Cyclotron magnet design rules

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. ... capable of producing a very uniform 17,000 gauss field ... tapered from 12-inch pole stems to 10-inch pole faces.

McGuire, The Iowa State University 1.5 MeV Undergraduate Cyclotron (1961) — p. PDF 7 (printed 479) carries the quoted 20 kW sentence; the magnet paragraph is on PDF 5 (printed 477) and Table 1 on PDF 9 (printed 481)

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 for accelerators and beam transport lines typically call for < +250 u precision transversely and vertically and < +500 u longitudinally. Rotational tolerances are typically < +0.2 mrad in roll, pitch and yaw.

Tanabe, Iron Dominated Electromagnets, Lecture 8: Core Fabrication, Assembly, Installation and Alignment (2005) — p. PDF p.27 (slide 'Magnet Fiducialization') for the alignment numbers; PDF p.3 for the retrofit sentence

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: ΔB/B0 ≤ 0.01% ; Quadrupole: ΔB'/B'0 ≤ 0.1% ; Sextupole: ΔB''/B''0 ≤ 1%

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. PDF 10 (printed 74)

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: Editorial note, tabletop extrapolation: the engineering menu at the reference machine's energy class — modest dee voltage (1-2 kVpp), 1e-5 torr, a machined pole profile, not heroic RF or UHV — is what the deck describes pursuing below ~300 keV. It documents the approach, not a completed machine: the existence-proof framing is withdrawn, and the census carries the documented Niell beam record separately.

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.

The maximum magnetic field of the unmodified design is B = 1.27 T and is B = 1.77 T for the lid design. ... B = 1.77 T corresponds to a Dee frequency of 27.0 MHz

Morrow, Focusing in the Houghton College Cyclotron — Houghton College thesis (2015) — p. PDF 54 (printed 49) and PDF 55 (printed 50)

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

A Haskris H-4057 water chiller, capable of 3.8 L/min (1.0 gpm) ... Since the diffusion pump requires at least 0.8 L/min, the maximum that can be supplied to the magnet is 3.0 L/min ... the magnet requires 6.1 L/min

Loucks, Initial Results from the Houghton College Cyclotron — Houghton College thesis (2007) — p. PDF p.36 = printed p.36 (Loucks thesis Sec. 3.2 Magnet); the cited '35-36' range is correct, all figures are on 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 finished magnet forgings satisfactorily met these specifications. The chemical check analysis of the steel, well within our specifications, was: C 0.110, Mn 0.330, P 0.010, S 0.030, Si 0.015, Ni 0.060

Livingston & Howard (eds.), The Oak Ridge Relativistic Isochronous Cyclotron — ORNL-2648, OSTI 4275955 (1958) — p. PDF 118 (printed -113-) for the chemistry; PDF 119 (printed -114-) for the quoted yoke sentence

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.

The axial focusing, as shown above, takes place for any positive values of the field decay exponent. Therefore, orbital stability in both directions takes place only for 0 < n < 1.

Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 18-20

Editorial note, tabletop extrapolation: The governing stability rule for the weak-focusing reference machine: check the FEMM-derived B(r) for 0 < n < 1 over the working radii. Two refinements: n tends to zero at the machine center by symmetry, so the requirement bites from the first working orbits outward; and the value n takes is the designer's shaping choice - weak-focusing machines run it small at inner radii, rising toward extraction.

Cited in: Beam Dynamics: An Interactive Laboratory

its passage without noticeable losses of particles becomes possible only due to the fact that the beam crosses it for 1-3 revolutions, and the first harmonic of the magnetic field with a large amplitude is absent

Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 37

Editorial note, tabletop extrapolation: In the reference machine Qr = sqrt(1-n) sits just below 1 everywhere, so first-harmonic field symmetry is the load-bearing tolerance: a coherent distortion driven by B1 grows while the resonance condition holds, and the crossing survives when B1 is small (the quote's condition) and the crossing fast. How small is computed for the actual machine - the beam-dynamics laboratory's imperfection tools do it; pole tilt and off-center coils are the usual B1 sources.

Cited in: Beam Dynamics: An Interactive Laboratory

When transferring the energy of radial betatron oscillations into axial oscillations, the amplitude of the latter turns out to be twice the amplitude of radial oscillations.

Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 39

Editorial note, tabletop extrapolation: Very concrete for the reference machine: if the edge-field falloff pushes n through 0.2 near the last turns, dwelling ions grow vertically as far as the coupling perturbation drives them - into the dee aperture if allowed. Keep n below ~0.2 out to the extraction radius, or cross the resonance fast (dg-152, dg-694).

Cited in: Beam Dynamics: An Interactive Laboratory

If the task is to obtain an average field with a value of the field decay index n close to constant for all radii, then the axial gap g can vary in accordance with the expression

Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 49

Editorial note, tabletop extrapolation: A one-line pole-taper recipe for the builder tool: pick n (e.g. 0.02-0.2), machine the gap to this power law, verify in FEMM.

if the field is formed such that the deviation from the isochronous one for all operating radii is no more than 5 G, then this corresponds to a deviation of the RF phase... by no more than 5 degrees

Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 50

Editorial note, tabletop extrapolation: The 5 G <-> 5 deg pairing is that machine's arithmetic, not a portable spec: phase slip accumulates with turn number, harmonic and energy gain per turn, so integrate it turn by turn from the measured B(r) and RF parameters, and set the reference machine's shimming tolerance from the resulting phase-acceptance budget.

the so-called calibration coefficients are introduced to the level of the field created by the windings, which, as a rule, are not large and amount to ~1-2% of the current value

Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 50

Editorial note, tabletop extrapolation: For the reference machine's FEMM-vs-Hall-probe comparison: compare field SHAPE versus radius and current first - a residual that is genuinely a scale error can be absorbed in a per-coil factor (checked for current-independence, since saturation makes such factors drift), while a shape mismatch means geometry, B-H data or probe calibration, and no scale factor should paper over it. The cited 1-2% is that machine's correction, not a normal-mismatch budget.

Then the RF phase shifts to the values at which the particles cross the accelerating gaps with the optimal phase. Thus, conditions are created for the additional focusing of particles in the axial direction at the first revolutions by a high-frequency electric field. Depending on the configuration of the central region of the cyclotron, the level of the magnetic field in the center is raised to an amount of a few tens to a few hundred gauss

Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 50-51

Editorial note, tabletop extrapolation: Usable on a next machine: shim a small central cone so B falls gently from center outward, and set the central-region phase so the electric focusing helps rather than hurts - then verify the resulting field index and phase history by model; RF electric focusing means n~0 first turns are not wholly unfocused even before the bump.

The presence of the resonance makes it possible to use the first harmonic of the field with a small amplitude (usually a few gauss) to obtain a significant increase in radial amplitudes.

Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 64-65

Editorial note, tabletop extrapolation: The dR formula tells the builder exactly what turn spacing a ~kV energy gain buys at 4-inch radius (fractions of a mm), i.e. whether a septum/foil extraction is geometrically feasible for a next machine.

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

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

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

Cited in: Beam Dynamics: An Interactive Laboratory

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

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

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

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

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

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

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

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

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

There is little influence of the magnetic field on the discharge parameters as long as it reaches a certain minimum of roughly 0.1 T.

Wolf (ed.), Handbook of Ion Sources (1995) — p. 82

Editorial note, tabletop extrapolation: The reference machine's 0.59 T and a ~0.9 T successor both clear the handbook's 0.1 T minimum, so field-level effects on the ARC parameters should be small per the quote. Ignition and stable running still ride on pressure, geometry and surfaces (dg-372's ignition margins) - after a large field retune, a quick arc-parameter check beats an assumption.

there needs to be a base vacuum (with the ion source gas supply turned off) in the 10−6 Torr range ... Various turbo pumps ranging from 600 to 800 liters/second were used ... With a gas flow rate of 2.5 cc/min of hydrogen, the pressure in the main vacuum chamber is around 4 × 10−5 Torr.

Forringer, Phase Space Characterization of an Internal Ion Source for Cyclotrons — MSU dissertation (2004) — p. PDF p. 39 (printed p. 29) for the vacuum/flow practice; PDF p. 27 (printed p. 17) for the 4.5 T / 0.5 T endpoints

Editorial note, tabletop extrapolation: The reference machine's 0.59 T sits just inside the demonstrated field range - demonstrated at the endpoints, not characterized as uniform performance across it - and its existing turbo and 1e-6-class base pressure match the thesis's start conditions as-is.

A series of studies were made on a model magnet with poles 2 inches in diameter. This could be changed quickly and cheaply to give rough data over a wide range of parameters.

Creutz, Design and Construction of Synchro-Cyclotron — NYO-780 (1950) — p. 7

Editorial note, tabletop extrapolation: General magnet practice, transferable with its limits: a small bolt-together model surveys geometry cheaply (CIT's 2-inch scans were 'rough data over a wide range'), while saturation and B-H behavior do not scale - same-steel-same-B is what made scaled prediction land elsewhere (dg-1322). The model surveys shape; full-size verification still happens, or FEMM plays the model's role (dg-1089).

The coil height giving the minimum cost was found for a field of 20,000 gauss. Since the cost curve had a flat minimum this resulted in little increase in cost.

Creutz, Design and Construction of Synchro-Cyclotron — NYO-780 (1950) — p. 8

Editorial note, tabletop extrapolation: General magnet economics in FORM: minimize steel + copper + power cost for your own prices and expect a flattish minimum near the optimum - CIT's flatness belonged to a 20-kilogauss design at 1950s prices, so re-run the small optimization with today's numbers before leaning on the flatness for convenience deviations.

with 20,000 gauss at the center, produced a field of 96.7 percent of this value at 96.5 percent of the total radius (corresponding to the magnetic index n = .2), with an approximately linear decrease in field from center to edge.

Creutz, Design and Construction of Synchro-Cyclotron — NYO-780 (1950) — p. 9-10

Editorial note, tabletop extrapolation: The transferable practice is the method: measure H(r), compute n(r) from its local slope, and place the working radius where n stays in the focusing band - do not set a shim target from endpoint percentages, and do not adopt n = 0.2 as a goal without orbit, phase-slip and extraction analysis.

Cited in: Beam Dynamics: An Interactive Laboratory

Shim studies showed it would be very difficult to hold up the field out to a radius greater than 90 percent of the pole face radius. This was due to the pole cross-section being too small just below the pole face.

Creutz, Design and Construction of Synchro-Cyclotron — NYO-780 (1950) — p. 9

Editorial note, tabletop extrapolation: Directly applicable planning figure: budget usable beam radius near 90% of the 8-inch pole (~3.6 in) - and let the machine's own field map set the real number (dg-098's fringe accounting).

A method of measuring the relative field in the gap at points along a radius to .1 percent was developed and used on later detailed shim studies on this magnet.

Creutz, Design and Construction of Synchro-Cyclotron — NYO-780 (1950) — p. 9

Editorial note, tabletop extrapolation: A 0.1% relative radial map (differential Hall probe or flip coil) was that team's entry ticket; derive the next machine's actual requirement from its field and orbit tolerances, and qualify the probe's calibration, positioning, thermal drift and repeatability as part of building the capability.

The deflection of the poles under the magnetic load was found to average .002 to .004 inches for the model.

Creutz, Design and Construction of Synchro-Cyclotron — NYO-780 (1950) — p. 9

Editorial note, tabletop extrapolation: Historical calibration context, not a prediction: estimate the next machine's load from magnetic pressure B^2/(2 mu0) over the pole area and its structure's stiffness, distinguish per-pole motion from total gap closure, and always shim and map at operating excitation, not cold.

The Hiperco tests were repeated but dropped when this material was found to be dimensionally unstable.

Creutz, Design and Construction of Synchro-Cyclotron — NYO-780 (1950) — p. 9

Editorial note, tabletop extrapolation: Any exotic Co-Fe edge ring for the next machine's pole edge needs dimensional and magnetic checks after machining, heat treatment, assembly and excitation cycling - modern grades and treatments may behave differently from CIT's stock. Low-carbon steel is the conventional baseline, not a guaranteed adequate answer.

A final pair of model poles was machined out of the steel forgings actually used for the full-scale magnet poles. The results were satisfactory, and the design was frozen.

Creutz, Design and Construction of Synchro-Cyclotron — NYO-780 (1950) — p. 10

Editorial note, tabletop extrapolation: Transferable principle: validate on material representative of the production poles - measure coupons from the actual pole stock or the finished poles themselves; same-lot shim stock is a reasonable extra precaution but is beyond what the source demonstrates.

The machining of the pole tip was held to +/- .0025 inches on almost all dimensions.

Creutz, Design and Construction of Synchro-Cyclotron — NYO-780 (1950) — p. 11

Editorial note, tabletop extrapolation: A few-mil pole tolerance is achievable in a good hobby/job shop - derive the next machine's actual requirement from gap sensitivity and the field-uniformity budget, and remember final mapping and shimming absorb what machining leaves.

The chamber parts into two halves in a vertical plane through the center of the magnet, permitting the removal of the chamber without disturbing the magnet pole tips.

Creutz, Design and Construction of Synchro-Cyclotron — NYO-780 (1950) — p. 15

Editorial note, tabletop extrapolation: Directly applicable packaging rule: make the next machine's chamber removable or serviceable in place without unbolting pole tips or shims - and still re-verify the field after any reassembly that could have moved iron. Undisturbed tips make the recheck quick, not unnecessary.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

disclosed a re-entrant cavity resonator mode between the two pole pieces of the magnet with the vacuum tank walls as the return circuit resonant near the lower frequency limit. This was easily suppressed by strapping the pole pieces together.

MacKenzie et al., Design of the Radio-Frequency System for the 184-inch Cyclotron — UCRL-64 (1948) — p. 22

Editorial note, tabletop extrapolation: The pole-chamber geometry of an 8-inch machine forms the same class of parasitic cavity - sweep or model the assembled structure, and add a verified pole-to-pole RF bond if a mode lands near the operating band; don't strap preemptively, since added straps can perturb the intended RF structure or form current loops.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

the inner face, or back, is made of 1/2 in steel ... this house serves as a magnetic shield for the oscillator tube. A crude replica (1/16 size) was tested by the magnetic measurements group ... using the 1/16-scale 184-inch model magnet, and this shielding was found sufficiently effective, the field being cut from 140 Gauss to less than 20 Gauss. This is further reduced at the 9C21 elements by means of a 1/2 in steel sleeve slipped over the cooling jacket. The magnetic force on the oscillator box amounts however to 450 lbs.

MacKenzie et al., Design of the Radio-Frequency System for the 184-inch Cyclotron — UCRL-64 (1948) — p. 20

Editorial note, tabletop extrapolation: LDMOS amplifiers, fans and ferrite-cored parts near a 0.59 T magnet want a steel housing - and the source's method is the transferable part: they verified the shielding on a scale model before committing, and budgeted the large attractive force on the box. Measure the fringe field at the amplifier location and check the housing's effect; do not assume a thickness.

The autographs indicate a rapid spreading vertically of the beam at about 81 1/2 inches. This agrees quite closely with the point at which n = 0.2 from magnetic measurements.

Vale, 184-inch Cyclotron Vertical Beam Oscillations in the Region of 82-inch Radius — MDDC-984 (1947) — p. 3

Editorial note, tabletop extrapolation: Fully applicable as a diagnostic: map B(r) on the bench, compute n(r) and the tunes, and if the reference machine's beam stalls early, the n = 0.2 crossing is suspect number one - but confirm with tracking and check field-error resonances and aperture before moving the target radius.

accelerating particles past the radius where n = 0.2 in the 184-inch cyclotron has been postponed, since the available energy of the ions at this radius is within 5 per cent of the maximum of the system

Sewell, Henrich & Vale, Some Operating Phenomena Associated with the 184-inch Cyclotron — MDDC-1092 (1947) — p. 4

Editorial note, tabletop extrapolation: Budget a next machine's energy at the n = 0.2 radius, not the pole edge - and where shims can push the n = 0.2 contour outward, that buys usable energy more surely than chasing radius into the fringe (dg-152's taper rule is the design form of the same point).

Cited in: Beam Dynamics: An Interactive Laboratory

Mag. field, k-gauss 14 - 19

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

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: the reference machine's 0.59 T is a factor 2-3 below this tabulated population; pushing a next machine toward 1.2-1.5 T multiplies energy 4-6x at fixed pole radius - the route every tabulated machine took. The Stanford correction is the design-vs-operating-point lesson in miniature: the census itself splits design and as-run onto separate sheets, and the two differ.

Weight, Fe 6 ; Cu 4 tons. Winding 3/4 in x 1/16 in strip.

Howard, Cyclotrons and High-Energy Accelerators, 1958 — ORNL-2644 (1958) — p. 106

Editorial note, tabletop extrapolation: Extrapolating down the census, an 8-in-pole machine sits in the fraction-of-a-ton class - hobby-crane scale, and the reference machine's 757 lb H-frame agrees - while every inch of added pole diameter on a next machine is bought with steeply growing steel.

Pole tip dia. 31 in. Beam radius, max 12.6 in. Field gap, center 5.5 in. ... Dee dia. 29 in. Dee aperture 3 1/4 in.

Howard, Cyclotrons and High-Energy Accelerators, 1958 — ORNL-2644 (1958) — p. 26

Editorial note, tabletop extrapolation: Sanity template for a next machine on 8-inch poles: ratios of this class suggest a 1-1.4 in gap, a 0.5-0.8 in dee aperture, and energy planned at a 3.2-3.6 in beam radius rather than the pole edge - starting proportions to check against the machine's own field map and stability analysis, not expected dimensions.

Field drop-off 3-4 %

Howard, Cyclotrons and High-Energy Accelerators, 1958 — ORNL-2644 (1958) — p. 164

Editorial note, tabletop extrapolation: Directly transferable as a SHAPE target for the reference machine's field: the fixed-frequency population converged on a smooth, monotonic few-percent total drop. The total constrains the average only - the stability check remains the local n(r) map (n > 0 throughout, staying clear of 0.2; dg-003, dg-138), which the same total drop can satisfy or violate depending on where the fall concentrates.

Cited in: Beam Dynamics: An Interactive Laboratory

Magnetic field variable, by only changing the coil current, from 14 to 18 kg with 1 to 2.5% field drop-off at the exit (r = 16 cm).

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

Editorial note, tabletop extrapolation: The builder can trim B to match a fixed RF (or vice versa) and expect the shim profile to survive over a modest range - PROVIDED the iron is not driven into locally different saturation, which reshapes the profile. Measure n(r) at both ends of the intended current range before trusting it.

Air-cooled coils. Iron ore blocks for shielding

Howard, Cyclotrons and High-Energy Accelerators, 1958 — ORNL-2644 (1958) — p. 127

Editorial note, tabletop extrapolation: Precedent that air cooling can work at this scale - two real machines did - not proof that a given coil can: adequacy is set by I^2R dissipation, winding geometry, insulation rating, duty cycle and airflow. Do the dissipation arithmetic (magnet-power calculator) and monitor winding temperature (dg-220) instead of citing precedent.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

It was found that distortion of the magnetic field when the tank is evacuated is negligible. Latest measurements of the magnetic field reveal a first harmonic inhomogeneity of approximately 0.03%.

Howard (ed.), Electromagnetic Research Division Quarterly, period ending 31 March 1952 — ORNL-1339 (1952) — p. 15

Editorial note, tabletop extrapolation: Two transfers: verify a next machine's field map with the chamber assembled and pumped (pole deflection under vacuum load is a real worry that proved negligible for them - measure once to confirm); and read 0.03% as what a carefully shimmed classical machine ACHIEVED - the new machine's allowable first harmonic comes from its own orbit-centering budget, and note 0.03% of a 0.5-1 T tabletop field is 1.5-3 G, so gauss-level targets and fractional targets must be kept straight.

it was not possible to operate the model magnet at the extremely low (3.5 kilogauss) field levels at which we might like to operate the full scale machine.

Jungerman, Kibbe & Peek, Central Region Studies for Incorporating an Axial Ion Source in the Davis 76-in. Cyclotron — UCD-CNL-49 (1966) — p. 5

Editorial note, tabletop extrapolation: Modern translation for the FEMM pipeline: a model (physical or FEM) validated at one excitation does not certify another — iron saturation state changes the profile shape, so re-run the field solution at every planned operating point, especially the lowest, and verify the real magnet across its full excitation range.

moving the 8 inch plug to 5.5 inches from the valley floor and to extend the caps to a length of 3 1/2 inches. These caps saturate at high levels, but fill in the central "hole" at low fields.

Jungerman, Kibbe & Peek, Central Region Studies for Incorporating an Axial Ion Source in the Davis 76-in. Cyclotron — UCD-CNL-49 (1966) — p. 6

Editorial note, tabletop extrapolation: Deliberately-saturating iron as a field-programming element is a trick FEMM (with the real BH curve) models well: a piece sized to saturate at the main operating point contributes mostly at low field - but saturated iron keeps its magnetization, so verify the high-field map still meets spec rather than treating the cap as magnetically gone.

The isochronous fields are obtained with trim coil settings computed by a linear program, and their greatest deviation from isochronism is less than 15 gauss in all cases.

