ring leaks that seem to move with each reassembly; the multi-pass cross-pattern with recheck is the fix either way.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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

Editorial note, tabletop extrapolation: 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.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

It is often necessary to provide some means for retaining an O-ring in a face seal groove during assembly and maintenance. An undercut or 'dovetail' groove has proven effective in many applications to keep the O-ring in place ... Design Charts II & III (see pp 7-8) provide dimensional recommendations for full and half-dovetail vacuum seal O-ring grooves. ... 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

Editorial note, tabletop extrapolation: 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.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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

Editorial note, tabletop extrapolation: A fabrication trap the builder can sidestep: demountable elastomer seals on both lids avoid weld distortion entirely on a thin flat chamber - the route the source machine retreated to after its frame warped. Where welding is preferred, controlled sequence and post-weld machining are the professional counters; for a garage build, not welding thin flat plates is the cheap answer.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

This stretch should be between 1%-5% with 2% as the ideal in most applications. A stretch greater than 5% is not recommended. The resulting stress on the O-ring will cause accelerated aging and cross section reduction.

Apple Rubber Products, Seal Design Guide — p. 11

Editorial note, tabletop extrapolation: 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.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

The maximum volume of the O-ring should never surpass the minimum volume of the gland... For a static crush seal application, it is recommended that the O-ring volume does not exceed 95% of the gland void.

Apple Rubber Products, Seal Design Guide — p. 14-16

Editorial note, tabletop extrapolation: Check fill arithmetic including worst-case ring tolerance before machining. Viton heated by RF or magnet proximity needs that free volume: elastomer linear expansion is around 1.6e-4/C, so use the volumetric coefficient (roughly three times the linear value) in the fill calculation.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

Surface finishes as rough as 64 to 128 micro-inches RMS can be tolerated. However, a finish of 32 micro-inches RMS is preferred ... Static Gland Detail Surface finish: 32 for liquids, 16 for vacuum and gases ... 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

Editorial note, tabletop extrapolation: For a rotating or sliding shaft feedthrough (target manipulator), back off to <=30% squeeze and finish the shaft to the guide's dynamic-service figures (16 RMS; 10-20 micro-inches called most desirable for dynamic seals) - a rough shaft raises friction, wear and leakage quickly.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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

Editorial note, tabletop extrapolation: Check the actual lubricant and elastomer grades against a manufacturer compatibility chart. Silicone grease on Viton is commonly compatible but must still clear vacuum-outgassing requirements; petroleum grease on Buna-N is usually acceptable (NBR is built for mineral oils) though additives vary - the firm rule is the quoted one: never lubricate a ring with its own chemistry.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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. ... The length of the O-ring centerline should be equal to the length of the groove centerline. Following is an equation to assist in determining the O-ring inside diameter. O-ring ID = (Groove CL length / 3.14) - O-ring CS

Apple Rubber Products, Seal Design Guide — p. 84

Editorial note, tabletop extrapolation: 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. Note the source's rectangular sizing implies zero nominal stretch while its circular-groove guidance ideals 2% - follow the section matching your groove shape.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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

Editorial note, tabletop extrapolation: Scaled to ~150 keV the same normalized geometry needs only ~500-900 V on the deflector - an easy supply. Entry-slit width is set against the local turn separation and beam width together (dg-495), not by a fixed prescription.

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

Editorial note, tabletop extrapolation: For a next machine's chamber welds, specify 304L filler and stock where practical: the low-carbon grade resists weld sensitization (carbide precipitation and intergranular attack near welds). Plain 304, welded cleanly, also serves - the lecture's 'most commonly used' is a preference with reasons, not an exclusion - and leak-tightness comes from joint design and cleanliness either way.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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

Editorial note, tabletop extrapolation: The actual formula for trading a next machine's lid thickness against magnet gap: a few mm of plate suffices at 8-12 inch chamber diameter IF the edge support is real (the lid-deflection calculator covers both edge conditions). Alloy choice buys yield margin at the price of 7075's poorer weldability and corrosion behavior - it stiffens nothing.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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

Editorial note, tabletop extrapolation: 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.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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

Editorial note, tabletop extrapolation: 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.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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

Editorial note, tabletop extrapolation: Proof that p-B11 alphas are observable far below the 675 keV resonance: the 1933 apparatus saw them at 60-70 kV using tens of microamps and large solid angle, so a lower-current machine compensates with integration time and geometry. Their alphas stopped in under 5 cm of air, hence the vacuum path to a PIPS detector.