Jungerman, Kibbe & Peek, Central Region Studies for Incorporating an Axial Ion Source in the Davis 76-in. Cyclotron — UCD-CNL-49 (1966) — p. 6

Editorial note, tabletop extrapolation: Calibration, not criterion: what any machine tolerates is the accumulated RF phase slip - the signed integral of the frequency error over ITS acceleration history - so run the phase-slip integral in the tracker for the actual field map, turn count and dee voltage, and let that set the gauss tolerance; a few-tens-of-turns classical machine and a hundreds-of-turns AVF machine land in different places by exactly that arithmetic.

the beam measured at extraction is augmented by possibly 10% by using 22 amps in trim coil number 1 rather than -145 amps. The former produces the central radial bump.

Jungerman, Kibbe & Peek, Central Region Studies for Incorporating an Axial Ion Source in the Davis 76-in. Cyclotron — UCD-CNL-49 (1966) — p. 6

Editorial note, tabletop extrapolation: Consistent with the classical-cyclotron instinct - a small central bump (field falling with radius from turn one) focuses the early turns where the ORNL 22-inch z-studies located most dee loss - as a HYPOTHESIS the correlation supports, not a demonstrated mechanism. Empirically checkable on the reference machine with shim washers at the pole center: calculate the phase-slip cost first, map the shimmed field, and measure both transmission and where the losses move.

the validity of the calculations and magnetic field data is supported by the fact that we obtained an internal beam of 21 MeV H2+ ions using the computed field on the first attempt.

Jungerman, Kibbe & Peek, Central Region Studies for Incorporating an Axial Ion Source in the Davis 76-in. Cyclotron — UCD-CNL-49 (1966) — p. 7

Editorial note, tabletop extrapolation: The 1966 encouragement for a next machine's compute-first pipeline (field map -> tracker -> build): careful measurement plus an honest tracker produced first beam on the computed field, first attempt, on that machine. One result is precedent, not promise - keep shim stock on hand, and let the pipeline earn trust machine by machine.

This region, called the "gap," should have a diameter about nine times as great as its axial dimension. ... n = - (R/H)(dH/dR) << 1/5 ... The desired field is one which decreases linearly with increasing radius to the outside "edge" of the gap.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. PDF p.6 = printed p.6 (TID-454, Technical Report No. 1, Sec. 1.1 Pole Tips, 'Introduction')

Editorial note, tabletop extrapolation: CORROBORATING, not new - the same premises underlie Livingston-Blewett and Wouters (corpus already carries 0<n<1 stability). TID-454's working condition is the stricter n<<1/5; note its own 130-in/14-in example is 9.3x. The reference machine's 8-in poles over a wide gap fall far short of 9x, which is exactly why usable radius is scarce; a next machine's gap choice should respect this proportion.

An effort to obtain a value of the pole-tip efficiency, E, which could be used as a goal for experimental magnet design gave E = 0.64.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 25

Editorial note, tabletop extrapolation: Gives the next machine's FEMM loop a quantitative habit: compute gap-flux/pole-base-flux utilization for each candidate tip and compare candidates against each other and against the report's 0.64 goal - treat the absolute expected range for a small pole as something the FEMM runs themselves establish.

It is shown that this can be increased to about 96 per cent by cutting a groove into the pole face just inside of the raised edge. This result may be obtained in several ways and is unquestionably correct.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 25

Editorial note, tabletop extrapolation: On 8-in poles the 92->96% difference is ~9% in energy at fixed field - cheap to try in FEMM and on the real shims; the tapered-pole-superiority claim and the NYO-780 comparison need their own citations before leaning on them.

The contour of the shim when the steel surface is not an equipotential is best determined experimentally. An approximate shim can be put on a pole which otherwise has its final form.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 8

Editorial note, tabletop extrapolation: The next machine's shim program: FEMM (finite permeability, saturation modelled) resolves much of what 1952 needed bench passes for - validate the final contour against a probe map where the nonlinearity is significant, as NYO-780 (p.7) did with its bolt-together model magnets.

If the spikes are cylindrical, the field due to them may be treated approximately as that of point charges placed at their tips with strength m = MA.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 8

Editorial note, tabletop extrapolation: Handy closed-form sanity check for slender, demonstrably saturated cylindrical features (a spike or thin button) before FEMM; treat the excitation independence as approximate - the saturated region and residual susceptibility still move a little with drive - and don't stretch the point-charge picture to fat cones.

1. The resistance of the coil is proportional to its mean circumference. 2. An amount of steel approximately proportional to two times the height of one coil, plus the radial width of the coils, is required to complete the magnetic circuit.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. PDF p.25 = printed p.25 (TID-454, Sec. 1.2 Magnet Coils, 'Introduction')

Editorial note, tabletop extrapolation: The compounding is the point - on any H-frame rebuild, fat coils cost twice (copper AND the longer steel circuit around them), so invest in space factor and cooling before adding turns.

The costs which are affected are the combined costs of steel, copper, and energy.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 30-32

Editorial note, tabletop extrapolation: This collection's only explicit dollar-optimization of magnet proportions: redo the sweep with 2026 unit costs (scrap steel, surplus copper, $/kWh over expected machine life and duty cycle) - after re-reading the source for the variable definitions, since a cost formula reused without its unit system is a trap. NYO-780 p.8 did the equivalent sweep by model.

For operating convenience, the coils should be made smaller than is indicated because the total cost is a slowly varying function of the coil outside diameter near the minimum of cost.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 30

Editorial note, tabletop extrapolation: Licence to trade cost-optimality for access, cooling clearance, or stock material sizes - the optimum is a plateau, not a peak. How much plateau: evaluate the cost function at the smaller diameter and report the actual penalty rather than assuming it is a few percent. Same flat-minimum finding as NYO-780 p.8 (coil height); cite both.

It appears that the unit costs can only be determined after the cyclotron has been in operation for several years, so estimates must be employed.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 30

Editorial note, tabletop extrapolation: A 1952 statement of the plan's own doctrine, applied with modern tools: use estimated lifecycle costs with a sensitivity check on the uncertain inputs, update from quotations and commissioning actuals as they arrive, and avoid polishing the spreadsheet past its input accuracy.

It is quite clear from either equation that this factor, optimum x, depends on scale factor. The assumptions made cause the value of x given by the equation to be too large.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 31

Editorial note, tabletop extrapolation: Two cautions in one: treat big-machine coil proportions (including TID-454's own x~1.4) as non-transferable to an 8-12 in machine, and rather than mechanically shaving the computed value, redo the optimization at the actual scale with a geometry-dependent field/cost model.

The generator should match the coil in the sense that the quotient of the maximum voltage output and the maximum current should be equal to the resistance of the coil.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 33

Editorial note, tabletop extrapolation: When sizing a surplus supply for the next machine's coil - or the turn count for a given supply - pick turns so the coil's HOT resistance sits at the supply's V_max/I_max corner: copper rises 20-40% in resistance from cold, so a cold-matched coil starves at temperature. And confirm the supply can actually hold its corner continuously; not every surplus unit can.

Both the above statements need qualification and are useful only as guides.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 33

Editorial note, tabletop extrapolation: Quick shape checks for an H-frame rebuild - square-ish coil cross section and flat wide return yokes - with the author's own warning not to treat them as optimization results.

it should be made of magnetically good steel, and the optimum size is rather critical ... the quality of steel used in this part of the magnet [the yoke] is less important.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 33-36

Editorial note, tabletop extrapolation: For a next machine's steel shopping: spend on clean low-carbon (1006/1008) pole and pole-base stock and size the pole base deliberately - it is the critical dimension - while the return yoke tolerates lower-grade steel. Lower-grade still means characterized enough to size its area with margin (dg-132's measure-or-assume-conservatively), not mystery plate on faith.

This field strength depends on the design and the size of the magnet and cannot be determined without a model magnet.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 33-38

Editorial note, tabletop extrapolation: The steel-vs-power tradeoff behind "how hard to push B" - for a fixed 757-lb-class magnet the answer comes off the real excitation curve, not theory; FEMM plays the role of the model magnet for first passes.

Cited in: Choosing Your Machine

In most cases, the ratio is not so sensitive to the current used to excite the magnet as the corresponding absolute value and the required accuracy of current control is reduced.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 38-40

Editorial note, tabletop extrapolation: The principle survives the instruments: when Hall-mapping a next machine's shims, log B(r)/B(0) with an always-live reference probe at center. Simultaneous ratioing cancels the common-mode excitation drift - saturation-driven profile changes, probe drift and cross-calibration error remain, so keep decent regulation and repeat-check a few points.

the field obtained is proportional to the inside radius of the coil and a high field can be obtained by increasing the scale ... the power p and the volume of conductor v increase with the cube of the inside radius.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 116

Editorial note, tabletop extrapolation: SCALE-SCOPED (megagauss-era context), and useful for estimating specific coils: it explains why small-bore air-core inserts and compact analyzing magnets are economically comfortable while large air-core fields carry punishing power bills - run the numbers for the actual coil rather than treating the scaling as a feasibility verdict.

For fields of 10^5 gauss and above, the situation is quite different; the power and maximum current density become important factors and more complicated designs are useful.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 122

Editorial note, tabletop extrapolation: Locates amateur work far below the exotic regime: for sub-kG correction coils, steering windings and test solenoids a simple winding is usually adequate - but 'usually' is earned by computing NI, resistance, I^2R heating, temperature rise and current density for every coil, since a small high-duty coil can be power-limited at any field. [Note revised 2026-08-23: earlier note said 'sophistication buys nothing'.]

Helmholtz coils have cross sections small in comparison with their radii squared, and thus require excessive power where a high field is required.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 108

Editorial note, tabletop extrapolation: The right doctrine for any air-core uniform-field fixture - probe-calibration coils, a beamline corrector, a small synchrotron's reference field: choose the winding section from the ampere-turns, resistance, I^2R and temperature-rise arithmetic, and reach for thick optimized sections when that arithmetic shows a power problem - a classic thin Helmholtz pair is fine where it doesn't.

the ions which were the chief contributors to the current at resonance are lost by defocusing and ions of more positive phases are now the chief contributors.

Cohen, Spatial Distribution of Current on an Internal Cyclotron Target — ORNL-1348 (1952) — p. 9

Editorial note, tabletop extrapolation: Explains an observation class on the reference machine: probe current can look tolerant of field/frequency error while the surviving phase distribution, turn spacing, transmission and attained radius shift underneath - reinforcing ORNL-1347's rule that current on target is not evidence the energy is what B-rho says (at a FIXED radius the momentum is still ~qBr; what moves is which ions get there and how). Whether self-selection broadens your tuning curves is testable with phase- or energy-sensitive measurements - treat the width cautiously either way.

Beyond these requirements the advantages and disadvantages of various magnet configurations that might be used become more subtle and must be weighed against such factors as the cost, ease of beam extraction, and maintenance requirements.

Oak Ridge National Laboratory, A Proposal for the Mc² Isochronous Cyclotron — ORNL-3540 (1963) — p. 162

Editorial note, tabletop extrapolation: Scale-free requirements-hierarchy discipline - with the hard-requirements LIST being machine-specific: for a classical weak-focusing machine it is the field law (falling field, n inside its stable band), focusing, and achievable power; isochronism is the AVF machine's version, and a synchrocyclotron's differs again. State yours first, then trade the soft criteria as the source does.

A magnet of this design places all the critical dimensions on the iron geometry and minimizes the sensitivity to errors in coil placement. It is reasonable to expect that the final magnet would have to be shimmed after construction

Oak Ridge National Laboratory, A Proposal for the Mc² Isochronous Cyclotron — ORNL-3540 (1963) — p. 172

Editorial note, tabletop extrapolation: Directly scale-free: machined iron holds its dimensions in a way wound copper cannot, and 'shim after construction' is a scheduled step rather than a failure mode. Trim coils, where fitted, are a separate adjustability decision with their own warm-magnet limits (dg-160).

The model tests to date have been directed at determining the gross characteristics of various configurations ... Future models will include one very accurate version on which measurements suitable for orbit calculation can be made.

Oak Ridge National Laboratory, A Proposal for the Mc² Isochronous Cyclotron — ORNL-3540 (1963) — p. 172

Editorial note, tabletop extrapolation: Maps onto the FEMM-first pipeline: cheap comparative FEMM runs play the role of crude models; only the chosen geometry earns a high-fidelity field map for the Python tracker.

Transistor-regulated power supplies with 1 part in 10^4 stability are used to energize coils which contribute more than 1% to the magnetic field.

Oak Ridge National Laboratory, A Proposal for the Mc² Isochronous Cyclotron — ORNL-3540 (1963) — p. 274

Editorial note, tabletop extrapolation: Scale-free budgeting instinct (from a 42-gauss analogue machine): spend regulation money in proportion to field contribution. The 1% line and any source-sharing arrangements are that design's choices; the general form is regulation ~ field tolerance / coil contribution, applied against your own stability budget (dg-027).

Gap tolerance +/- 0.004 in.

Oak Ridge National Laboratory, A Proposal for the Mc² Isochronous Cyclotron — ORNL-3540 (1963) — p. 137

Editorial note, tabletop extrapolation: 810-MeV provenance: the spec belongs to a 53-ft isochronous magnet, and even the RELATIVE number (5e-4 of the 8-in gap) is that machine's, not a scale-free constant - the transferable content is the framing: derive the next machine's gap tolerance from its allowed field error via a magnetostatic model or measured dB/dg, then stack machining, assembly and thermal terms; sanity-check the result against the 5 G / 5-deg-phase budget.

the position of unstable equilibrium at the median plane can be found The current-carrying loop also tends to center itself with respect to the magnetic center of the field

Howard (ed.), Electromagnetic Research Division Quarterly, period ending 30 September 1952 — ORNL-1383 (1953) — p. 22

Editorial note, tabletop extrapolation: A near-zero-cost magnet diagnostic - but engineer the five minutes it runs: compute the wire's I^2R heating and use a current-limited supply with short energizations, restrain the loop and add travel stops (a free conductor in a tesla-scale field moves hard when energized), and keep hands clear at switch-on. Use it as the coarse locator of median plane and center, then confirm with the Hall-probe map.

the median plane of the 22-inch cyclotron, at 6", 11", and 22" diameter, coincides with the geometric median plane within +/- 0.125" and that the magnetic center coincides within +/- 0.25"

Howard (ed.), Electromagnetic Research Division Quarterly, period ending 30 September 1952 — ORNL-1383 (1953) — p. 22

Editorial note, tabletop extrapolation: The measure-both discipline transfers; the inch values do not - they are one machine's observed alignments, not acceptance limits. Derive the reference machine's own tolerances from its pole radius, gap, harmonic budget and central-region sensitivity, then survey against those.

Inasmuch as the equivalent diameter of the pole pieces is 44 in., the machine is more appropriately identified as the 44-in. cyclotron.

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

Editorial note, tabletop extrapolation: The reference machine's H-frame is the analogous asset: energy upgrades - gap, shims, dees, RF power - can stage around the same 757-lb iron for years. The platform reading is the editorial lesson drawn from ORNL's staged reuse of one magnet line (1.5 MeV, then 5 MeV, then proposed heavy ions); the quote itself carries the renaming.

One of these coils consists of an insulated conductor wrapped half-way around the magnet pole piece and attached so that the pole piece completes the circuit.

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

Editorial note, tabletop extrapolation: A field-trim knob that steers orbits without touching iron - as a modeling hypothesis for a next machine: specify ampere-turns and the return-current path, run the magnetostatic and orbit analyses (FEMM models it directly), check contact heating and forces, and only then test; variable-energy operation is a beam measurement away, not a feature to advertise from the wiring diagram.

The removal of the flat shims from the tank increased the magnet gap to 13 1/2 in. and provides sufficient clearance to permit operation of the dees at a potential of 100 kv.

Howard (ed.), Electronuclear Research Division Semiannual, period ending 20 September 1953 — ORNL-1663 (1954) — p. 18

Editorial note, tabletop extrapolation: For a next machine the same ledger applies at 5-13 kV: dee-to-liner spark distance plus dee aperture plus liner clearances must fit inside the gap, and gap given to voltage clearance is field taken from energy - in the gap-dominated, fixed-ampere-turn regime (dg-021's measured caveat on the ideal scaling). Decide voltage and gap together (dg-181).

Beam radius, in. 11 / 20; Proton energy, Mev 1.5 / 4.9; Magnetic field, oersteds 6400; Magnet gap, in. 13.5; Maximum dee-to-dee potential, kv 100; Frequency, megacycles/sec 9.7 (spec table, condensed)

Howard (ed.), Electronuclear Research Division Semiannual, period ending 20 September 1953 — ORNL-1663 (1954) — p. 18

Editorial note, tabletop extrapolation: The nearest professional sibling to a next machine in this collection - same ~0.64 T field class and ~9.7 MHz as the reference machine's 0.59 T / 9 MHz. Use it to sanity-check B-f consistency; note the 100 kV (vs ~1.3 kV) buys energy per turn and fewer turns - less phase slip and interception - while the energy-radius relation stays set by the field.

the magnet pole faces (tank walls) are being ground with a portable grinder to provide a very uniform magnetic field, as near +/- 0.01% as possible. This will then provide a standard base for the various magnetic shim designs

Howard (ed.), Electronuclear Research Division Semiannual, period ending 20 March 1954 — ORNL-1670 (1954) — p. 20

Editorial note, tabletop extrapolation: For a next machine's shim development: establish and map the unshimmed field to the best flatness attainable FIRST, so every FEMM-predicted shim is measured against a known zero rather than an uncharacterized pole error. Set the flatness target from a phase budget, not a fixed gauss figure: accumulated slip is roughly 360 deg x N_turns x dB/B for a uniform mismatch, so a many-turn low-voltage machine needs proportionally tighter field than a few-turn one. (Also proof that hand tooling on installed poles was acceptable ORNL practice - no magnet disassembly required.)

Grinding and shimming of the tank walls to produce a flat magnetic field was continued. The magnetic field is now uniform to within 0.05%.

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

Editorial note, tabletop extrapolation: Calibrates expectations, not a budget line: sustained professional effort on the 44-inch bought 5e-4 base-field uniformity against a 1e-4 aspiration - so plan for the ground pole to fall short of its target and for shims to close the remaining gap, with the actual allowable derived from the machine's own phase-budget arithmetic and verified by mapping. How the 0.05% split between grinding and shimming the report does not say.

The one-quarter-scale model magnet is of the closed-yoke type. ... Its total weight will be 14.4 tons; 12.7 tons will be iron and 1.7 tons will be copper. The magnet gap will be in a vertical plane to provide the greatest access for making field measurements. The pole tips are removable so that shims of any shape can be inserted readily.

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

Editorial note, tabletop extrapolation: For any next-machine shim-test rig (or a scaled FEMM-validation magnet), design for the measurement campaign: open sightlines for the Hall probe, pole tips that unbolt, gap oriented for jig access - the orientation serving the probe rather than mimicking the final machine is the editorial reading of ORNL's choice.

the weight and power requirements would each be less than the corresponding sector-magnet requirements by at least a factor of ten.

Bromley & Bruner, The Design of a Focusing and Analyzing System for the 27-inch Cyclotron Beam — NYO-3823 (1954) — p. 6

Editorial note, tabletop extrapolation: DIRECT - the as-built comparison (p.32) was 355 lb for the doublet pair vs an estimated 3 tons for a sector condenser. At a next machine's rigidity (~7x lower than Rochester's 4e5 G-cm) a doublet becomes a benchtop object; the no-deflection tunability argument is the one to remember when laying out the line.

With this as a guide we apply an extra factor of safety and take a = 3, c = 1.5, hence the magnet poles are given by xy = +/- 2.25 cm^2

Bromley & Bruner, The Design of a Focusing and Analyzing System for the 27-inch Cyclotron Beam — NYO-3823 (1954) — p. 29

Editorial note, tabletop extrapolation: DIRECT method, not numbers: measure the real beam first, then stack explicit margins on the way to the pole constant. A next machine's envelope comes from its own extraction simulation or measurement; margin-then-round-up is what prevents discovering an undersized bore after the coils are wound.

Morley Machine Company, Rochester, N.Y., produced milling cutters conforming to this equation ... Subsequent work has shown that circular arcs would have been satisfactory.

Bromley & Bruner, The Design of a Focusing and Analyzing System for the 27-inch Cyclotron Beam — NYO-3823 (1954) — p. 29

Editorial note, tabletop extrapolation: A candidate money-saver for a next machine's quads: circular-arc (or round-stock) tips - validated by checking the integrated multipoles and end effects in FEMM against the beam's actual field-quality requirement, which is where the modeling time belongs; adequacy depends on aperture fraction used and multipole tolerance, so it is not automatic.

Measurements have shown that the effective length of the magnets is as much as 20% greater than the physical length.

Bromley & Bruner, The Design of a Focusing and Analyzing System for the 27-inch Cyclotron Beam — NYO-3823 (1954) — p. 29

Editorial note, tabletop extrapolation: DIRECT: for short quads the fringe extension is a first-order effect, not a correction - and it scales with aperture, which is why short, fat quads see the largest effect. Get l_eff per magnet from the FEMM/tracker pipeline; ignoring it produces significant focal errors.

This low field avoids saturation difficulties in the magnet iron and high excitation power requirements. Furthermore, it enables us to dispense with water cooling in the windings.

Bromley & Bruner, The Design of a Focusing and Analyzing System for the 27-inch Cyclotron Beam — NYO-3823 (1954) — p. 30

Editorial note, tabletop extrapolation: DIRECT: at a next machine's rigidity, transport-quad pole-tip fields of a few hundred gauss are plausible - compute the actual requirement from aperture, length and focal geometry (the formula) - and where field and current density land as low as the source's, unsaturated iron with air-cooled random-wound coils is exactly the regime they describe. Confirm with the dissipation arithmetic before skipping water (dg-708). OCR trap - the text layer renders the B^1/2 exponent as B^2; page image verified B^1/2.

A field of 1 kilogauss requires NI = 5000 ampere turns. As a safety factor, we have designed for 6000 ampere turns. ... Each coil will have exactly 3000 turns and the coils in each unit are connected in series

Bromley & Bruner, The Design of a Focusing and Analyzing System for the 27-inch Cyclotron Beam — NYO-3823 (1954) — p. PDF p.31 (printed page 28)

Editorial note, tabletop extrapolation: DIRECT wiring doctrine for any home-built multipole: gradient symmetry comes from forced equal current, not matched resistances - which is also why surplus-wire coil construction works, since the series circuit forgives resistance mismatch between coils.

For fields above about 8 kilogauss, saturation effects begin to set in, and the field becomes less uniform near the pole boundaries.

Bromley & Bruner, The Design of a Focusing and Analyzing System for the 27-inch Cyclotron Beam — NYO-3823 (1954) — p. 43

Editorial note, tabletop extrapolation: DIRECT sizing rule with scale caveat: the 8 kG threshold is geometry- and steel-specific, but the logic (uniformity budget, not raw B_sat, sets the working field; bend radius follows) applies to any analyzer dipole on a next machine. At ~170 keV protons rho is a few cm even at modest fields - the analyzer becomes a bench magnet.

The effect of the fringe field is to shift the effective pole boundary outward, and this is taken into account empirically by adding to the right-hand side of III-20(b) a term 0.4 G

Bromley & Bruner, The Design of a Focusing and Analyzing System for the 27-inch Cyclotron Beam — NYO-3823 (1954) — p. 43

Editorial note, tabletop extrapolation: For a next machine's analyzer designed in FEMM, the sanity check is the concept, not the constant: compute the effective field boundary from the longitudinal field integral of the simulated fringe and compare against the steel edge - an offset of very roughly half a gap is the expected order. Do not equate the 0.4G term with a tracking code's FINT parameter (FINT conventions carry fringe focusing integrals, a different quantity).

the methods for correcting for the fringe fields effects ... are not sufficiently precise to warrant basing the magnet design on the second-order calculations.

Bromley & Bruner, The Design of a Focusing and Analyzing System for the 27-inch Cyclotron Beam — NYO-3823 (1954) — p. 50

Editorial note, tabletop extrapolation: DIRECT design-philosophy rule for the whole next-machine campaign - match model order to input-data quality. Also note the companion check they DID run (pp.49-50), that the bent beam clears the back of the magnet with ~5 cm margin for the full 6 cm beam - a 30-second calculation that catches a catastrophic layout error.

an extension of the energy range much beyond 1.3 E0 requires an unreasonably large vacuum chamber at the exit of the magnet.

Alford, Bilaniuk & Hawrylak, Broad Range Spectrograph for Use with the Rochester 27-inch Cyclotron — NYO-9683 (1961) — p. 7

Editorial note, tabletop extrapolation: SCALE-HONEST only when the scaling is done: the geometry fixes E/E0 ratios, but reaching a given E takes B*R. For ~170 keV protons, B-rho ~ 0.06 T-m, so an R ~ 5-10 cm bench version needs roughly 0.6-1.2 T - iron-pole territory, not a few hundred gauss. Still compelling as a teaching-lab focal-plane instrument; copy the optics and size the field honestly.

By relaxing the original requirements for extremely high field uniformity, a considerable simplification of the Browne-Buechner design was achieved in reducing the magnet yoke structure to a simple C-shape.

Alford, Bilaniuk & Hawrylak, Broad Range Spectrograph for Use with the Rochester 27-inch Cyclotron — NYO-9683 (1961) — p. 7

Editorial note, tabletop extrapolation: DIRECT and very relevant to a next machine - the whole report is a case study in not copying the flagship instrument (Browne-Buechner at MIT) but re-deriving requirements from the local physics program. Compact C-yokes, deferred correction hardware ("add spacers only if needed" - they never were), and unconventional yoke placement are all fair game once the real spec is known.

the location and magnitude of these non-uniformities were the same at both 6.8 and 14 kilogauss, and it was not expected that these variations would have any significant effect

Alford, Bilaniuk & Hawrylak, Broad Range Spectrograph for Use with the Rochester 27-inch Cyclotron — NYO-9683 (1961) — p. 11

Editorial note, tabletop extrapolation: Two ideas worth writing into a mapping procedure, each with its limit: (1) an error that scales rigidly with excitation CAN be absorbed by end-to-end calibration for a relative instrument - after a trajectory or resolution check shows it does not bend the optics; reproducible is necessary, not sufficient. (2) Degrading NMR signal above some field is a prompt to investigate - saturation inhomogeneity is one suspect among probe tuning, gradients and positioning; confirm with B-vs-I behavior before concluding.

The tips formed the top and bottom of the vacuum chamber of the magnet, while the side walls of the chamber were strips of non-magnetic stainless steel welded to the tips.

Alford, Bilaniuk & Hawrylak, Broad Range Spectrograph for Use with the Rochester 27-inch Cyclotron — NYO-9683 (1961) — p. 9

Editorial note, tabletop extrapolation: The poles-as-chamber pattern eliminates the gap-wasting separate tank (the alternative Bromley rejected on machining/gasketing grounds, nyo-3823 p.6) - carry the METHOD and derive the gap tolerance from the analyzer's own field-error and resolution budget, minding weld distortion across the span.

modifications to <B> to yield isochronism out to the 29th entry in the radial table and with the flutter field modified by a small amount to smooth out effects of measurement errors. In addition, Fourier components of argument greater than 99 have been dropped since these components are sufficiently small to have a negligible effect on the particle motion. The radial spacing of the table entrys is interpreted as increased by the factor 64/8.75 corresponding to the ratio of pole diameters ... In the Fourier analysis the measured field has been assumed to have perfect 120 [deg] symmetry.

Blosser & Gordon, Computational Study of a Resonant Extraction System for a 3-Sector Cyclotron — MSUCP-9 (1961) — p. 6

Editorial note, tabletop extrapolation: The historical analog of the CadQuery->FEMM->field-map pipeline, plus the habit worth copying exactly as MSU practiced it: document every cleanup applied to the field the tracker ate. For an as-built machine, keep the RAW map too - symmetrizing and smoothing erase the very error harmonics that drive resonances - and use the cleaned copy only for idealized nominal studies; check magnetic similarity (saturation behavior) before radially scaling any model field.

The powerful effect of a cos 0 field component in a cyclotron ... is clearly evidenced by the large changes in the phase plot which result when the small 1% bump is added.

Blosser & Gordon, Computational Study of a Resonant Extraction System for a 3-Sector Cyclotron — MSUCP-9 (1961) — p. 22

Editorial note, tabletop extrapolation: Cuts both ways near nu_r = 1: the demonstration is why first-harmonic errors get 'great respect' - so Fourier-analyze the candidate field map and track the measured B1(r) through the local tune to learn what YOUR machine's shim asymmetries cost; and a deliberate bump coil is a powerful orbit-steering experiment once its ampere-turns are sized from that same analysis, not assumed few-turn-cheap.

The process is a trial and error search, with general guidelines and test criteria for success.

Rainwater et al., The Columbia University Nevis Synchrocyclotron Major Modification — NEVIS-189 / R-774 / CU-295 (1971) — p. 5

Editorial note, tabletop extrapolation: Directly transferable design-process pattern for any pole or shim work on a next machine: let FEMM play the role of the Nevis model magnets, with analytic tune formulae as the accept/reject criteria - within FEMM's 2-D limits (azimuthal structure needs a 3-D model or the measured map; the playbook's tracker closes that loop). The final accept/reject is the measured field, exactly as it was at Nevis.

a final "touch up" machining of these pieces, with the final iron in place on the basis of magnetic field mapping studies.

Rainwater et al., The Columbia University Nevis Synchrocyclotron Major Modification — NEVIS-189 / R-774 / CU-295 (1971) — p. 5

Editorial note, tabletop extrapolation: Fully transferable at any scale — design a next machine's shims and center plugs as bolt-on, pin-located pieces so field-map-driven iteration does not mean remaking the poles.

The value of mu used was found experimentally by measuring the field from a precisely known configuration of conductors

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

Editorial note, tabletop extrapolation: A model-calibration pattern for the FEMM pipeline: one known-geometry measurement (a wire loop, a known coil) in the actual gap BENCHMARKS the model at that operating point - repeat at several magnet currents and locations before trusting the saturation model across the map; one point pins one point, not the whole BH curve.

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

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

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

a magnetic mirror built into the upper end of the arc hood by the simple insertion of a steel bearing ball 1/8 in in diameter. ... Before the steel ball was added the top of the graphite hood glowed a bright orange color when the arc was operating, because of the intense electron bombardment. After the ball had been added the top of the hood was found to remain black when the arc was operating. This result is taken as evidence of a strong mirror action.

Fulbright, A Hooded Arc Ion Source with a Magnetic Mirror Feature — NYO-9358, University of Rochester (1962) — p. 2

Editorial note, tabletop extrapolation: Nearly free to TRY on a filament hooded source running in the main field - a bearing ball is stock hardware and the hood exists - but not automatic: whether electrons reflect depends on Bmax/B0 at the ball, injection pitch angles and collisions, so replicate the source's own A/B glow test (hood-top color/temperature with and without the ball) and check the companion negative result (dg-1288) before counting on it.

in this case unsuccessful ... also a hairpin-shaped 60 mil tungsten wire, is mounted with its plane vertical, parallel to the magnetic field of the cyclotron, rather than perpendicular as in the first source.

Fulbright, A Hooded Arc Ion Source with a Magnetic Mirror Feature — NYO-9358, University of Rochester (1962) — p. 3

Editorial note, tabletop extrapolation: An honest negative result from 1961 that still stands. The filament-orientation reading (injection angle into the mirror deciding loss-cone membership) is a HYPOTHESIS consistent with the one observed difference - local electric fields and emission distribution matter too - so plan the mirror experiment as an A/B test with the glow diagnostic and vary filament orientation if the first try fails.

The properties of a magnetic field in space make it impractical to obtain a properly shimmed field if the gap length is much greater than one-half the radius p.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 12

Editorial note, tabletop extrapolation: An 8-12 in. pole with a 1-2 in. gap sits far inside this limit, which is why small cyclotron shims work at all; the rule bites for any short-radius bending/analysis magnet where a generous gap is tempting for access.

is the maximum allowable space rate of change of the magnetic field in a direction toward the edge of a gap.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 15

Editorial note, tabletop extrapolation: The transferable move: translate a beam-geometry tolerance into a measurable dH/dx budget via the curl-free midplane relation - a quick LOCAL gradient check to run on a field map when flux-line bowing is the relevant tolerance. It is a calutron criterion, not a cyclotron field-quality spec: orbit, focusing, flutter and resonance checks still decide.

the quantity (NI)g represents 85 to 95 per cent of the total mmf required (i.e., the efficiency ranges from 85 to 95 per cent), and Eq. 7 can be used to give a useful first approximation

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 21

Editorial note, tabletop extrapolation: The same arithmetic every H-frame designer runs today (Wouters and Zickler's CAS notes corroborate the sizing). The 85-95% efficiency band is the source's result for WELL-PROPORTIONED iron-return magnets: use it as a sanity check on FEMM excitation for a magnet in that class, and expect worse from lean yokes, corners, or parasitic joint gaps (dg-128).

the product of the power and weight of a coil conductor depends on the ampere turns and the mean diameter of the coil.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 22

Editorial note, tabletop extrapolation: The cleanest statement in this collection of the copper-vs-power trade: double the copper, halve the dissipation, at fixed NI. Lets a coil be resized on one line when a surplus supply or a heat limit is the binding constraint.

For continuous operation, 1600 amp/sq in. is about the upper limit used for oil-cooled coils. This compares with 1000 amp/ sq in. for open bus bars cooled by free convection

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 22

Editorial note, tabletop extrapolation: Brackets modern air-cooled small-magnet guidance from the 1940s operating side - mapped to the right geometry: the 2.5 A/mm^2 was for OIL-cooled calutron coils, and the 1.55 A/mm^2 for open bus bar with free-convection area a wound coil does not have. A passively cooled wound tabletop coil therefore belongs below both, in the ~1 A/mm^2 territory of the coil rules (dg-092), unless its own thermal test justifies more.

both the first cost and the power cost of a magnet increase almost proportionately with an increase in beam radius.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 24

Editorial note, tabletop extrapolation: Useful scaling honesty for any pole-diameter trade study — going from 8 to 13 in. poles at fixed final energy is a near-linear cost move, not a quadratic one, so long as the field comes down as the radius goes up.

Cited in: Choosing Your Machine

The forces tending to separate the halves are surprisingly large and if overlooked can be disastrous.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 19

Editorial note, tabletop extrapolation: Directly relevant to removable pole caps and bolt-on shim plates on a small H-frame: check the retention for lateral load wherever the joint geometry can see one - splits with a component parallel to the flux see spreading, while a complete cap on a plane parallel to the pole face mainly sees the axial pull. The formula is the diametral-split case, not every joint's.

Force on conductor (lb) = 1/1750 X kilogauss X amp X length (in.) Force between pole faces (lb) = 1/1.735 X (kilogauss)^2 X area (sq in.) Heating at center of conductor, degC = 0.00940 (Cu) / 0.00821 (Ag) X 10^6 X (inches of width of conductor)^2 X (amp/sq in.)^2

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. PDF 31 (printed p. 21), Table 1.1 'Magnet Design Data', TID-5215 Vol. 1

Editorial note, tabletop extrapolation: The 1.735 pole-force constant is the imperial twin of B^2/2mu0 and matches it to 1%; the hot-spot width formula is a one-line check before winding wide flat strip on a driver-amplifier-fed coil.

With the size and proportions of the gap selected from the foregoing considerations and the required field strength and uniformity determined, several magnet types could be conceived which might satisfy the requirements. ... After the type of magnet has been selected, it is possible to calculate approximately the weight of copper and steel

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. quoted principle on PDF 25 (printed p. 15) as cited; the order-of-operations sequence is on PDF 24 (printed p. 14), Sec. 6 'GENERAL DESIGN PROCEDURE'

Editorial note, tabletop extrapolation: Coils-near-gap is the reason cyclotron coils hug the poles rather than the yoke; the usable-fraction-of-pole-area argument is exactly the good-field-radius economics of a small machine.

Cited in: Choosing Your Machine

In accurate determinations of the absolute magnetic field intensity, only angular throws of 180 deg are considered satisfactory.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 72

Editorial note, tabletop extrapolation: The flip coil remains the cheapest absolute cross-check on a Hall probe - an NMR-free lab can tie its Hall calibration to a geometry-defined coil area plus a CALIBRATED integrator, provided the flip is a true reversal with aligned endpoints.

A 1 per cent change in the exciting current produces an error of only 1 per cent in the changes in the magnetic field.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 72

Editorial note, tabletop extrapolation: The classical answer to shimming with a wandering surplus supply: map relative structure differentially, pin the absolute scale with occasional flips. The cancellation assumes both coils see a common, effectively linear B(I) - check the local dB/dI, saturation and hysteresis on an iron magnet first. A two-channel Hall differential inherits the immunity only with simultaneous sampling and matched, temperature-stable channels.

stainless-steel filings (being slightly magnetic) sprinkled in this area will arrange themselves along the lines of force without accumulation.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 81

Editorial note, tabletop extrapolation: Historical techniques worth knowing, deployed with modern care: filings near a strong magnet accelerate and infiltrate - use them sealed in a flat transparent container, never near open vacuum hardware or the pole gap; the discharge-tube method needs a sealed commercial tube plus mercury/UV/HV precautions, and the machine's own ion source is not a movable substitute for it. As qualitative first looks before a probe survey, both still earn their keep.

a linear scale model built from steel with the same magnetic properties as planned for the prototype magnet and operated at the same field strength will give results directly applicable to the prototype.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 25

Editorial note, tabletop extrapolation: The physics that lets FEMM stand where models stood — and the terms of validity are the same for both: correct B-H data and correct geometry. Any cheap sub-scale mock-up of a planned magnet obeys it too, provided the steel matches and B is held, not NI.

since the X Beta model was built to 1/8 scale it seemed true that the results would be more accurate than those which could be obtained on a 1/16-scale model.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 149

Editorial note, tabletop extrapolation: The mesh-refinement decision in physical form: coarse resolution for excitation, force and leakage questions; fine resolution only for the finest field-uniformity region - spending fine-model effort on questions the coarse model already answers is waste in either medium. Accuracy also rides on geometric similarity, material scaling and construction error, not scale alone.

The usual measurements made included a magnetization curve, a comparison of gap performance at different points in the magnet, uniformity contour maps, determination of magnetic forces, the density of flux through various parts of the magnet

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 26

Editorial note, tabletop extrapolation: A ready-made deliverables checklist for a FEMM campaign on a new magnet: produce the quoted five (B-H behavior, gap comparisons, uniformity contours, forces, member-by-member flux audit) and add the modern staples - efficiency and leakage accounting and a stray-field map - as the extended set; the point is a defined deliverables list agreed before the runs, not after.

With 3400 oersteds in the gaps the efficiency obtained was 95.4 +/- 2.0 per cent. Within experimental error they were the same at both field strengths. This indicates that the magnet design is rather conservative.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 140

Editorial note, tabletop extrapolation: A two-point excitation scan (measured B vs I against the linear NI prediction) is the coarse global check on an H-frame - it flags that saturation is happening somewhere, not where: localizing the saturating member takes FEM or local flux measurements. Local saturation can also hide inside an unchanged global efficiency, so treat a clean two-point result as necessary, not sufficient.

By dividing the flux difference between any two loops by the area enclosed in the difference of the two loops, the average leakage flux density in that area can be calculated. Through the proper selection of pairs, either the vertical component of the leakage flux or the horizontal component may be found.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. PDF 142 (printed p. 132) for the quoted 10,000-15,000 gauss judgment (cited page 141 is off by one); method on PDF 140-143 (printed 130-133), Sec. 2.5 'Flux-density Measurements'

Editorial note, tabletop extrapolation: The 10-15 kG working band for structural mild steel is the same number modern small-magnet guidance gives (cf. Wouters; Zickler CAS) — and the loop-audit method is the measurement twin of integrating B over member cross-sections in a FEMM postprocessor: every member gets a number, every number gets a verdict.

the corresponding permeability would drop to 118, which is dangerously low. In certain localized regions it might even be lower.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 151

Editorial note, tabletop extrapolation: A quantitative 'too far' AS THAT PROJECT JUDGED IT: mu ~ 100-150 at the working point was their failure territory, fixed by 24% more iron. What a given magnet tolerates depends on its mmf budget and field-quality needs; the transferable instruction is auditing against the ACTUAL steel's B-H curve - the same reason a FEMM model of an H-frame is only as good as the B-H table fed to it.

It was found that when the number of turns on the end coils was 50 per cent of a full coil, the field in tanks adjacent to the yokes was 4.0 per cent low.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 139

Editorial note, tabletop extrapolation: The pattern transfers to any edge-compensation knob - outer-radius shim thickness, trim turns near a yoke window, correction-coil ampere-turns: measure the deficit at two settings, extrapolate linearly to zero as the FIRST estimate, then confirm with a third measurement - saturation and coupling bend the response, so one iteration is the hope, not the promise.

a steel faceplate was placed over the face of the core, as shown in Fig. 3.14, to spread out the flux evenly before it crossed the gap.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 141

Editorial note, tabletop extrapolation: The reason laminated or relieved pole structures carry a continuous pole face; applies to any lightening-hole or bolt-pattern pole cap on a small magnet - size the face sheet against saturation (thickness x permeability doing real work), don't just add a modest skin.

The magnetic forces were then combined with the force of the atmospheric pressure to give the total force. Magnetic force in tons = (kilogauss)^2 (area in square inches) / (1.735)(2000)

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. PDF 144 (printed p. 134), Sec. 2.6 'Magnetic Forces'

Editorial note, tabletop extrapolation: On a tabletop the same ledger is short but identical in kind — gap pull, atmospheric load on the chamber, unbalanced pull on any asymmetric iron — and the mean-of-squares point matters wherever the field is nonuniform over the loaded area (pole edges, shim steps).

the space between the tank and the cores must be great enough so that the maximum separation is never more than twice the minimum separation.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 146

Editorial note, tabletop extrapolation: Useful thinking for a shim pack, pole-cap seat, or chamber-lid-under-pole arrangement: a deliberately larger uniform standoff can pass where a tiny irregular one cannot - at the price of added reluctance (more ampere-turns for the same field), so treat enlarging the gap as a trade to compute, and validate the 2:1 criterion's adequacy for the new geometry rather than assuming the calutron number.

The magnetic performance of the track is better than predicted from the model experiment.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 191

Editorial note, tabletop extrapolation: The historical calibration point for a predict-then-verify magnet pipeline: one faithful same-steel scaled-model campaign landed close on global quantities and erred conservative because the prototype's iron out-performed the model's. One campaign is precedent for the METHOD - predict, then verify at full scale - not an accuracy guarantee for models or FEM in general: each pipeline earns its own error bars (dg-080's 3% benchmark, dg-817's first-beam case).