Cited in: Experiments by Energy Band

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

Editorial note, tabletop extrapolation: At the reference machine's ~1.3 kV the turn spacing is smaller still, so geometry matters doubly: a thick tip costs single-turn radial resolution first, and a shield mounted AHEAD of the collector can shadow it into reading zero while beam exists - the quoted case. A bare, grooved copper collector is the safe default until turn-resolved measurements are wanted.

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

Editorial note, tabletop extrapolation: With ~2.6 keV total gain per turn at ~150 keV, the reference machine's turn spacing at extraction is ~0.9% of r - about 0.7 mm at r = 3.2 in - so build the septum mount with millimetre-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

Editorial note, tabletop extrapolation: Judge a next machine first on internal-probe current at full radius: documented machines commonly ran internal currents several times their extracted beam (MIT's optimum was 4:1), so a gap of that order is precedented rather than failure. The rung-by-rung extraction picture is dg-595's; the census cross-checks are dg-260's.

allows most of the resonant beam to pass into the deflector channel without striking the channel walls. In the MIT cyclotron 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, with copper tubing also soldered to the bar for cooling. Other designers use a long V slot in a tungsten-strip septum, so the heat is distributed over an extended surface

Livingston & Blewett, Particle Accelerators (1962) — p. 184

Editorial note, tabletop extrapolation: At the reference machine's beam power the thermal load is small but not zero - intercepted power is loss current times energy per charge (1 uA of 500 keV beam is 0.5 W into a very small spot) - so compute it, and keep the slotted geometry: it maximizes transmitted current into the channel either way.

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

Editorial note, tabletop extrapolation: At the reference machine's 100 keV-1 MeV scale the instantaneous shift is ~0.01-0.1%. Whether it can be ignored is a turn-count question: with hundreds of volts to kilovolts per turn a sub-MeV machine has phase budget to spare, but the check is the accumulated slip against the +/-90 deg window (dg-273), not the per-turn number.

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

Editorial note, tabletop extrapolation: Lets the builder compute whether a probe or future septum can distinguish final turns: at ~150 keV, r ~ 9.6 cm and the reference machine's 2.6 keV total gain per turn, dR = (r/2)*(2.6/150) ~ 0.8 mm - tight for a probe, and doubling volts-per-turn doubles it.

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

Editorial note, tabletop extrapolation: The master rate table for the reference machine's PIPS window (150-675 keV) - as fitted A0 coefficients: a count-rate prediction folds in the angular terms, solid angle, target thickness and integration time (the experiments-by-energy arithmetic). What the table quantifies exactly is what reaching the resonance is worth: ~240x in A0 from 150 to 650 keV.

Cited in: Experiments by Energy Band

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

Editorial note, tabletop extrapolation: Gives the builder the extraction-voltage scale for a next machine: deflector voltage scales linearly with beam energy at fixed geometry, so a ~100 keV beam needs about a fifth of a 472 keV machine's figure in the same channel. Given the source's formula/number discrepancy (see formula field), size from the formula and confirm by measurement.

H2+/9 H+/7 H+/5 H+/3 H+ H2+

Yuly et al., Modifications on the Houghton College Cyclotron (2010) — p. 15-18

Editorial note, tabletop extrapolation: Prevents misidentifying beam in the reference machine's B-field sweeps: a peak at one-third the expected field is a CANDIDATE for the same ion on the 3rd harmonic - confirm by species diagnostics or scaling tests, since another species/harmonic combination can land at the same field.

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

Editorial note, tabletop extrapolation: The same lesson as the p-B11 cross-section curves: sub-barrier yield rises steeply with particle energy, so extra beam energy buys far more counts than the same fractional increase in current. The specific sweep numbers are one fusor's; the steepness is the physics.

Cited in: Experiments by Energy Band

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

Editorial note, tabletop extrapolation: Reinforces energy-over-current for the builder: sub-Coulomb-barrier reaction rates reward every extra keV steeply - though not by a fixed orders-per-10-kV law; Hull's own steps differ between jumps.

Cited in: Experiments by Energy Band

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

Editorial note, tabletop extrapolation: Diagnostic direction, not verdict: a sharp cutoff in the radial current profile is CONSISTENT with phase slip - and also with aperture interception, wall collisions or vertical-envelope loss - so discriminate by what moves it: RF frequency and dee-voltage changes shift a phase-slip radius, mechanical interception does not, and field trim tells its own story.