It would appear that the only feasible method of making corrections when the necessity arises is by trial and error.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 181

Editorial note, tabletop extrapolation: A 1944 warning that survives every FEMM run: analysis predicts changes to an as-built field only if the change is modeled as executed - and even then B-H uncertainty, hysteresis, stress and omitted 3-D features can dominate. Plan shimming as measure-cut-measure iterations with FEM as the starting estimate, and keep shim stock adjustable.

It was concluded from these tests that the force on the Alpha tanks tending to push them out of the gaps lies somewhere between 9.71 and 4.53 tons.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. force bracket on PDF 190 (printed p. 180) as cited; the quoted 2.5-in. creep sentence is on PDF 189 (printed p. 179)

Editorial note, tabletop extrapolation: Anything ferromagnetic sitting in or near the gap on nominal-symmetry grounds - chamber, probe carriages, shim plates, tools - needs positive mechanical retention: the destabilizing force is smallest at the symmetric position and grows as the part displaces, which is exactly when it is hardest to stop.

A check of the accuracy of this method was made by determining the same line twice, and this check indicated that the error was not greater than 1/16 in.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 192

Editorial note, tabletop extrapolation: Three habits for a home lab, each with its honest scope: repeat-trace to establish a method's REPEATABILITY (absolute accuracy needs an independent reference); calibrate the current meter, usually the floor of a B-vs-I curve; and normalize survey data to a monitor reading so supply drift cancels out of shape maps - valid once shape invariance over the current excursion is verified and the hysteresis cycle is reproducible.

C 0.15 per cent maximum, Mn 0.5, P 0.04, S 0.045, Si 0.2... Rowland ring was machined from... the same heat as the cyclotron magnet.

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (1951) — p. PDF p.14 (printed p.7), sections 3.1-3.2

Editorial note, tabletop extrapolation: For a next machine's magnet, low-carbon steel chemistry is worth a mill cert, and a sample ring (or bar) from the same stock measured on a cheap B-H rig turns FEMM's material curve from a guess into a measurement. Same measure-your-own-steel discipline as nyo-780.

(1) in the median plane the variation of the intensity with radial distance must conform closely to a fairly well defined relation, and (2) inside the exit radius ... the field must be accurately symmetrical

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (1951) — p. 14

Editorial note, tabletop extrapolation: DIRECT — the same decomposition (radial law, azimuthal symmetry, median-plane flatness) is how a tabletop field survey should be organized, each with its own instrument and its own fix.

the amount of testing required to arrive at a final shim design was much less than anticipated. This was due in part to the fact that the geometry of parts limited the possible variations more closely than was expected.

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (1951) — p. 17

Editorial note, tabletop extrapolation: With FEMM the model-magnet role is filled by simulation (ucrl-31 showed the scale-model method itself; MacKenzie AECD-1850 the model-test discipline), but the balanced verdict is the lesson — physical iteration budget should go where the computable model is least trustworthy (saturation, real steel, mechanical tolerances).

The steel for both the cyclotron magnet and the model was poured from the same heat and it can be assumed magnetic properties are identical.

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (1951) — p. 18

Editorial note, tabletop extrapolation: The transferable rule is representative material between test article and final article: a next machine's FEMM model should use a B-H curve measured on the actual purchased steel - on coupons matching the real stock's processing and orientation where possible - not a library curve for the nominal grade; same-heat stock reduces one variability source, it does not guarantee identity after different forging and machining.

the supporting structure for the coils failed, presumably under the magnetic forces. The coils became distorted and short circuits developed.

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (1951) — p. 19

Editorial note, tabletop extrapolation: DIRECT at any scale: coil-on-coil and coil-on-iron forces scale with NI and B and have crushed amateur windings - brace windings as if they will be pushed, not just held up. (The outer return-path steel in UW's recovery is that machine's expedient; whether added steel raises gap field depends on where the circuit's reluctance actually sits - FEMM answers it.)

drifting of the exciting current, inaccurate flipping, inconstancy of the fluxmeter, and temperature effects

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (1951) — p. 26

Editorial note, tabletop extrapolation: The differential trick ports to modern probes with its limits stated: two matched Hall/NMR channels read as a difference suppress the CORRELATED (common-mode) part of supply and thermal drift - each channel's independent drift, gain mismatch and temperature coefficient survive subtraction, so calibrate individually, synchronize acquisition, characterize the common-mode rejection, swap channels periodically, and anchor the percentage scale with an absolute reference reading.

at the exit radius the parameter n = - (r/B)(dB/dr) shall have the value 0.4.

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (1951) — p. 29

Editorial note, tabletop extrapolation: DIRECT as an as-built spec that produced a working field: UW's n = 0.4 exit value and ~1% monotonic interior droop sit in the same territory as this collection's Wouters and Livingston rules. Adopt the criteria's STRUCTURE as a FEMM shim-study objective - uniform interior, monotonic decrease, a defined extrapolation convention, a specified exit index - and set the NUMBERS from the machine's own stability and extraction analysis: 0.4 was their exit choice, not universal physics.

A 3 inch x 1/2 inch shim was used, and 25 inches was selected as the exit radius... a useable shape... of the induction between 13,900 and 15,000 gausses... reduced... by 1.2 per cent and 2.2 per cent respectively.

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (1951) — p. PDF p.30 (printed p.19), end of section 3.34 / start of 3.35

Editorial note, tabletop extrapolation: A variable-energy or B-scanned tabletop machine must verify field shape at the extremes of its intended excitation range, not just the design point - iron saturation moves the shim's effect as B changes.

the results indicated a force greater than 35 tons for the cyclotron magnet. For comparison the force of atmospheric pressure is 24 tons.

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (1951) — p. 30

Editorial note, tabletop extrapolation: A ferromagnetic chamber lid or pole-integrated cover sees magnetic clamping of the same ORDER as the vacuum load at tabletop fields (B^2/(2*mu0) vs one atmosphere - dg-177's arithmetic): check deflection in both states (energized and not) and expect assembly/disassembly forces. A non-magnetic lid opts out of the magnetic term entirely.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

showed that the model data could be used as a basis of prediction with confidence.

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (1951) — p. 33

Editorial note, tabletop extrapolation: The FEMM-era version — survey the bare magnet, reconcile with the simulation, THEN machine shims from the reconciled model. Same model-then-verify discipline as MacKenzie's aecd-1850.

The function of the spikes is to produce a sharp increase in the induction at the center of gap without producing a minimum anywhere in the radial dependence.

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (1951) — p. 33

Editorial note, tabletop extrapolation: A central field bump gives axial focusing in the first turns, where small machines lose most of their beam - and a machined center button is one of the cheapest beam-current experiments available. The no-minimum constraint is the careful part: model and map B(r), check the field index, isochronism cost, and RF/vacuum clearance before installing.

notably the bolts securing the one-inch thick sections of the cover plates, the screws holding the copper liners, and a gap where the shim is relieved to accommodate water lines, (3) accidental asymmetries in the construction and placing of the coils, and (4) non-uniformities in the steel

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (1951) — p. 33

Editorial note, tabletop extrapolation: An H-frame yoke is asymmetric by construction. Keep fasteners, liner screws, and cooling-line reliefs symmetric in the pole region; for unavoidable asymmetries, measure the azimuthal Fourier harmonics and judge them against orbit tolerances - a bare field survey doesn't by itself say the beam doesn't care.

this correction was made the criterion for final adjustment rather than reference to mechanical measurements.

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (1951) — p. 41

Editorial note, tabletop extrapolation: Shim the measured field, not the dial indicator: use the mapped field as the final acceptance criterion, calibrate shim sensitivity from the first iteration and extrapolate to plan the next, and expect a floor - every local correction has extended influence. Whether a given pole tilt is VISIBLE on a tabletop survey depends on gap, probe resolution and orbit radius, so establish the machine's own sensitivity from that first shim iteration rather than assuming thousandths show.

at smaller radii the field is uniform, while larger radii correspond to the conclusion of the acceleration process where misdirection of the beam does not have serious consequences.

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (1951) — p. 42

Editorial note, tabletop extrapolation: Sets a realistic bar as HISTORICAL performance: a carefully shimmed 60-inch-class iron magnet held azimuthal variation to a few parts in 1e4 over its working radii, and UW judged the spec at the radius that mattered dynamically (~80% in their machine - because inner radii were already uniform and the outermost turns tolerate misdirection). For a tabletop machine, pick the radius-weighting and the tolerance from its own orbit tracking and extraction plan; the UW numbers calibrate ambition, not the spec sheet.

an azimuthally symmetric field may still have a dish-shaped median surface.

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (1951) — p. 42

Editorial note, tabletop extrapolation: DIRECT physics: a displaced or dished magnetic median surface costs vertical aperture and can steer the circulating beam into a dee lid at small gap heights. Put a dip-needle analog (or vertical probe-pair difference) in the survey plan, keep deliberate shims matched top-and-bottom - and REMAP the median surface after shimming: symmetric shims avoid adding first-order asymmetry, but changed gradients can still move a pre-existing displaced surface. Needle details PDF p.44, map Fig. 3.13 p.45.

Sie bestimmt die maximal erreichbare Energie der Ionen und diese ist somit nur vom Magnetfeld und dem Radius der Austrittsbahn abhängig [tr.: energy depends only on field and exit radius]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 31

Editorial note, tabletop extrapolation: For 0.5 T and 10 cm usable radius, zeta = 0.05 T m gives ~120 keV protons; doubling either B or rho quadruples the ceiling. Low dee voltage doesn't lower it - but capture, phase acceptance and losses can keep the beam from ever reaching rho, which is the caveat behind 'regardless of dee voltage'.

Beträgt die Steifigkeit etwa 0,040 Tm, so liest man ab, dass die maximale Energie von Protonen ca. 76 keV [tr.: at 0.040 T m protons reach about 76 keV]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 31-32

Editorial note, tabletop extrapolation: Recomputed and correct: 0.040 T m gives ~76.6 keV protons; the same chart logic at 0.06 T m (0.6 T, 10 cm) gives ~172 keV. Read the geometry carefully: 1.0 T with a 40 mm orbit needs 40 mm of USABLE-FIELD radius - the physical pole must be larger, by the fringe margin the field map shows (dg-1382). Scale energy targets from rigidity, not from voltage.

Um den Magneten nicht zu überlasten, sollte er im Dauerbetrieb höchstens mit der Hälfte des maximalen Spulenstroms betrieben werden [tr.: run at no more than half the maximum coil current in continuous duty]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 37

Editorial note, tabletop extrapolation: For any other borrowed or surplus magnet, use its actual continuous-duty specification (maximum and continuous ratings differ) and verify winding temperature under your duty cycle - half-of-maximum is this book's conservative default when no continuous rating is known. The choose-field-by-homogeneity move transfers as stated; record the chosen point as a thermal/homogeneity compromise, not a hard limit.

Bei allen drei zentralen Feldstärken beträgt die relative Inhomogenität bei r = 70 mm maximal nur 0,02 % bzgl. B0 [tr.: at r = 70 mm the inhomogeneity is at most 0.02 percent of B0]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 35

Editorial note, tabletop extrapolation: The 0.02% figure is a commercial NMR-class magnet's vendor-chart datum at gap/pole-ratio 0.5 - a CANDIDATE uniformity level: check its adequacy against your machine's allowable cumulative phase slip and turn count, and confirm with a two-dimensional map (radial AND azimuthal) before concluding no shimming is needed; a home H-frame with a tighter gap will differ in both directions.

In den Deckel ist eine Vertiefung mit einem Durchmesser von 150 mm und einer Tiefe von 12 mm eingefräst. Dort befindet sich eine Hallsonde für die Messung der magn. Flussdichte. In diese Vertiefung wird der obere Pol des Magneten abgesenkt; so erhält die Kammer im Magneten einen festen Sitz. Außerdem konnte dadurch die Kammerhöhe auf ca. 72 mm verringert werden. Unter Berücksichtigung der Materialstärke beträgt der minimale Polabstand des Magneten schließlich ca. 75 mm. [tr.: a 150 mm diameter, 12 mm deep recess is milled into the lid. A Hall probe for measuring the flux density sits there. The upper pole of the magnet is lowered into this recess, giving the chamber a fixed seat in the magnet; the chamber height could thereby be reduced to ~72 mm, and allowing for material thickness the minimum pole spacing is finally ~75 mm]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 37, 57

Editorial note, tabletop extrapolation: Every millimetre of gap costs ampere-turns; the recessed-lid trick keeps the poles within a few mm of the dee envelope while fixing the chamber and giving the field probe a home. Size the recess floor (and any thin base) by an actual vacuum-vessel calculation - plate deflection and buckling for the real material and span - not by copying this machine's dimensions; and note the probe reads the field at the recess, not the median plane, so calibrate the offset.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

Da der Innendurchmesser des Dees 140 mm beträgt, hat ρ den Wert 70 mm und ist damit um 5 mm kleiner als der Polradius [tr.: dee ID 140 mm, rho 70 mm, 5 mm less than pole radius]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 37

Editorial note, tabletop extrapolation: Treat the 5 mm as this machine's geometric margin, not a rule: COLUMBUS runs a very LARGE gap-to-diameter ratio (75/150 = 0.5), so its field is far from flat at the edge anyway and the machine needs no extraction. For a 20 cm pole with a 2-3 cm gap the ratio is much smaller and the flat region proportionally wider - but the usable radius still comes from a measured or FEMM field map plus orbit-excursion and clearance checks, not from a fixed edge offset.

Es ist nämlich leichter, das Magnetfeld von 185 mT auf 370 mT zu erhöhen als die Frequenz von 2,82 MHz auf 5,64 MHz [tr.: easier to raise B from 185 to 370 mT than f from 2.82 to 5.64 MHz]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 37-39

Editorial note, tabletop extrapolation: A fixed-frequency resonator plus a 2:1 field range covers both hydrogen species IF the machine works at both fields - field quality, source output and capture must each hold at both points, so verify rather than assume. Two peaks at B and 2B are consistent with H+/H2+ but not unique to them (q/m degeneracy, dg-1432); use them as a species INDICATION to confirm.

Somit erhöht sich die Stoßrate und damit auch der Ionenstrom mit zunehmender magnetischer Flussdichte, wie Abb. 8.5 für 0 ≤ B ≤ 160 mT zeigt. Interessant ist der Abfall des Ionenstroms bei Magnetfeldern größer als ca. 160 mT. Eine Erklärung hierfür könnte darin liegen, dass sich die Plasmasäule nun noch weiter verengt und sich damit weiter vom Extraktionsschlitz entfernt. Dadurch sinkt die Extraktionsfeldstärke in diesem Bereich und der Ionenstrom nimmt wieder ab. [tr.: the collision rate and hence the ion current rise with increasing flux density, as Fig. 8.5 shows for 0-160 mT; interesting is the drop of ion current above about 160 mT - one explanation could be that the plasma column narrows further and moves away from the extraction slit, lowering the extraction field strength there so the ion current falls again]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 64-65

Editorial note, tabletop extrapolation: On a higher-field machine expect the optimum to sit elsewhere: scan source output against B and against slit position empirically. The narrowing-column picture predicts alignment sensitivity grows with field - a hypothesis worth testing with a slit-position scan, not a sub-millimetre tolerance to design to in advance.

Im Betrieb müssen die Spulen des Magneten mit Wasser gekühlt werden. Dies geschieht durch ein (von Schülern selbst entwickeltes) Kühlsystem, das mit Hilfe einer Heizungspumpe für den notwendigen Durchfluss von ca. 10 l/min sorgt. Ein Druckausgleichsgefäß stellt den notwendigen Betriebsdruck von ca. 1 bar während des Betriebs her. Sollte das Kühlsystem einmal ausfallen, so wird der Magnet über einen Notschalter abgeschaltet. [tr.: in operation the magnet coils must be water-cooled, by a student-built cooling system whose central-heating circulator provides the necessary ~10 l/min flow; an expansion vessel maintains the ~1 bar operating pressure; should the cooling fail, the magnet is switched off by an emergency switch]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 36

Editorial note, tabletop extrapolation: Size cooling from the measured coil loss, allowable winding temperature and coolant temperature rise - the 10 l/min is this magnet's number. A fail-safe interlock (flow AND winding temperature, arranged so failure trips rather than merely alarms) is cheap against a coil rewind; whether an air-cooled coil set needs duty cycling depends on its thermal design, not its power class.

Ein Steuergerät liefert eine zur Flussdichte proportionale Spannung, die für die weitere Auswertung verwendet wird [tr.: a controller supplies a voltage proportional to B used for evaluation]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 36, 70

Editorial note, tabletop extrapolation: A fixed probe reads ITS OWN location's field, not the median plane's: map the probe output against a median-plane measurement across the full operating range and both ramp directions (saturation and hysteresis bend the relation), fit the transfer curve, and carry its uncertainty into every specific-charge assignment - a one-point offset calibration is the minimum, not the goal.

Aus dem Diagramm 5.1 liest man für diesen Strom einen Wert zwischen 300–400 mT für die Flussdichte ab [tr.: for this current one reads 300-400 mT off Chart 5.1]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 35-37

Editorial note, tabletop extrapolation: A home H-frame with 20 cm poles and a 3 cm gap reaches ~0.6 T with 15-20 kAT, so this surplus-magnet class is a legitimate alternative to winding your own - check the actual coil topology (series vs parallel feeds change the current arithmetic) and take B from a measurement or the manufacturer's chart at YOUR gap.

Approximately 8 kilometers of 13 gauge copper wire were wound around the six inch pole pieces for the electromagnet.

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 15

Editorial note, tabletop extrapolation: A concrete scale anchor - kilometre-class wire on a hand-wound magnet is real, with the resistance and cooling that implies - but budget a NEW magnet from its own ampere-turn requirement, winding window, current density and duty cycle; pole diameter alone doesn't set wire length.

although a permanent magnet was considered for the Cyclotrino, it used an electromagnet because the field could be tuned

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 16

Editorial note, tabletop extrapolation: Field tunability is a resonance-hunting knob a permanent-magnet machine gives up - which it can buy back through RF adjustment, measured-field frequency selection, shims or trim coils; the precedent documents the convenience of the tunable field, not a prohibition on permanent magnets.

The magnet used was a 30.5 cm Varian NMR type electromagnet, which consumed 500 watts during operation at approximately 1 T. ... [Knox College:] The magnet was a nuclear magnetic resonance magnet with a maximum field of 2 T and approximately 20 cm diameter pole faces.

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 16

Editorial note, tabletop extrapolation: NMR magnets bring high field uniformity - their design point - and the Cyclotrino figure (500 W at ~1 T on a 30.5 cm machine; the survey does not specify whether 30.5 cm is the pole diameter) is strikingly low power for the field. Compare against a hand-wound H-frame only with gap, field volume and cooling on the table; the shopping advice that survives any comparison: check surplus NMR listings before winding coils.

This cyclotron utilized a 0.55 T electromagnet with pole faces 10.18 cm in diameter, and with an oscillating potential of approximately 2000 V, it produced hydrogen ions with kinetic energies of around 80 keV.

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 11

Editorial note, tabletop extrapolation: A 10 cm, half-tesla, 2 kV machine made beam - these numbers CALIBRATE one demonstrated design point; they are not independent minima (resonant acceleration works at lower field or voltage with corresponding changes in frequency, radius and turn count), so use them as an anchor for expectations, not a floor for feasibility.

for smaller machines a larger increase index is more appropriate, to provide stronger focusing

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 24

Editorial note, tabletop extrapolation: Budget the resonance-versus-focusing trade against the planned turn count quantitatively: integrate phase slip through the proposed B(r) for your turn count rather than assuming percent-level falloff stays cheap, and keep the index inside the weak-focusing stability window (0 < n < 1) everywhere the beam runs.

an interlock which shuts down the magnetic if less than 2.5 liters per minute of chilled water are supplied

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 36

Editorial note, tabletop extrapolation: The transferable pattern is the method, not the numbers: independent low-flow and over-temperature interlocks wired to POWER DOWN the load, with trip points derived from the coil's insulation limits or measured thermal performance (including sensor lag) - Houghton's 2.5 L/min floor and their coil ceiling are that machine's settings, not defaults.

The magnet, shown in Figure 20, is a GMW model 3473-70 with 15.2 cm pole faces and an [adjustable] pole gap of 0 to 9.9 cm ... The maximum current useable with the magnet is 70 A and at that current the magnet consumes 4.1 kW of power. The power supply however, a Powerten R62B-4050, can only support a maximum of 50 A, at which the magnetic field strength is 1.127 T

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 36

Editorial note, tabletop extrapolation: Anchors the mass/power/gap scale for buying rather than building a 15 cm magnet, and illustrates a procurement lesson worth internalizing: spec the supply WITH the magnet - a 70 A magnet behind a 50 A supply is a 50 A magnet.

The field was mapped using an acrylic disc, an aluminum disc that was marked with the 360 degrees of a circle, and a F. W. Bell 5070 Teslameter. The acrylic disc was milled to fit the aluminum disc such that they shared the same axis of symmetry, and so that the aluminum disc could rotate freely. The acrylic disc was attached to the lower pole face with tape ... The aluminum disc was milled to hold the Teslameter so that the probe could slide radially. ... because of the flaws in the Houghton College mapping apparatus and the probable misuse thereof

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 37

Editorial note, tabletop extrapolation: A two-disc rotary jig is an afternoon's shop work with systematic polar coverage - and this documented failure is the caution: validate the jig against a reference (manufacturer curve for the centre field; separate checks for probe calibration, angular registration, orientation and repeatability - the centre curve alone cannot validate the coordinates).

It was assumed that the magnetic field strength at all points would scale linearly with the magnetic field at the center.

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 36

Editorial note, tabletop extrapolation: One map plus one excitation curve replaces a full map at every operating point, a large time saving; the shortcut degrades as iron saturates, so maps taken near maximum excitation should be spot-checked rather than scaled.

It ranges from zero in the center of the magnet to almost 3.5 in the fringe field.

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 38

Editorial note, tabletop extrapolation: This magnet's measured profile - n near zero over most of the radius, rising steeply in the fringe - is what motivates shimming or pole shaping on flat-pole stock generally: no vertical magnetic focusing where n=0, local radial defocusing where n>1. Whether a given profile actually loses the beam is an orbit/tune calculation, not a glance at the n curve - run it before cutting shims.

The magnet yoke was soft iron scrap, and the pole pieces were 11.4 cm steel round stock which were then wound with 13.5 gauge wire.

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 16

Editorial note, tabletop extrapolation: A documented precedent that scrap return-path iron plus machined round-stock poles can serve a small machine - the machine as a whole made beam, though the survey doesn't isolate the magnet's contribution. For a new build, characterize candidate scrap (saturation, consistency, joints) and remember the return path needs cross-section, not pedigree.

[a] chamber with a diameter of 200 mm and a height of 75 mm. ... Diameter of the Dees 140 mm (5.5 in) Flux density 185 mT (H+) | 370 mT (H2+) ... Dee Voltage 0.5 - 3.0 kV Final Energy ~ 4,1 keV (H+) | 7,5 keV (H2+)

Wolf & Prechtl, COLUMBUS — A Small Cyclotron for School and Teaching Purposes — THPO001, Proceedings of Cyclotrons2022 (2022) — p. 2

Editorial note, tabletop extrapolation: A long-serving teaching machine running protons at half its field capability eases magnet, RF and matching demands at the cost of energy. The quoted energies imply a ~48-50 mm detection radius (nonrelativistic equilibrium-orbit calculation at the stated fields - a derived number, not a printed one); treat the table as the published 2022 configuration without assuming every entry is a measured operating value.

At the very beginning there were two big problems: How to get a magnet for the homogenous field and How to get a suitable vacuum-chamber. The first problem was solved by the Research Institute of Jülich. Prof. Dr. Maier and his team donated a Bruker BE-15. … The second problem was solved by VACOM, a company specialized in vacuum-components. VACOM built the vacuum-chamber, i.e. Fig. 1, for us free of charge.

Wolf, Frank & Held, COLUMBUS — A Small Cyclotron for School and Teaching Purposes — WE1PB03, Proceedings of Cyclotrons2013 (2013) — p. 1

Editorial note, tabletop extrapolation: For an educational build, soliciting institutional donations for the few components a home or school shop cannot make is a documented alternative to surplus-market hunting.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

The pole-diameter is 150 mm (~ 6 in). The pole pitch is adjustable from 50 - 120 mm (~ 2 - 5 in). The flux-density is up to 2 Tesla depending on the spacing of the poles. At a distance of 100 mm the flux-density is up to 0.7 Tesla.

Wolf, Frank & Held, COLUMBUS — A Small Cyclotron for School and Teaching Purposes — WE1PB03, Proceedings of Cyclotrons2013 (2013) — p. 1

Editorial note, tabletop extrapolation: When adopting a surplus laboratory magnet, the published pole diameter, pitch range and field-versus-spacing figures are the sizing inputs; the field available at the actual chamber-plus-walls spacing is the number that matters.

A flat field without flutter was selected since it is a simpler configuration for this very low energy and the high harmonic provides adequate electrostatic axial focussing

Clark, Halbach, Kunkel, Leung, Li & Young, A Compact Permanent Magnet Cyclotron for Accelerator Mass Spectrometry — Proceedings of Cyclotrons'95, Cape Town (1995) — p. 3

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: removing hills and valleys is viable at low energy only where the RF harmonic and dee geometry demonstrably supply the axial focusing the flutter no longer provides — the LBNL machine ran at harmonic 15 with electrostatic focusing doing that job. Verify axial stability by analysis or tracking before deleting flutter from a design; low energy alone does not guarantee it.

In this design H is 15 and the minimum number of orbits is 40, giving the required R = 1800 ... The magnetic field in the midplane is 1 T. For high mass resolution, the orbits need to be isochronous; a flat magnetic field uniform to about 2 parts in 104 must therefore be maintained

Clark, Halbach, Kunkel, Leung, Li & Young, A Compact Permanent Magnet Cyclotron for Accelerator Mass Spectrometry — Proceedings of Cyclotrons'95, Cape Town (1995) — p. 1, 3

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: sets the scale of what field quality buys — the source pairs 2e-4 flatness with 40 turns at harmonic 15 to reach R = 1800. A machine running few turns on the fundamental tolerates far looser fields; derive the flatness budget from turn count, harmonic, and the allowed cumulative RF phase slip, not by copying this figure.

The permanent magnets for each pole are grouped into 2 sections, the "crown" section and the "barrel" section. For example, as shown in Figure 4, for the upper pole the crown section is placed above the pole and directs magnetic flux down into the pole and gap. The barrel section is placed outside the pole and directs flux inward toward the pole and gap ... A cylindrical yoke completes the magnetic path

Clark, Halbach, Kunkel, Leung, Li & Young, A Compact Permanent Magnet Cyclotron for Accelerator Mass Spectrometry — Proceedings of Cyclotrons'95, Cape Town (1995) — p. 3

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: a proven topology for energizing round cyclotron poles from permanent magnets with no coil at all. The two magnet groups give two knobs (axial and radial flux feed) for setting field level and radial profile, but they are coupled through the shared pole, fringing and return yoke — set them with magnetic modeling and a field map, not as independent controls.

The pole is machined to high accuracy since it is what the gap "sees" and thus determines the accuracy of the magnetic field. The permanent magnet comes in blocks, which can be of coarser arrangement since they are farther from the midplane

Clark, Halbach, Kunkel, Leung, Li & Young, A Compact Permanent Magnet Cyclotron for Accelerator Mass Spectrometry — Proceedings of Cyclotrons'95, Cape Town (1995) — p. 3

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: concentrate the machining budget on pole faces and gap parallelism; commercial magnet blocks with ordinary tolerances are acceptable upstream of an iron pole — the key enabler for building a precise field from inexpensive stock magnets. The pole filters high-spatial-frequency block errors; low-order errors (remanence spread, block placement, gap and yoke asymmetry) still reach the midplane, so confirm with a tolerance analysis and a field map.

The permanent magnet comes in blocks, which can be of coarser arrangement since they are farther from the midplane

Clark, Halbach, Kunkel, Leung, Li & Young, A Compact Permanent Magnet Cyclotron for Accelerator Mass Spectrometry — Proceedings of Cyclotrons'95, Cape Town (1995) — p. 3

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: distance from the midplane is the tolerance relief for short-wavelength errors — block placement and discretization errors attenuate with distance, so the rough assembly sits far from the gap and the iron pole does the smoothing. Coherent and low-order errors survive the distance, and standoff costs flux; evaluate the needed distance and the residuals with a sensitivity model or a field map.

Initially, a program which analytically calculated the indirect and direct magnetic fluxes from various candidate configurations was used to define the dimensions of the magnets, poles, and yoke. The computer program POISSON was then used to verify and optimize this solution

Clark, Halbach, Kunkel, Leung, Li & Young, A Compact Permanent Magnet Cyclotron for Accelerator Mass Spectrometry — Proceedings of Cyclotrons'95, Cape Town (1995) — p. 3

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: the analytic pass explores the design space cheaply; the FEA pass is reserved for verifying one or two survivors. Free 2-D solvers fill the POISSON role today — noting that a 2-D axisymmetric model verifies the nominal design only, so discrete-block and assembly asymmetries need 3-D modeling or a measured field map.

within the acceleration region between 5 cm and 12 cm, the field is flat to within 7 parts in 104. This small deviation was anticipated since slightly larger than optimum barrel magnets were installed, to be cut back later for shimming

Clark, Halbach, Kunkel, Leung, Li & Young, A Compact Permanent Magnet Cyclotron for Accelerator Mass Spectrometry — Proceedings of Cyclotrons'95, Cape Town (1995) — p. 3

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: a margin in the removable direction is cheap insurance in a PM circuit — cutting blocks back is routine, adding material means buying new magnets. It is one trim mechanism among several (iron shims, flux shunts, repositioned blocks, correction coils); choose the adjustment mechanism and its planned range at design time rather than biasing every PM installation high by default.

After assembly, measurements of the magnetic field were made. These are shown in Figure 7. As can be seen, within the acceleration region between 5 cm and 12 cm, the field is flat to within 7 parts in 104 ... [Figure 7 caption:] Magnetic field measurements across 4 diameters in midplane

Clark, Halbach, Kunkel, Leung, Li & Young, A Compact Permanent Magnet Cyclotron for Accelerator Mass Spectrometry — Proceedings of Cyclotrons'95, Cape Town (1995) — p. 3, 4

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: two practices transfer directly — map along several diameters, not one, so azimuthal asymmetry of the PM assembly is caught; and where magnets were deliberately installed oversize, expect the first-assembly field high and outside final spec. This magnet's 7e-4 against a 2e-4 target is the pre-trim state, not the requirement met.

The field is slightly outside this range at a 4-5 cm radius, where the first 5 turns occur, but this contributes only a negligible amount of phase shift and axial defocusing

Clark, Halbach, Kunkel, Leung, Li & Young, A Compact Permanent Magnet Cyclotron for Accelerator Mass Spectrometry — Proceedings of Cyclotrons'95, Cape Town (1995) — p. 3

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: weight the flatness budget by turns spent at each radius — phase error integrates per turn, so a small out-of-spec zone crossed in a few turns can be tolerable while the many-turn outer region must meet spec. Confirm by computing cumulative phase slip and axial focusing through the zone; few-turn regions are not automatically free (coherent errors and resonance proximity can still matter).

The resulting loss in variability of the field strength is acceptable because the instrument is intended to be used for only one single ion mass with charge 1, although scaling of injection energy, rf frequency and dee voltage could be used to accelerate other ions ... No coils or power supplies and no cooling are required for the magnet. This reduces the utility requirements for the spectrometer system as a whole. This reduction and the small size and weight make the system "portable", conceivably permitting utilization in medical studies in hospitals, or for environmental monitoring in trucks or airplanes

Clark, Halbach, Kunkel, Leung, Li & Young, A Compact Permanent Magnet Cyclotron for Accelerator Mass Spectrometry — Proceedings of Cyclotrons'95, Cape Town (1995) — p. 1

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: a fixed-field PM magnet trades away tuning range — B fixes the orbit and RF frequency scale, and the electrical settings (frequency, dee voltage, injection energy) must be matched to it; they are matching parameters for reaching a different ion, not substitutes for field adjustment. Best suited to machines committed to one species and one configuration at a time. The cooling eliminated is the magnet's own; RF and other systems keep theirs.

calculations of the magnetic field using the computer program POISSON indicate that the field should be uniform to approximately +/- 2 parts in 104 throughout the acceleration region, and +/- 1 part for the majority of the trajectory

Young, Bertsche, Clark, Halbach, Kunkel, Leung et al., Development of a Compact Permanent Magnet Cyclotron for Accelerator Mass Spectrometry — Proceedings of PAC1993 (1993) — p. 3

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: axisymmetric 2-D FEA predicts the nominal field of an azimuthally symmetric PM magnet only — segmentation, assembly and material-variation errors are 3-D and need their own tolerance analysis or a measured map. The companion as-built paper (dg-1553) measured 7e-4 pre-trim, 3.5x this prediction, attributed to deliberately oversize barrel magnets awaiting cut-back — prediction and measurement reconcile only through that shim provision, not as direct agreement.

Magnet material, such as samarium cobalt, is placed in contact with the iron pole pieces. The iron concentrates and directs the magnetic flux to the pole faces. For one pole, the magnets are oriented so that the magnetization vector points toward the pole face. For the other pole piece, the magnets are oriented so that the magnetization points away from the pole face. A magnetic flux return ('yoke') connects the magnets to complete the circuit. The midplane of the accelerator is placed between these poles

Young, Bertsche, Clark, Halbach, Kunkel, Leung et al., Development of a Compact Permanent Magnet Cyclotron for Accelerator Mass Spectrometry — Proceedings of PAC1993 (1993) — p. 2, 3

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: the iron pole and yoke strongly shape the flux the blocks supply, but the gap field is set jointly by the magnetization layout and the iron circuit — model both. The two assembly-critical facts remain: consistent magnetization polarity per pole (toward one face, away from the other) and a properly closed flux-return yoke.

A typical hybrid dipole magnet (Fig. 1) consists of DT4E poles, yokes, Sm₂Co₁₇ permanent magnet blocks, a copper trim coil, outer tuning plates, NiFe alloy plates, and aluminum structural parts. In this configuration, the PM blocks provide the main magnetic field, while the trim coil allows for fine adjustment of the field strength within a limited range. This design significantly reduces power consumption compared to traditional electromagnets, while still preserving operational flexibility. To improve adaptability, an outer iron plate mechanism is incorporated for coarse field tuning ... to address the negative temperature coefficient of permanent magnets, NiFe alloy plates are placed near the magnet poles. These act as passive compensators to stabilize the magnetic field against temperature variations

Hsu, Jan, Chu & Lin, Integrating Permanent Magnets and Electromagnets — A Hybrid Dipole Magnet Design — WEBD3, Proceedings of IPAC2025 (2025) — p. 1

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: a small PM-based magnet need not be untunable — layering a modest trim coil and a movable iron shunt onto a PM circuit restores fine and coarse adjustment within a limited range (±1.25% fine on this prototype) at a small fraction of an electromagnet's power. Enough for drift, matching and calibration; not the wide excitation range of a full coil.

The trim coil is made of 2 × 3 mm2 copper wire and contains 42 turns ... The integrated magnetic field increases by approximately 0.086% for every 1 A of coil current (Fig. 4). With a coil current range of ±15 A, the magnetic field can be adjusted by approximately ±1.25%

Hsu, Jan, Chu & Lin, Integrating Permanent Magnets and Electromagnets — A Hybrid Dipole Magnet Design — WEBD3, Proceedings of IPAC2025 (2025) — p. 2

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: a prototype calibration datum, not a scaling law — coil authority depends on gap reluctance, yoke geometry, saturation and coil placement, so compute or measure d(BL)/dI for the actual circuit. Percent-level trim on a PM-driven iron circuit is the right order for covering temperature drift; whether it also covers assembly tolerance needs a tolerance budget, not an assumption.

the outer plate can be used to pre-adjust each magnet to a similar magnetic field before installation. Once installed in the accelerator, the trim coil can then be used for final fine-tuning during operation ... This gap is adjusted using aluminum spacers of different thicknesses ... When the outer plate gap is reduced from 10 mm (baseline) to 0 mm, the integrated field increases by about 1.85%. Conversely, when the gap increases to 20 mm, the integrated field decreases by around 0.14%. This coarse tuning method is simple yet effective during magnet pre-alignment and calibration

Hsu, Jan, Chu & Lin, Integrating Permanent Magnets and Electromagnets — A Hybrid Dipole Magnet Design — WEBD3, Proceedings of IPAC2025 (2025) — p. 1, 2

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: a movable external iron shunt is a zero-power, percent-class field adjuster where the circuit geometry gives it authority — verify with a model or measurement for the specific circuit. Note the strong asymmetry in the prototype data: closing the 10 mm baseline gap gained 1.85%, opening it by the same 10 mm lost only 0.14%, so nearly all the authority lies on the closing side.

Ni30Fe70 alloy plates are used to passively compensate for the temperature dependence of the PMs. These plates are placed near the magnet blocks and tested in a temperature-controlled environment (Fig. 6) that includes heaters, fans, and acrylic covers. At 20 °C, every 2 mm increase in NiFe plate thickness (Fig. 7) reduces the integrated magnetic field by 0.4%. Without NiFe plates, the field drops by 0.043% per degree Celsius. With 4 mm thick NiFe plates, this drop is reduced to 0.027% per degree

Hsu, Jan, Chu & Lin, Integrating Permanent Magnets and Electromagnets — A Hybrid Dipole Magnet Design — WEBD3, Proceedings of IPAC2025 (2025) — p. 2

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: uncompensated PM field drift of order 4e-4 per degree Celsius matters wherever the resonance condition is fixed. Low-Curie-point NiFe shunt material trades a known static field loss (0.4% per 2 mm of plate here) for a 37% drift reduction on this prototype (0.043 to 0.027% per degree), with thickness as the design variable — characterize the tradeoff for the chosen magnet and compensator materials rather than copying these numbers.

These blocks (Fig. 2) are not formed as a single piece, but are assembled by gluing smaller magnetized units together. This method allows us to fabricate magnets in flexible sizes and shapes, while maintaining field performance. Dimensional tolerances and flux consistency were kept within acceptable ranges based on simulation results

Hsu, Jan, Chu & Lin, Integrating Permanent Magnets and Electromagnets — A Hybrid Dipole Magnet Design — WEBD3, Proceedings of IPAC2025 (2025) — p. 1

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: small stock magnets glued into arrays are a legitimate substitute for expensive custom blocks when grade, magnetization vector, polarity, dimensions and bonding are controlled. Set the dimensional and per-block flux acceptance from a simulation of their field effect, as the source did, and verify the assembled magnet with a field map — a spot gaussmeter reading is a screen, not a flux acceptance test.

In non-magnetic assembly, the yoke and pole are first aligned and fixed, and the PM blocks are inserted afterward. In this project, we used the first method, with magnetic force. Because the magnetic attraction during assembly can exceed several hundred kilograms, this process presents engineering and safety challenges. To address this, we developed a systematic and repeatable assembly process using custom-designed fixtures. We also found that applying a reverse magnetic field during the process can help reduce the attractive force and make the assembly smoother. The fixtures include mechanical guides, magnetic shielding, and locking mechanisms to ensure safe, controlled, and staged installation

Hsu, Jan, Chu & Lin, Integrating Permanent Magnets and Electromagnets — A Hybrid Dipole Magnet Design — WEBD3, Proceedings of IPAC2025 (2025) — p. 2

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: methods that transfer at any scale — never free-hand strong magnets toward iron; use guided, locking fixtures that control the approach axis and stage the force; and consider the insert-magnets-last sequence or a bucking field when the full-force path is unmanageable. A reverse field applied to PM material must stay well inside the magnets' coercivity and recoil limits and brings its own stored energy — model the forces and limit the current before relying on it.

The magnet prototype is 150 mm in length. At room temperature (20 °C), the measured central magnetic field is 0.7545 T, and the integrated field is 0.13964 T·m. These measurements (Fig. 3) closely align with the simulation predictions, confirming the accuracy of both the magnetic and mechanical design ... [Figure 3 caption:] Z scan of magnetic field measurement

Hsu, Jan, Chu & Lin, Integrating Permanent Magnets and Electromagnets — A Hybrid Dipole Magnet Design — WEBD3, Proceedings of IPAC2025 (2025) — p. 2

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: measurement-versus-simulation agreement on a field scan is a core acceptance test that closes a PM magnet build — one test, complemented as applicable by alignment and repeatability checks, integrated-field or multipole mapping, and temperature characterization. Quoting the measurement temperature alongside the value is essential practice for PM systems because of their temperature coefficient.

The magnet current was determined with a Type K potentiometer operating across a 0.0005 ohm manganin shunt. The center magnetic field (B0) was accurately correlated with the magnet current by means of a nuclear resonance gaussmeter. All field measurements were accurate and reproducible to better than four gauss out of 17,000.

Burns, Experimental Program with the Iowa State University Undergraduate 1.5 Mev Cyclotron — Proceedings of the Iowa Academy of Science 68(1), 483–491 (1961) — p. 3

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: current-based field setting calibrated against an absolute probe remains the economical pattern — run it with a fixed ramp/history procedure and periodic probe rechecks, since hysteresis, magnetic history, temperature and supply drift all move the current-to-field calibration. This 1961 undergraduate machine got few-gauss reproducibility from a shunt, a potentiometer and an NMR probe.

The magnetic field (B1) at which the ions are in exact cyclotron resonance at the r.f. supply frequency (f1) is given by the cyclotron resonance equation, B1 = 2πmf1/e (MKS units) ... The difference between the actual center field value (B0) and the field B1 at some larger radius r1 is defined as the tune-down (δB): δB = B0 − B1 ... Fig. 2 shows that with r2 less than 8 cm, δBm is observed to be zero. As r2 is increased, the peak of the resonance curve (Bm) is seen to shift to the right and δBm increases. This shift is in agreement with theory and is due to the drop-off of the magnetic field strength with increasing radius ... [Figure 2 axis label:] B1=16,830 gauss

Burns, Experimental Program with the Iowa State University Undergraduate 1.5 Mev Cyclotron — Proceedings of the Iowa Academy of Science 68(1), 483–491 (1961) — p. 3-5

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: tune-down versus probe radius is a beam-based check on the integrated field profile — how much extra center field the ions need to stay near resonance out to a given radius. Compared against a curve computed from the field map with an orbit-and-phase model (RF-frequency error, injection phase and centering included), it is an end-to-end consistency check of field survey plus orbit model, not a standalone field measurement. The source itself rates δBm as less well established than the curve widths, with uncertainties over ten percent possible from reading Bm off the graphs.

The study of the beam height was carried out before the magnetic field was adequately regulated, and the results are only qualitative ... The experimental measurement of the width of the resonance curve shown in Fig. 2 was the most accurate part of the program. The curves were reproducible, and the maximum error in their widths amounted to only a few per cent.

Burns, Experimental Program with the Iowa State University Undergraduate 1.5 Mev Cyclotron — Proceedings of the Iowa Academy of Science 68(1), 483–491 (1961) — p. 6

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: field-supply regulation bounds every beam measurement made through a field sweep — verify that field stability is small against the required measurement uncertainty before quantitative field-sensitive scans. Data taken before the supply is stabilized will likely have to be repeated.

It was found that changes in the magnetic field strength of only a few gauss can result in a large reduction of the beam strength ... it can be noted in Figure 4 that the interval of δB values for which the relative intensity, I, is equal to 1 decreases with increasing target radius

Mueller, Proton Orbit Calculations for the Iowa State University Cyclotron — Proceedings of the Iowa Academy of Science 68(1), 492–501 (1961) — p. 2, 9

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: period support for gauss-level (parts-in-1e4) field-tolerance thinking in small-cyclotron design — computed for this machine's field profile, voltage and phase model, and consistent with its companion measured tuning curves. For another machine, derive the allowable field error from its own field map, RF voltage, turn count and phase-slip model, or measure it with an intensity-versus-field sweep. The transferable lesson is that the tolerance comes out in gauss rather than percent — the budget itself must be computed, not copied.

The gradient, ∂B/∂r, of the magnetic field of the ISU cyclotron was measured with the field and gradient meter developed by Thoburn (5). The magnetic field, B, was obtained by numerical integration of this gradient.

Mueller, Proton Orbit Calculations for the Iowa State University Cyclotron — Proceedings of the Iowa Academy of Science 68(1), 492–501 (1961) — p. 5

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: orbit quantities (focusing, phase slip) depend on the gradient, and numerically differentiating a noisy point-by-point field survey amplifies error — measuring the gradient directly, or fitting before differentiating, is the robust order of operations for gradient-dependent quantities. The integration to B(r) needs an absolute anchor (a calibrated field value at some radius) and accumulates probe baseline and spacing errors, so check the integrated map against independent absolute-field measurements. A two-coil differential probe is buildable at hobby scale.

When n = −(r/B)(∂B/∂r) = 0.2 a resonance condition occurs between the vertical and radial oscillations of the proton. This resonance which occurs at r = 10.1 cm in the ISU cyclotron is possibly responsible for a major loss in beam intensity at large radii ... The effect of the resonant condition, n=0.2, is difficult to determine. The resonant condition does not occur until r=10.1 cm. At this point the beam intensity is quite low already; a detailed experimental study is to be carried out later

Mueller, Proton Orbit Calculations for the Iowa State University Cyclotron — Proceedings of the Iowa Academy of Science 68(1), 492–501 (1961) — p. 8

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: compute the radius where the measured field profile crosses n = 0.2 and treat it as a resonance-warning radius — whether appreciable coupling loss actually occurs there depends on coupling strength, crossing rate, field errors and orbit centering, so confirm with tracking or a transmission measurement before writing the region off. On steep-edged small poles this radius can arrive well inside the pole edge.

z ~ A = [πeV0 sin θ/E − π²er(∂Bz/∂r)/Bz]^(−1/4) (3) The envelope of these oscillations is given by Z = kA/Amax (4) where k is one-half the dee height and Amax is the maximum value of A ... It can be noted that the beam height does not change considerably with a change in the tune-down. In Equation 3 the second term is dominant for radii greater than 6 cm. Hence, the beam height is dependent almost completely on the ratio of the gradient of the magnetic field to the magnetic field. In the ISU cyclotron, which has a relatively large magnetic field gradient, the beam height vs. radius curve is approximately linear for radii greater than 6 cm

Mueller, Proton Orbit Calculations for the Iowa State University Cyclotron — Proceedings of the Iowa Academy of Science 68(1), 492–501 (1961) — p. 10, 11

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: the field map gives the relative axial-envelope shape — in this model beam height at radius follows (dB/dr)/B and barely responds to tuning — but an absolute vertical target size also needs the injected vertical phase space, apertures and RF-gap focusing propagated through. Use the map for the envelope shape and the compression trend; a pronounced field droop buys strong axial compression toward the target radius, at the cost of phase slip.

A magnetic field approximation developed by Dr. D. E. Hudson was used in this study. This relationship is shown graphically in Figure 2; the mathematical expression is: (2) B(r) = [17,000 + 0.25cm−2r2 + 0.232cm−3r3 − 0.0118cm4r4 + 6.21cm−11.6 10−10 r11.6] gauss.

Moses, Proton Orbits in a Small Cyclotron — Proceedings of the Iowa Academy of Science 70(1), 403–414 (1963) — p. 4

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: an analytic field fit gives an orbit integrator smooth, differentiable input — critical because focusing depends on dB/dr — and the polynomial-plus-steep-power form captures the flat-center/sharp-edge shape typical of small unshimmed poles. The same functional form fits modern FEA field maps. Before using any transcribed fit, verify it reproduces the source's own quoted landmarks (here, n = 0.2 at r = 10.1 cm).

[Drawing IUAC/CYCLO/11, sheet 1 of 1:] POLE TIP-SPARE ... QTY: 02 NOS ... 310.00 ... 35.00 ... Magnet steel-AISI-1010 ... 15 Kg [cf. IUAC/CYCLO/10 POLE TIP-1: 305.0 +/-0.2, 30.00 +/-0.02, 17 Kg]

IUAC, e-Tender 09/GOR/2024–25 — H-Dipole Water-Cooled DC Electromagnet for the Table-Top Cyclotron: Engineering Specification and Acceptance Tests (2024) — p. PDF pp.18 and 29 for the text (printed 18, 29); drawing IUAC/CYCLO/11 is PDF p.57 (printed 57, Annexure-L)

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: a professional lab building a teaching machine chose exactly the H-frame, ~1.2 T, ~30 cm pole class that amateur cyclotrons occupy — and made removable pole shoes plus a spare set a procurement line item, the natural hedge for the shimming and re-profiling iterations small magnets commonly need. Pricing spare pole stock alongside the main steel order is insurance worth evaluating on any build.

[Magnet data table:] Field homogeneity at the median plane — better than 18 x10-3 up to radius of 120 mm (expected as per simulation) ... Field mapping in the median plane of the magnet should be carried out. Homogeneity of the magnetic field at different radial and angular positions w.r.t. the central field (B/B) shall be measured and compared with the results obtained using simulations ... Homogeneity of B/B ~18x10-3 over a radius of 120 mm of the pole is required as per design

IUAC, e-Tender 09/GOR/2024–25 — H-Dipole Water-Cooled DC Electromagnet for the Table-Top Cyclotron: Engineering Specification and Acceptance Tests (2024) — p. 13, 18

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: a design/spec number from a modern professional team for a small teaching cyclotron — 18e-3 out to ~79% of pole radius, expected from simulation and verified by mapping at acceptance. Context for what an unshimmed as-designed pole can look like, not a target to copy: derive the field-quality requirement from the machine's own phase-slip and orbit tolerances (the ISU worked example, dg-1547/dg-1588, ran at 2e-4), and give the mapping instrument resolution substantially finer than whatever criterion it must verify.

[Coil Data table:] Total Magnetizing force (for two coils) — 64800 Ampere-Turns; No. of coils — 02 (Top and bottom); No of turns per coil — 162; Conductor size — 10 mm x 10mm x 6 mm diameter bore (OF-OK oxygen free copper grade ASTM C10200); Operating Current — 200 A; Approximate total length of one coil — 214.5 m; Approximate weight of one coil — 135 Kg; Approximate resistance per coil — 0.05 Ohm; Approximate operating voltage (for two coils) — 20 V

IUAC, e-Tender 09/GOR/2024–25 — H-Dipole Water-Cooled DC Electromagnet for the Table-Top Cyclotron: Engineering Specification and Acceptance Tests (2024) — p. 18, 19

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: a complete, self-consistent coil design point (ampere-turns, turns, current, conductor, resistance, voltage, mass) published with enough detail to scale from — sitting just above the 0.6-1 T fields most amateur machines run. The low-voltage high-current choice (about 20 V at 200 A for ~4 kW total) shows a water-cooled hollow-conductor solution where amateur designs often accept hotter air-cooled solid-wire coils; scaling it needs the magnetic-circuit, thermal, ampacity and hydraulic calculations redone for the new geometry.

machined preferably from single solid piece of soft Iron, low carbon, high quality magnetic steel (e.g. AISI-1010 or its equivalent or better) ... [Table-2, typical chemical composition:] C ≤ 0.1%; Mn ≤ 0.450%; Si ≤ 0.02%; N 0.005%; Balance: Iron ≥ 99.18% ... [Table-3, magnetic properties:] Maximum value of relative permeability > 5000; Coercive Force 60-120 A/m; Saturation Induction 2.15 T ... The material supplier should provide (i) ultrasonic test report of supply material as per EN 10160 class S1/E1 or ASTM A578 or any applicable international standard ... the material shall be procured and utilized only after receiving the written approval from IUAC

IUAC, e-Tender 09/GOR/2024–25 — H-Dipole Water-Cooled DC Electromagnet for the Table-Top Cyclotron: Engineering Specification and Acceptance Tests (2024) — p. 20

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: concrete, checkable acceptance numbers for magnet iron — chemistry, permeability, coercivity, saturation — rather than the vague 'low-carbon steel' guidance common in amateur builds. Approving mill certificates and a sample B-H curve before purchase is a method any builder can copy when buying nominal 1010-class stock; the certificate check is what catches near-misses — common 1018 stock (0.15-0.20% C) fails this chemistry outright, and a trade designation alone guarantees neither the permeability nor the coercivity row.

The excitation curve (measured magnetic field versus current) of the electromagnet should be measured from 0 to maximum current of 220 A (10% higher than the nominal value of 200 A) at a step of 10 A, keeping the Hall probe positioned in the median plane of the magnet, at the centre of the pole. This excitation curve should be recorded at each excitation level of the current and the measured magnetic field.

IUAC, e-Tender 09/GOR/2024–25 — H-Dipole Water-Cooled DC Electromagnet for the Table-Top Cyclotron: Engineering Specification and Acceptance Tests (2024) — p. 13, 26

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: the transferable protocol is the shape, not the numbers — sweep in defined steps to a test current the design's ratings explicitly allow, probe fixed at a defined reference point, every level recorded with temperature and cooling conditions. Read saturation from the change in slope dB/dI of the recorded curve, not from an assumed percentage overhead; driving another magnet 10 percent past nominal without checking coil, cooling and supply ratings is not part of the method.

Field mapping in the median plane of the magnet should be carried out. Homogeneity of the magnetic field at different radial and angular positions w.r.t. the central field (B/B) shall be measured and compared with the results obtained using simulations. Deviation in the parallelism of the pole faces, deviation in the horizontal positions of (top and bottom) pole centres beyond the limit of the tolerances would be directly reflected by the loss of symmetry in the measured data of the magnetic field on the either sides of the pole centre.

IUAC, e-Tender 09/GOR/2024–25 — H-Dipole Water-Cooled DC Electromagnet for the Table-Top Cyclotron: Engineering Specification and Acceptance Tests (2024) — p. 43

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: treats the field map as a mechanical diagnostic, not just a pass/fail check — left/right asymmetry about the pole centre points to gap or centring errors before any disassembly, and comparing the measured map to the simulation closes the loop on the field computation the design was based on. Asymmetry is not a unique signature, though: rule out probe alignment and mapping-coordinate errors (repeat maps, reversed scan directions) before blaming the iron.

The upper pole and lower pole of the magnet shall be concentric within ± 0.1 mm. The parallelism between the top and bottom poles shall be within ± 50 microns ... [spec table:] Pole gap — 51±0.05 mm (Nominal) ... Pole gap and pole dimensions should be measured by CMM ... Measurement of radial offset between the upper and lower half magnets

IUAC, e-Tender 09/GOR/2024–25 — H-Dipole Water-Cooled DC Electromagnet for the Table-Top Cyclotron: Engineering Specification and Acceptance Tests (2024) — p. 13, 18, 41, 43

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: quantifies the assembly precision a professional team demands so the field-homogeneity spec survives bolting-up — tenth-millimetre concentricity and 50 micron parallelism. Within reach of careful amateur fitting, but verifying them takes a defined datum scheme and suitable metrology (surface plate and indicator for parallelism; concentricity needs a datum-referenced measurement, not a bare dial indicator). Use the list as the inspection checklist, with each machine's own tolerances derived from its field spec.

The magnet coil shall be excited using with rated current for 24 hours to achieve the maximum field of 1.2 Tesla for long term stability ... The long term temperature stability of the coils (48 hours) should be monitored together with the magnetic field to ensure no variation in the magnetic field is observed. Safety interlocks for testing the temperature sensors should be confirmed ... The local hot spots, evidence of overheating and other faults during the testing shall be recorded.

IUAC, e-Tender 09/GOR/2024–25 — H-Dipole Water-Cooled DC Electromagnet for the Table-Top Cyclotron: Engineering Specification and Acceptance Tests (2024) — p. 26, 43

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: couples thermal soak testing to field measurement — coil heating can move the field through gap-geometry changes and through supply-regulation limits (a current-regulated supply removes the resistance path but not the geometric one), so stability is proven with field and temperatures logged simultaneously. The transferable method is concurrent logging with staged current increases; set soak durations from the coil's measured thermal time constants and equipment ratings rather than copying 24/48 hours, and have fault protection validated before any long unattended run.

The designed field has been modelled with CST Microwave Studio for 3D and POISSON code for 2 D related designs. The final measured value should match the designed value of 1.2 T. Relevant documents of design can be supplied, if the vendor requires during technical bid discussion.

IUAC, e-Tender 09/GOR/2024–25 — H-Dipole Water-Cooled DC Electromagnet for the Table-Top Cyclotron: Engineering Specification and Acceptance Tests (2024) — p. 43

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: confirms that a modern professional teaching-magnet design still rests on a 2D POISSON-class solve cross-checked in 3D — the same two-tier workflow available to amateurs through free 2D field solvers plus selective 3D checks. The acceptance criterion is written against the simulation, making the model the effective contract baseline — though 'match the designed value' is stated without a numeric tolerance, which a real acceptance procedure needs.

The IUAC personnel will witness and participate in the complete process of fabrication, testing and field mapping of the electromagnetic system at the vendors site ... The final acceptance of the system is defined as successful supply, installation and acceptance tests at IUAC to substantiate compliance with the specification ... All testing equipment shall be arranged by the vendor at no extra cost ... After shipment to IUAC, the magnet will be tested by IUAC personnel with full power to check the magnetic field is maintained as per design, before releasing the payment.

IUAC, e-Tender 09/GOR/2024–25 — H-Dipole Water-Cooled DC Electromagnet for the Table-Top Cyclotron: Engineering Specification and Acceptance Tests (2024) — p. 13, 15, 26

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: a clean template for outsourcing a magnet build while keeping engineering control — approve materials and drawings first (the steel goes through written approval before procurement, dg-1612), witness the factory tests, repeat the field checks at full power after shipping, and only then accept and pay. Anyone commissioning a magnet from a job shop can scale down the same factory-then-site structure.

Stability of power supply, at least 100 ppm ... [compliance sheet:] Equipment required for field mapping: a) 3D magnet field mapping system with Hall probe, associated control software for the field mapping ... DC Power supply rating: Voltage: 20V, Current: 200 Amps ... CMM and allied measuring instruments ... In-house electrical testing facilities: Insulation Resistance, Hipot Test, Inductance ... Inhouse Hydraulic Testing Facility for Coils ... Note: Final Testing of assembled magnet will be performed at supplier premises, hence supplier is required to provide a list of testing facility available in-house.

IUAC, e-Tender 09/GOR/2024–25 — H-Dipole Water-Cooled DC Electromagnet for the Table-Top Cyclotron: Engineering Specification and Acceptance Tests (2024) — p. 40, 41

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: the equipment list doubles as a checklist of what a serious small-magnet test stand contains, and 100 ppm shows what a professional team asks of a mapping/energizing supply. It is one machine's specification, not a universal requirement: derive the allowable current stability from the machine's own B-I slope, field tolerance and RF phase-slip budget — the answer is usually far tighter than an unregulated bench supply but need not be 100 ppm.

Fig. 9 Differing ion launch heights simulated in SIMION, green dots are location of measured peaks and valleys (dots heights are not representative of data height). Note height of DEE lid is at 36 mm. Also note beam blow up at r = 110 mm, this is where n = 0.2 resonance resides, see reference [2].

Koeth, Hanebuth, Hoffman & Schneider, Rutgers 12-Inch Cyclotron Ion Source Studies: Part II (2007) — p. 4

Editorial note, tabletop extrapolation: Both numbers are read from the figure and its caption. The transferable point is the method it illustrates: the useful radius of a weak-focusing machine is bounded not by the pole edge but by where the field index reaches a resonant value — on THIS machine, n = 0.2 at r = 110 mm of a 152 mm pole radius, and the simulation blows up there. Map your own n(r), find your own resonance radii, and place target and deflector inside the demonstrated usable radius; where n = 0.2 lands is your taper's choice (dg-1729).

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

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

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

Initially, to satisfy the cyclotron resonance condition, the pole tips of the 12-Inch Cyclotron magnet were Blanchard ground to provide parallelism to better than 1 part in 10,000. As will be seen, this pure vertical field does not provide any beam focusing effects, all but a very few of the generated ions are lost on either the top of bottom plate of the DEE. Indeed, during commissioning of the cyclotron, only a trickle of beam current, less than a nano-ampere, made it to the periphery. Desiring beam currents of at least 10µA in intensity, a program to study and modify the cyclotron to achieve this goal is under way.

Koeth, Report on the 12-Inch Cyclotron Magnet Study: Measurements, Modeling, and Future Plans (c. 2005) — p. 1

Editorial note, tabletop extrapolation: The canonical educational-machine failure mode, and a machining-quality trap in reverse: extreme pole parallelism is exactly what leaves the beam without an axial restoring force (radial stability, with tune near 1, survives — it is the vertical plane that empties into the lids). The sub-nA periphery current is this machine's measured commissioning figure, a realistic 'before' anecdote rather than a class-wide baseline; the 10 µA goal is the authors' aspiration, not an achieved value anywhere in this document.

After much debate, a simple linear tapered pole tip design with an overall 2% decrease of Bz was settled upon. The magnet gap was to increase radially, starting from a minimum of 2.010 inches at r = 0 to 2.018 at r = 5.0 inches, the maximum possible ion radius. The author obtained the needed soft 1006 iron material. The pole tips were machined with azimuthal symmetry about r = 0.

Koeth, Report on the 12-Inch Cyclotron Magnet Study: Measurements, Modeling, and Future Plans (c. 2005) — p. 1

Editorial note, tabletop extrapolation: The Rutgers retrofit geometry, fully dimensioned: a 0.008-inch gap opening (computed: 2.018 − 2.010) over 5 inches of radius on a ~2-inch gap, cut in soft 1006 iron, targeting a 2% Bz droop. Two readings for your own design: the tolerance implication — pole-face errors must be small against 0.008 inch or they swamp the intended index — and the method: calculate or map YOUR Bz(r), derive n(r), and iterate by shim or re-cut, because the field response to a given taper belongs to the whole magnetic circuit, not the taper alone. The 2% is the design target; the source's own profiles fall considerably more by r = 5 inches once pole-edge fall-off is included.

Complete transverse stability. It has thus been shown for axial stability, n must be greater than 0, and for radial stability n must be less than 1. Total transverse stability exists in the region of: 0 < n <1

Koeth, Report on the 12-Inch Cyclotron Magnet Study: Measurements, Modeling, and Future Plans (c. 2005) — p. 3

Editorial note, tabletop extrapolation: The design inequality for a weak-focusing machine, derived in this report from scratch: away from the central region, 0 < n < 1 buys simultaneous linear axial and radial stability (at r = 0 itself n = 0, as the source's own next passage states — the center is handled by other means, dg-1729/dg-1835). It is a LOCAL linear-stability window: resonances (dg-1682), acceleration and field errors still get their say. Sign convention: this document's leading minus makes n > 0 a falling field; the companion AVF paper uses k = d ln⟨B⟩/d ln R with opposite sign, so reconcile n = −k before mixing formulas.

For details beyond the scope of this document, coupled resonances between the transverse motions further limit the value of n. n values of 0.2, 0.25, 0.33, 0.5 (and others higher) need to be avoided. Since, the ions to be accelerated begin at r = 0, n = 0 and will only climb as the radius increases. If n = 0.2 needs to be avoided, then the rate at which Bz decreases must be moderated such that only near the maximum ion radius does n approach 0.2.

Koeth, Report on the 12-Inch Cyclotron Magnet Study: Measurements, Modeling, and Future Plans (c. 2005) — p. 3

Editorial note, tabletop extrapolation: Actionable sizing constraint for a taper design: it converts 'make the field droop' into 'droop slowly enough that the low-order resonances arrive only at the very end of the spiral.' The printed n list is physically standard — at n = 0.2 the tunes satisfy νr = 2νz (the Walkinshaw difference coupling), at 0.25 νz = 1/2, at 0.33 νr = √2·νz, at 0.5 νr = νz (all computed from νz = √n, νr = √(1−n)). Note the same document's p.7 attaches 0.2 and 0.5 to νz instead — the source is loose with its labels across pages, so identify resonances from BOTH tunes computed off your own n(r), never from a symbol's name.

In order to achieve this difficult goal, a Hall probe was mounted on a platform that was threaded onto a long screw (~12 in.) whose motion was driven by a computer-controlled stepper motor. This entire unit was set upon three adjustable “leveling” screws protruding from an aluminum mounting fixture secured to the bottom pole of the magnet. An aluminum fixture was used as not to distort the field and likewise the measurement. The three leveling screws allowed adjustment to ensure the probe’s travel in the median plane.

Koeth, Report on the 12-Inch Cyclotron Magnet Study: Measurements, Modeling, and Future Plans (c. 2005) — p. 3

Editorial note, tabletop extrapolation: A buildable field-mapper: one lead screw, one stepper, three leveling screws, an aluminium fixture — with the craft detail being the three-point leveling, which keeps the scan at the intended median-plane HEIGHT (off-plane travel samples Bz at the wrong z; Br contaminates through probe tilt and cross-axis sensitivity, not height per se). The nonmagnetic rule extends past the plate: ordinary screws, lead screws and steppers are commonly ferromagnetic, so qualify every part near the gap or keep the motor remote, as any probe carrier near a 0.5-1.2 T gap demands.

The Hall probe was connected to a Gauss meter whose analog recorder output was the input for a multimeter. The output of the multimeter was fed into a data acquisition unit, and the number of steps taken by the motor was read by the computers serial port. A LabView program wrote the gaussmeter’s value and probe’s position into a text file. The gauss meter was calibrated against a very well known NMR magnet, and a precisely located “magnetic needle” gave the probe’s position calibration.

Koeth, Report on the 12-Inch Cyclotron Magnet Study: Measurements, Modeling, and Future Plans (c. 2005) — p. 3

Editorial note, tabletop extrapolation: Two calibrations, not one: absolute field against an NMR reference, and probe POSITION against a precisely located magnetic needle. Field calibration alone leaves the scan's radial origin unknown — and the interesting structure (taper, edge roll-off, n(r)) is all position-referenced. The magnetic-needle trick is cheap and is the same idea this group later industrialized into the coil-wrapped iron-needle field bumps of the 2011 AVF study.

Linear Fit to Tapered Pole Tips' B-field at 3 Coil Currents ... y = -0.0039x + 1.1624 R² = 0.9846 ... y = -0.0033x + 1.029 R² = 0.9846 ... y = -0.0025x + 0.7587 R² = 0.9862 ... Fig.1 Radial measurements at three different magnet currents: 20, 30, & 40A

Koeth, Report on the 12-Inch Cyclotron Magnet Study: Measurements, Modeling, and Future Plans (c. 2005) — p. 3

Editorial note, tabletop extrapolation: Hard numbers for a real 12-inch H-frame's excitation curve: about 0.76 T at 20 A, 1.03 T at 30 A, 1.16 T at 40 A — the tesla-per-amp halving between steps (0.0271 vs 0.0133 T/A) is THIS iron's saturation announcing itself. Computed honestly with P = I²R at fixed resistance: the 30→40 A step buys its 0.133 T at about 2.85× the incremental copper power per tesla of the 20→30 A step (700R/0.133 versus 500R/0.271). The fit slope is the normalized radial FIELD gradient, about −0.34% of central field per inch at 40 A — not the physical pole-taper angle. Where another magnet's payback ends is its own B(i) curve's business. (Fit values and R² read from the rendered Fig. 1; the 20/30/40 A assignment follows the curve intercepts, since the printed legend order is 30, 20, 40.)

We normalized the measured field profile for the three different operating currents: 20, 30, and 40 Amperes. Each field profile, as one would expect, had a peak field at r = 0. The data was linearly scaled to bring this peak field to unity. The simultaneous plotting of these normalized profiles, as shown in Figure 2, confirms that the field index’s (n’s) profile does not vary with field strength, even into the beginning of the saturated régime. This generously allows for just one analysis of the field profile.

Koeth, Report on the 12-Inch Cyclotron Magnet Study: Measurements, Modeling, and Future Plans (c. 2005) — p. 4

Editorial note, tabletop extrapolation: A genuine labour saver, within its validated window: on this magnet the normalized profiles overlaid across 20-40 A (into the onset of saturation), licensing one field-index analysis for the operating points inside that range. On another magnet, earn the shortcut the same way — normalized scans at several currents spanning YOUR operating point — and re-check before trusting it deeper into saturation than the comparison went (here ~1.16 T, the test endpoint, not a threshold).

Fig.2 Simultaneous normalized field plot of the three current values: 20, 30, and 40 Amperes. The vertical dashed lines indicate, r = 0 – the center, r = 5 – the maximum ion radius, r = 6 – the pole tip edge, and r = 8 – the reference point. … Nominal magnet operation is about 32 amperes.

Koeth, Report on the 12-Inch Cyclotron Magnet Study: Measurements, Modeling, and Future Plans (c. 2005) — p. 4

Editorial note, tabletop extrapolation: A concrete radius budget from one as-built machine: the beam uses 5 of the 6 inches of pole radius — the outer inch is where this pole's field rolls off — with nominal operation about 32 A. How much pole another machine must reserve depends on its gap-to-pole ratio, shaping and uniformity requirement: derive it from a field model or map rather than transplanting the 5/6 fraction.

Because of the round pole tips, it seemed natural to take the 2D slice of the magnet in the plane where the pole tips were the widest – at one half of the depth of the magnet. Again, the 2D approximation is only valid when the magnet is considered in the non-saturated regime. With a nominal operating field of 1 Tesla this approximation becomes suspect. It should be noted that the pole tip material is fully annealed, hot rolled 1006 steel, possessing a very large µ.

Koeth, Report on the 12-Inch Cyclotron Magnet Study: Measurements, Modeling, and Future Plans (c. 2005) — p. 4

Editorial note, tabletop extrapolation: Transferable with the author's own hedges intact: for round poles he took the 2-D slice where the tips are widest (half the magnet depth) — a natural choice for that geometry — and warned the planar approximation 'becomes suspect' at the nominal 1 T because saturation breaks it. Modern practice softens the cliff: include real B-H data and validate against measurement or a 3-D solve near the knee (dg-1691). Fully annealed hot-rolled 1006, chosen here for its very large µ, is the pole-tip material of record.

made to be denser (thus higher resolution) in the region of interest, namely, between the poles, while setting a less dense mesh for regions of little interest. A greater number of horizontal mesh lines, as compared with vertical mesh lines, were required to resolve the slight inclination of the pole tips.

Koeth, Report on the 12-Inch Cyclotron Magnet Study: Measurements, Modeling, and Future Plans (c. 2005) — p. 5

Editorial note, tabletop extrapolation: Concrete meshing guidance for exactly this problem: the taper physics lives in a 0.008-inch gap change over 5 inches (the retrofit spec, dg-1680), so resolution along the gradient direction is what buys a correct modeled field index — in Poisson/Superfish that meant more horizontal than vertical mesh lines. The principle transfers to FEMM as LOCAL refinement in the gap and along the tapered pole boundary (its unstructured triangles have no line-count knob); in any code, finish with a mesh-convergence check on Bz and dBz/dr before trusting n(r).

The coil current density was empirically set. The construction of the actual 12-inch cyclotron coils is unknown, as the coils came from a surplus source. The current density was varied in PSF through several points, until the peak 1.22 Tesla was achieved in the center of the gap. This corresponded to a PSF setting of 30,000 Ampere-turns. ... A comparison of PSF’s output with the linear portion of the actual measured B(i) curve can yield insight into the construction of the coils, which was determined to be about 850 windings per coil.

Koeth, Report on the 12-Inch Cyclotron Magnet Study: Measurements, Modeling, and Future Plans (c. 2005) — p. 5

Editorial note, tabletop extrapolation: A recoverable-datasheet method for surplus coils: fit a magnetostatics model's excitation until it reproduces the measured field, then read effective turns from matched ampere-turns over the linear region — N = (fitted A-turns)/I, with the per-coil-versus-total convention stated explicitly, which this memo leaves ambiguous: 30,000 A-turns over 850 turns implies ~35 A on a per-coil reading, while the document's stated ~32 A nominal (dg-1687) with 850 turns gives 27,200 — a bookkeeping tension to resolve on your own magnet, not an error to copy. The 850 turns is the inferred construction of THESE coils, not sizing guidance.

Fig.6 PSF B(i) curve, note lack of saturation ... Fig.7 Actual measured B(i) curve

Koeth, Report on the 12-Inch Cyclotron Magnet Study: Measurements, Modeling, and Future Plans (c. 2005) — p. 5

Editorial note, tabletop extrapolation: A cautionary pair at the target scale: the same 2-D model that matched the measured radial field SHAPE missed the excitation curve's saturation knee entirely — as run, evidently without material nonlinearity doing its job. The correct lesson is narrower than 'knees cannot be modeled': a nonlinear 2-D solve with a real B-H curve can capture saturation (3-D leakage it cannot), so give the code proper steel data, then validate BOTH B(i) and the field shape against measurement through the knee. (Measured curve endpoints — roll-over above ~0.03 kA, ~1.17 T at 0.05 kA — read from the rendered Fig. 7, whose x-axis is printed in kA.)

Zooming in on the gap region, it is clear, though slight, that the gap linearly opens up with an increase of radius. Near the pole tip’s edge, a rounded transition prevents localized saturation in the iron, thus radially extends the useful field region .

Koeth, Report on the 12-Inch Cyclotron Magnet Study: Measurements, Modeling, and Future Plans (c. 2005) — p. 5

Editorial note, tabletop extrapolation: A cheap machining detail with a real payoff on a small pole: breaking the pole-tip edge with a rounded transition rather than a sharp corner spreads the local flux crowding and — the source's stated purpose — radially extends the useful field region. Validate the chosen radius with a nonlinear field model; how much usable radius it buys is your geometry's answer.

The above analysis shows an ever increasing νz, with three clear regions of growth, see Figure 12. Initally, νz starts off at zero, climbs quickly up to a radius of 2 cm, then the increase takes on a slower rate of increase up to a radius of 9 cm. After 9 cm the rate if νz increase is exponential. Keep in mind that the maximum ion radius is 12.7 cm where νz reaches a value of 0.7 – well beyond the difference instability located at νz = 0.2, which comes at a radius of about 10 cm.

Koeth, Report on the 12-Inch Cyclotron Magnet Study: Measurements, Modeling, and Future Plans (c. 2005) — p. 6

Editorial note, tabletop extrapolation: The MODELED tune footprint of this machine's weak-focusing field: νz from zero, climbing fast to ~2 cm, a long gentle rise to 9 cm, then steeply beyond — 0.7 at the 12.7 cm maximum radius. Read it as the shape to expect from a tapered pole and recompute from your own B(r), not as a measured or transferable curve. Notation flag, computed: the passage puts 'the difference instability at νz = 0.2' at r ≈ 10 cm — where this machine's n ≈ 0.04 gives νz = √n ≈ 0.2, so the label is self-consistent as a TUNE — while the canonical Walkinshaw difference resonance sits at n = 0.2 (νz ≈ 0.45); the same document's p.3 uses n = 0.2 (dg-1682). The source mixes the two notations across pages; derive your resonance radii from computed νr and νz.

As shown in Figure 13 the profiles of the measured field and the modeled field are precisely matched in the region utilized for acceleration. This is an encouraging result, as pointed out earlier; the measured field profile followed a single line directly facing the magnet, while the modeled profile followed a single line 90o azimuthally from the measured path. If there was to be a discrepancy between the measured and modeled data, it would have been expected to be at a maximum difference between these two paths. A discrepancy does become pronounced at a radius greater than 6-inches, the “lower” strength field is the measured field. This is just as one would expect, as the measured path does does not have a vertical yoke piece to coral in the field lines, and thus they leak out easier.

Koeth, Report on the 12-Inch Cyclotron Magnet Study: Measurements, Modeling, and Future Plans (c. 2005) — p. 6

Editorial note, tabletop extrapolation: A validation result with a built-in lesson about where the comparison stops being fair: measured (open-side azimuth) and modeled (yoke-side) profiles matched precisely inside the acceleration region and split beyond 6 inches, the open side reading lower — no yoke there to corral the return flux. Practice for an H-frame: take scans at several azimuths, compare like against like where possible, quantify residuals, and EXPECT 2-D/3-D disagreement in the fringe — interior agreement on one cut is encouraging, not proof.

In the case that we do find an azimuthal field distortion, it will most likely have a periodicity of 2, which is inherently an unstable Azimuthal Varying Field (AVF) condition. A minimum periodicity of 3 is required for a stable operating point. ... The first option is to “shim” out the AVF. By use of the 2-D field mapper, we can identify lulls in the field and manually install thin iron shims to shorten the gap and bring up the field to the desired value.

Koeth, Report on the 12-Inch Cyclotron Magnet Study: Measurements, Modeling, and Future Plans (c. 2005) — p. 7

Editorial note, tabletop extrapolation: Both halves transfer with one correction. Diagnostic: determine the azimuthal harmonic CONTENT by Fourier analysis of a 2-D map rather than inferring it from the defect — an off-center pole shows up first as m = 1, a two-lobe (m = 2) component is the case this source singles out as inherently unstable, and its minimum-periodicity-3 statement is the author's claim, presented without derivation. Remedy: entirely amateur-accessible — thin iron shim stock laid in the mapped low spots to shorten the gap locally — followed by re-mapping, since the shims move the average field and the harmonics together.

The pink trace (lowest) in Figure 15 displays the sole effect of Thomas focusing, - AVF focusing without a spiral edge. It is interesting to note that in our case, weak focusing is in fact stronger than the colloquially termed AVF “strong focusing.” This peculiararity arises from the fact that our small (1.2MeV) cyclotron does not noticeably suffer from relativistic effects. If it did, the magnetic field would need to increase with radius, as opposed to our decreasing field, in order to keep the more “massive” ions in step with the RF.

Koeth, Report on the 12-Inch Cyclotron Magnet Study: Measurements, Modeling, and Future Plans (c. 2005) — p. 7

Editorial note, tabletop extrapolation: The qualitative result matters for a 100 keV-1 MeV machine and cuts against the modern instinct: with no relativistic detuning to fight, a non-relativistic machine may use a FALLING field, and this study found its tapered weak focusing stronger than its unspiralled Thomas alternative. No numeric ratio should be carried: Fig. 15's ordinate is printed 'field index - n' while text and caption call it νz, and its weak-focusing trace disagrees with the p.6 νz ≈ 0.7 value — if the plotted quantity were νz² the tunes would be its square roots — an internal inconsistency of the source, flagged. AVF earns its complexity when a rising (isochronous) field is needed, and can still be chosen at low energy for acceptance or tune control; this machine's own later spiral tips (dg-1745) are that choice made deliberately.

The light green trace (left and uppermost trace) in Figure 15 corresponds to the pole tip design shown in Figure 14. It is clear that νz grows very rapidly with even a slight spiral. Because of the cataclysmic beam instability at νz = 1, and other serious instabilities at νz = 0.2, 0.5 and so on, use of a spiral edge does not does not seem favorable.

Koeth, Report on the 12-Inch Cyclotron Magnet Study: Measurements, Modeling, and Future Plans (c. 2005) — p. 7

Editorial note, tabletop extrapolation: A caution, not a verdict, on spiral sectors at small radius: THIS slight-Archimedean design's modeled tune ramped so fast (νz = 1 by ~7 cm, read from the rendered Fig. 15's varchimedes trace) that the author judged spiral edges unfavourable for the machine, citing the νz = 1 instability and lines at 0.2 and 0.5. Whether a small pole has room to spread the ramp depends on sector count, flutter and spiral angle: plot the full tune trajectory against the resonance lines for YOUR field map and track through any crossing — the same group's 2011 study did exactly that and built a working 270° spiral (dg-1745), so treat this page as one design iteration's lesson.

AVF focusing can be used to supplement weak focusing. In this context, the weak focusing comes from the average radial gradient’s field index, denoted as k, where: k = d ln〈B〉/ d ln R . The tune is proportional to the relative focusing strength. Following the treatment of J.J. Livingood,[6] one can write the axial tune in terms of the average field index, flutter, and the instantaneous edge angle: νz² = -k + F(1+tan²ξ) The radial tune is written as νr² = 1+k … The rms variation of the vertical field is called flutter and is denoted as F. The azimuthal magnetic field component, Bθ, is also proportional to the flutter.

Koeth, Hine, Hoffman, Krutzler, Ponter, Rosenberg, Ruisard & Schneider, Comparison of Azimuthally Varying with Constant Gradient Magnetic Fields with the Rutgers 12-Inch Cyclotron (2011) — p. 2

Editorial note, tabletop extrapolation: The design equation for combining a weak-focusing taper with AVF sectors, showing the two contributions add. Two convention traps, both resolved here: (1) this paper calls F 'the rms variation' — for the linear-in-F tune formula to be the standard Livingood form, F must be the MEAN-SQUARE fractional variation ⟨((B−⟨B⟩)/⟨B⟩)²⟩, i.e. the square of the rms fraction, exactly as the same program's later paper defines it (F² there = ⟨…²⟩, tune quadratic in its F; dg-1746) — reconcile against Livingood before numeric use; (2) k = d ln⟨B⟩/d ln R is NEGATIVE for a falling field, opposite in sign to the magnet study's n, so n = −k. The tan²ξ factor is why edge angle is a powerful and dangerous knob — it grows without bound (dg-1697).

Poor beam intensity motivated our search for an undesired azimuthal variation of periodicity two, which resulted in the 2-D Bz-field measurements of the weak focusing field shown in Figure 2. Since no detectable azimuthal variation was found, our quest to improve the beam intensity led us in other directions, including the ion source. [7]

Koeth, Hine, Hoffman, Krutzler, Ponter, Rosenberg, Ruisard & Schneider, Comparison of Azimuthally Varying with Constant Gradient Magnetic Fields with the Rutgers 12-Inch Cyclotron (2011) — p. 3

Editorial note, tabletop extrapolation: A worked example of ruling a suspect out: disappointing current, a plausible magnetic culprit (m = 2 azimuthal error), a 2-D map to test it — and a null result, above the mapper's detection threshold, that legitimately DE-prioritized the field and sent the effort in other directions, including the ion source (where the real gains turned out to live, dg-1728). The transferable discipline is testing the measurable suspect before redesigning anything; a null map does not convict the source by elimination.

The newly written MatLab analysis code plots Bz about a circle of any requested radius in 5° increments – the center of the circle is intuitively chosen. Although the data lies on a rectangular grid, a MatLab provided 2-D linear interpolation routine was used to determine the field at any requested location. ... In the weak focusing case, the magnet center was determined by sweeping the center of the circle first in the x and then the y directions. The standard deviation of the values about the measurement circle was calculated and stored. After a sweep in x or y that included the magnet center, the data was fit to a parabola, from which the minimum standard deviation, i.e. the center locations, could be inferred as seen is Figure 4.

Koeth, Hine, Hoffman, Krutzler, Ponter, Rosenberg, Ruisard & Schneider, Comparison of Azimuthally Varying with Constant Gradient Magnetic Fields with the Rutgers 12-Inch Cyclotron (2011) — p. 3

Editorial note, tabletop extrapolation: A reusable analysis for near-axisymmetric maps: you need not align the probe stage to the magnetic centre — find it afterwards in software by minimizing the azimuthal standard deviation of Bz (sweep the circle centre in x, then y, fit parabolas). The source applies it to the WEAK-FOCUSING case, where azimuthal uniformity is the expectation; on an AVF map the same minimization would chew on real sector harmonics, so centre those maps by fiducials or a symmetry-aware fit (the program's own N-harmonic method, dg-1792). On this magnet the correction moved the centre about half a grid step — (28.0, 27.0) to (28.5, 27.4), read from the rendered Figs. 3-5 annotations — and that half-step separated an apparent azimuthal error from a flat field (dg-1702).

– i.e. evaluation circle. The azimuthal analysis was then repeated, and the results are shown in Figure 5. Clearly each measurement point lies much closer to the average than was depicted in Figure 3. Comparison of the centers determined from the fit, show that the field is axisymmetric to 4 parts in 10,000.

Koeth, Hine, Hoffman, Krutzler, Ponter, Rosenberg, Ruisard & Schneider, Comparison of Azimuthally Varying with Constant Gradient Magnetic Fields with the Rutgers 12-Inch Cyclotron (2011) — p. 4

Editorial note, tabletop extrapolation: Two things transfer: an existence proof — a 12-inch magnet with ground, tapered poles measured axisymmetric to 4 parts in 10,000, so that class of number is achievable — and the warning that an off-centre evaluation circle MANUFACTURES azimuthal signal (for a radially graded axisymmetric field, predominantly a first harmonic, with higher orders from curvature). Before concluding a small magnet has an azimuthal defect, re-centre the analysis (dg-1701) and re-run; this machine's apparent variation vanished exactly that way.

A Programmable Logic Controller (PLC) based machine-protection system was implemented to allow safe, un-attended operation of the 12-Inch magnet. In the event of high-temperature condition or a coil cooling-water flow loss for more than 10 seconds, the PLC will slowly ramp the magnet down and latch it off, requiring an operator to reset. The PLC safety system was necessary as the scans could take in excess of 24 hours: a standard measurement grid of 129 x 129 points equals 16,641 measurement points, each measurement required ~ 5 seconds totaling an excess of 23 hours scan time.

Koeth, Hine, Hoffman, Krutzler, Ponter, Rosenberg, Ruisard & Schneider, Comparison of Azimuthally Varying with Constant Gradient Magnetic Fields with the Rutgers 12-Inch Cyclotron (2011) — p. 4

Editorial note, tabletop extrapolation: The source's own practice and thresholds, reported as such: 10-second flow-loss window, slow ramp-down rather than a trip, latching off until a human resets. The planning arithmetic transfers directly — points × (dwell + settle + motion) — and this machine's standard 129×129 map at ~5 s/point is a 23-hour job, which is why the protection exists: budget your own scan time honestly, and if it lands unattended, engineer fail-safe interlocks with a shutdown response derived from YOUR coil's thermal time constant and cooling failure modes, not copied from these numbers.

A result of a of field-bump calibration scan is shown in Figure 9, it also reveals the residual magnetization of the 12-Inch magnet. Four needles were needed to scale both dimensions; the fifth needle was used to break the symmetry, removing orientation ambiguities. The variation of the peak amplitudes indicate the probe was traveling in a plane slightly tilted with respect to the median plane. However, this effect seems to be insignificant in the measurement of actual AVF field. A vertical sensitivity study will be done. … To calibrate the hall probe’s position against the magnet’s mechanical center, magnetized iron needles were precisely placed around the pole tip to create field bumps, one such needle is displayed in Figure 8. The field-bump calibration was performed with the 12-Inch magnet deenergized. A full 2-D scan was completed; peaks found by fitting to the measured field bump were

Koeth, Hine, Hoffman, Krutzler, Ponter, Rosenberg, Ruisard & Schneider, Comparison of Azimuthally Varying with Constant Gradient Magnetic Fields with the Rutgers 12-Inch Cyclotron (2011) — p. 5

Editorial note, tabletop extrapolation: A cheap, precise fiducial method for a field map: coil-wrapped magnetized iron needles placed around the pole tip make sharp, fittable field bumps, surveyed with the magnet DE-ENERGIZED so the main field is absent (the scan still sees the poles' residual magnetization — the same data doubles as a residual-field measurement, and unequal peak heights revealed the probe plane's slight tilt). The five-needle pattern is the craft detail: four for scale in x and y, a fifth asymmetric so the map cannot be mounted rotated or mirrored. Achieved precision is not stated; fit quality on your own bumps decides it.

The first set of AVF pole tips measured were of the simplest design, and are shown installed with the cyclotron chamber removed in figure 10. With a periodicity of four, the hills and valley are each 45 degrees wide. They maintain a constant thickness out to the pole edge, except for a ¼ -inch chamfer to break the sharp corners. The data from the first scan is plotted in Figure 11. The four hills are prominent, however a small central bump is observed from the slug that ties the four vanes together. This weak focusing is required to promote a centrally localized focusing field since the flutter will be too small to be effective at the central convergence.

Koeth, Hine, Hoffman, Krutzler, Ponter, Rosenberg, Ruisard & Schneider, Comparison of Azimuthally Varying with Constant Gradient Magnetic Fields with the Rutgers 12-Inch Cyclotron (2011) — p. 5

Editorial note, tabletop extrapolation: The geometry as stated (four sectors, 45-degree hills and valleys, constant thickness, 1/4-inch chamfer, central slug) plus the central-region insight that matters most at small scale: flutter vanishes at r = 0, so a pure-AVF machine has no SECTOR focusing where ions are born — this design's central slug supplies a deliberate weak-focusing bump there, and the source states that requirement for its own field. Evaluate your own central region's full focusing budget (magnetic index plus RF-gap electric focusing and phase) rather than assuming the bump; most small AVF designs end up wanting one (the AKG270 kept it, dg-1717).

Figure 12 plots Bz(θ) over one quadrant displaying the relative evolution of the flutter with radius by individually plotting Bz(θ) for sixteen radii. The plot shows the emerging sinusoid flutter, despite the square stepped transitions between hills and valleys. Only for radii of 4-inches and greater does a ‘flat-top’ become apparent.

Koeth, Hine, Hoffman, Krutzler, Ponter, Rosenberg, Ruisard & Schneider, Comparison of Azimuthally Varying with Constant Gradient Magnetic Fields with the Rutgers 12-Inch Cyclotron (2011) — p. 5

Editorial note, tabletop extrapolation: An instructive measured fact about gap smoothing: square-cut sector iron produced a nearly sinusoidal Bz(θ) on this pole, with a flat top emerging only beyond 4 inches radius. The general lesson is that the gap filters sector geometry hard — machining need not chase a shaped profile blindly — but how much smoothing, where the designed flutter amplitude arrives, and what harmonics survive are set by gap-to-sector-width and radius ratios: solve or map YOUR geometry and take the flutter spectrum from that, rather than scaling this 4-inch mark by pole size.

SIMULATIONS Form start to finish, four software tools have been employed to simulate the beam dynamics of in these magnetic fields. SolidWorks was used to mechanically model the magnet, Maxwell 3D was uses to solve the field problem and generate the needed field report for SIMION to fly and track the ions in. Post processing was performed in MatLab. ... Maxwell 3D (M3D) was first benchmarked against our weak focusing PSF simulations. A 3-D magnet model, which included the weak focusing pole tips was designed in SolidWorks and then imported into Maxwell 3D. The problem was solved to have a nominal peak central field of 1 Tesla. To within measurement errors the models agreed.

Koeth, Hine, Hoffman, Krutzler, Ponter, Rosenberg, Ruisard & Schneider, Comparison of Azimuthally Varying with Constant Gradient Magnetic Fields with the Rutgers 12-Inch Cyclotron (2011) — p. 5

Editorial note, tabletop extrapolation: A four-stage pipeline — CAD, 3-D field solver, tracker, analysis — with the transferable discipline being the BENCHMARK step: before trusting the 3-D solver on new geometry, reproduce the old validated result on the old geometry (here Maxwell 3D reproduced the Poisson/Superfish weak-focusing field within measurement errors — the FIELD model, not the tracking chain, is what that comparison validates). Free-tool substitutions: FEMM only where a planar/axisymmetric approximation is defensible — a radial-sector AVF field is intrinsically 3-D, so budget for Elmer or another 3-D solver there — and verify the field-transfer and tracking layers separately (dg-1712's trap).

The Maxwell 3D current was nearly set the same, differences between the two resulting average field reports were aligned by normalizing the simulated data central Bz value to exactly match the measured central value. ... Figure 14. Comparison of measured and simulated average field of the radial sector tips. Good agreement is noted over the range of the ions travel, at most 1% deviation is seen at r=2.5.

Koeth, Hine, Hoffman, Krutzler, Ponter, Rosenberg, Ruisard & Schneider, Comparison of Azimuthally Varying with Constant Gradient Magnetic Fields with the Rutgers 12-Inch Cyclotron (2011) — p. 5

Editorial note, tabletop extrapolation: A quantified model-versus-measurement figure at the target scale, precisely bounded: after normalizing the simulated central Bz to the measured value, the AVERAGE-FIELD SHAPE agreed within 1% over the ion region (worst at r = 2.5 in). That is shape validation, not absolute-excitation validation — and not yet flutter, harmonic or tune validation, which need their own comparisons (dg-1721 does the 2-D map). The 45,000 A-turns for 1 T with these sector tips versus the Poisson model's 30,000 for 1.22 T with solid tips is suggestive of what valleys cost, but the two figures come from different codes and endpoints — measure the penalty on matched geometry before budgeting it. (The 45,000 A-t / 1 T / 0.25-inch-step statements are on p.5; the normalization sentence and Fig. 14 caption are on p.6.)

With acceptable agreement between the measurement and simulation, a spiral sector pole was simulated; again each vane had 45° angular width. The spirals were describe by an Archimedes spiral of the form θ=αr, where α=15°.

Koeth, Hine, Hoffman, Krutzler, Ponter, Rosenberg, Ruisard & Schneider, Comparison of Azimuthally Varying with Constant Gradient Magnetic Fields with the Rutgers 12-Inch Cyclotron (2011) — p. 6

Editorial note, tabletop extrapolation: A worked description of the trial spiral: 15 degrees of sweep per inch takes the edge through 75 degrees over a 5-inch ion region — this study's first spiral iteration, described with 45-degree vane widths in the same passage. The built optimized design swept 270 degrees total (AKG270, dg-1717). The number to copy is neither: sweep rate is the knob that trades edge-angle focusing against tune ramp (dg-1697, dg-1698), chosen from your own tune plot.

The resolution of the imported field has been set at 1 mm to conveniently match the 1mm:1 SIMION grid unit ratio. The M3D report file is a 6-column a comma separated variable file reporting x, y, z, Bx, By, and Bz at each grid point, with a spacing of 1-mm between grid points. To fully cover the ion accessible region in our cyclotron, the field region must span a volume with a radius up to 4.5 inches – the point of interception of deflector. Therefore the extent of the report spans ±115 mm (~ 4.55-inches) X ±115 mm X (~ 4.55-inches) X 53 mm (~ 1.04-inches) which contains 231 X 231 X 53 rows of data, an excess of 2.8 million points - causing the simple text data to become unwieldy, in excess of 500 MB.

Koeth, Hine, Hoffman, Krutzler, Ponter, Rosenberg, Ruisard & Schneider, Comparison of Azimuthally Varying with Constant Gradient Magnetic Fields with the Rutgers 12-Inch Cyclotron (2011) — p. 7

Editorial note, tabletop extrapolation: Concrete sizing for a tracker's field-map file: 1 mm resolution over the ion-accessible volume of a 12-inch machine is 231 × 231 × 53 points — 2.8 million rows, over 500 MB as text — so plan a binary or compressed intermediate format from the start. The printed axial figures do not reconcile (53 mm ≈ 2.09 in, yet the parenthetical prints "~1.04-inches", plausibly a half-extent; unresolved in the source — inspect your own file's z bounds rather than inferring). Size the map to cover the COMPLETE tracking domain out through every loss surface and relevant fringe region, not merely the aperture the beam is supposed to occupy.

As is seen in Figure 20, the maximum vertical excursion of the proton in the weak field was nearly four times that of the proton in the radial sector AVF field. This has two immediate implications. First, to accommodate a given ion source, the magnet gap of AVF field can be drastically reduced, implying a smaller and less expensive magnet. Alternatively, the magnet gap can be maintained, and a greater vertical angular distribution can be accepted, implying greater beam intensity at the periphery.

Koeth, Hine, Hoffman, Krutzler, Ponter, Rosenberg, Ruisard & Schneider, Comparison of Azimuthally Varying with Constant Gradient Magnetic Fields with the Rutgers 12-Inch Cyclotron (2011) — p. 9

Editorial note, tabletop extrapolation: The clearest quantitative case for AVF at this scale, kept to what the simulation shows: one proton, identical launch, ±9 mm excursion in the weak-focusing field versus ±2.5 mm in the radial-sector field (read from the rendered Fig. 20; 'nearly four times' is the authors'). The source's two implications — a drastically reducible gap, or more accepted vertical angle — are design directions whose actual payoff needs full acceptance tracking and a self-consistent magnet redesign, since gap changes move excitation and field structure together. Note the apparent tension with the same program's finding that its weak-focusing νz exceeds its Thomas-field νz (dg-1696): tune and single-trajectory excursion are different measures, and the Fig. 15 labeling problem (same card) leaves the tune comparison unresolved.

SPIRAL AVF DESIGN Finally, we present the optimized design for a set of spiral pole tips that are intended to guide beam. The result was a four sector Archimedean spiral sweeping 270 degrees, and will herein be referred to as AKG270. With the exception of the weak focusing central region, these pole tips aimed to satisfy the isochronous condition, in order to minimize the phase slippage, and reduce the minimum DEE voltage while preserving axial stability throughout the accelerating region.

Koeth, Hine, Hoffman, Krutzler, Ponter, Rosenberg, Ruisard & Schneider, Comparison of Azimuthally Varying with Constant Gradient Magnetic Fields with the Rutgers 12-Inch Cyclotron (2011) — p. 10

Editorial note, tabletop extrapolation: The design pattern worth copying is the HYBRID: weak focusing kept in the centre where flutter cannot help, spiral-AVF outboard where isochronism pays — that is what minimized phase slippage and dee voltage while preserving axial stability here. The 270-degree four-sector Archimedean sweep is this magnet's optimized answer (the authors credit their machine shop for cutting it); another machine re-runs the optimization on its own field map and takes whatever sweep its tunes demand.

The AKG270 radial trace space was explored first to identify the equilibrium orbits in 50 keV increments. Even, at 50 keV, non-linear behavior is noted in the larger stable orbits, exhibiting four-sided contours, behavior which is consistent with pole tips that have a sector periodicity of four. The corners of the four-sided nonlinear orbits become more pronounced and bulbous with increasing energy. By 250 keV four closed contours formed in the protracted corners, displayed in Figure 23. Thus, in addition to the primary Equilibrium Orbit, there are four off-center stable orbits.

Koeth, Hine, Hoffman, Krutzler, Ponter, Rosenberg, Ruisard & Schneider, Comparison of Azimuthally Varying with Constant Gradient Magnetic Fields with the Rutgers 12-Inch Cyclotron (2011) — p. 10

Editorial note, tabletop extrapolation: A phenomenon to look for on any sectored machine, from this worked case: the four-sector AKG270's radial phase space showed four-sided nonlinear contours already at 50 keV, sharpening with energy until four closed islands formed by 250 keV — genuine off-centre stable orbits alongside the primary one. Whether YOUR sector count produces islands, and at what energy, depends on the field harmonics and tunes: survey trace space at energy steps fine enough to resolve your calculated resonances (50 keV was this study's choice), and follow with RF-on tracking to learn whether real accelerating beam gets captured by them (a beam parked on an island reads as mis-steered, dg-1793).

The off-center equilibrium orbits were experimentally verified using the wire-loop orbit technique.[7] 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. Myriad other stable orbits made it difficult to perform this experiment in the median plane; instead a clear acrylic sheet was placed on the bottom pole tip to provide a flat surface on

Koeth, Hine, Hoffman, Krutzler, Ponter, Rosenberg, Ruisard & Schneider, Comparison of Azimuthally Varying with Constant Gradient Magnetic Fields with the Rutgers 12-Inch Cyclotron (2011) — p. 10

Editorial note, tabletop extrapolation: An outstanding no-vacuum, no-beam diagnostic: a current-carrying flexible loop settles onto stable orbit shapes of a real measured field for the price of magnet wire and a bench supply — a physical check on the tracker before the chamber ever pumps down. Physics to hold onto: the loop obeys T/ρ = I·B, so its effective rigidity is set by tension over current — circumference constrains which closed shapes are available but does not by itself select a particle energy (the source says as much; its extra orbits are the point of dg-1720). Practicalities: the acrylic sheet keeps the loop on a plane (not the median plane — a known offset), and 2.5 A in 30 AWG dissipates real heat, so current-limit, keep the duty short, and mind magnet forces. Setup as run: 30 AWG, 71 mm circumference, 2.5 A.

Both plots were normalized such that the peak central fields were 1 Tesla – this required at most a 5% adjustment to either data set. Figure 29 subtracts the measurement from the simulation. ... Figure 29. Subtracting the measurement from the simulation reveals 14% discrepancies at the outer pole tip edge. The two agree within 1% in the ion region.

Koeth, Hine, Hoffman, Krutzler, Ponter, Rosenberg, Ruisard & Schneider, Comparison of Azimuthally Varying with Constant Gradient Magnetic Fields with the Rutgers 12-Inch Cyclotron (2011) — p. 11

Editorial note, tabletop extrapolation: The most useful validation figure in this pair of documents, precisely bounded: after each map was normalized to a 1 T central peak (≤5% adjustment either way), the SHAPES agreed within 1% over the ion region and split by 14% at the outer pole-tip edge — cause not identified by the source, with fringe and edge effects the natural suspects but unproven. Budget trust accordingly: normalization means absolute solver accuracy is NOT bounded by the 1%, and the pole edge — exactly where an extraction deflector sits — earned measurement on this magnet and will on yours. (The measurement grid: 1/8-inch step at 30 A, from the rendered Figs. 27-28 plot titles.)

After locating the equilibrium orbits, a complete comparison of the focusing between the AKG270 poles and the weak focusing pole tips was performed using the simulated fields. The DEEs were removed from both cases to observe, if any, non-linear effects at large excursions. The radial and axial results are respectively shown in Appendix II-a and -b. In most of the radial cases the AKG270 radial trace space is bounded by the weak focusing pole tips. At the lower energies of 50 and 100 keV, the vertical trace space of the AKG270 poletips is larger than that of the weak focusing poles, indicating a greater angular acceptance from the ion source. This is due to the enhanced central focusing from the weak focusing bump.

Koeth, Hine, Hoffman, Krutzler, Ponter, Rosenberg, Ruisard & Schneider, Comparison of Azimuthally Varying with Constant Gradient Magnetic Fields with the Rutgers 12-Inch Cyclotron (2011) — p. 11

Editorial note, tabletop extrapolation: Where this hybrid field's acceptance advantage showed up: at the LOW-energy end — 50 and 100 keV vertical trace spaces larger than the weak-focusing poles' — and the source credits the AKG270's retained central weak-focusing bump, not the spirals. That is the hybrid logic confirmed at exactly the energies where source acceptance is decided. Methodological detail worth copying: the dees were removed from both simulations so the comparison probes field nonlinearity, not mechanical clipping. Radially, the weak-focusing field bounded AKG270 in most cases; simulated statics, not measured beam.

The average radial field profile, plotted in figure 6, is generated from the assembled average fields along the radius – this is needed to calculate the average field index, k. In the case of the axisymmetric weak focusing field, the average field index is the same as the instantaneous field index, n.

Koeth, Hine, Hoffman, Krutzler, Ponter, Rosenberg, Ruisard & Schneider, Comparison of Azimuthally Varying with Constant Gradient Magnetic Fields with the Rutgers 12-Inch Cyclotron (2011) — p. 4

Editorial note, tabletop extrapolation: Explains the tune shape the companion magnet study reported — near-zero νz to mid-radius, then a fast rise — and warns a designer who sizes a taper analytically: this machine's DESIGNED taper was a 2% droop (dg-1680), while the delivered profile falls ~12.5% by r = 5 inches because the pole-edge roll-off dominates the last stretch. Field index is the LOCAL derivative, not the accumulated drop — differentiate the measured profile to get n(r), and expect the edge, not the taper, to own the outer-radius focusing.

Figure 30. Average Bz as a function of radius for the AKG270 pole tips in the median plane.

Koeth, Hine, Hoffman, Krutzler, Ponter, Rosenberg, Ruisard & Schneider, Comparison of Azimuthally Varying with Constant Gradient Magnetic Fields with the Rutgers 12-Inch Cyclotron (2011) — p. 11

Editorial note, tabletop extrapolation: What a hybrid weak-focusing-plus-near-isochronous profile looks like in practice on a 12-inch pole, directly comparable with the same paper's weak-focusing profile (dg-1724): much flatter across the middle of the ion region. The design intent and its payoff — minimized slippage, the 6 kV-peak minimum dee voltage — are carried on their own cards (dg-1717, dg-1722). A flat average field approximates isochronism only in the nonrelativistic limit; a higher-energy design shapes ⟨B⟩ to track γ instead. Digitized values approximate.

The faces of the 9-inch pole tips were parallel within 0.0001 inches – no effort of shaping the field for focusing was expended. Ions were produced with a crude filament near the top lid of the cyclotron chamber, and the entire chamber was filled with hydrogen gas. Even with a maximum RF power of just 50 watts, thus a DEE Vp-p of 3300V, beam currents on the order of 10nAmps of 0.60 MeV protons were reproducibly achieved with the 9-inch magnet.

Koeth, Hanebuth, Schneider & Hoffman, Observation of Betatron Motion in the Rutgers 12-Inch Cyclotron (2006) — p. 1

Editorial note, tabletop extrapolation: A directly comparable data point for the 8-12 inch class: a flat-pole, gas-filled-chamber, filament-source machine at 3300 V dee reproducibly delivered ~10 nA at 0.60 MeV — a demonstrated outcome showing a crude first configuration can produce measurable beam, not a yield to expect. The 0.0001-inch figure is the reported PARALLELISM of the opposed pole faces (each face's own flatness is not stated), and is what a university shop achieved.

The experimenters were quickly disappointed when only fractions of a nAmp beam were achieved in the larger magnet. Much effort was put into understanding the problem. First, pole tips with a slight radial taper to promote focusing were designed, installed and characterized [2,3]. Still with only a slight increase in beam current with the installation of the new pole tips, the ion source came under suspicion. An analysis of the simple ion source suggested that the DEE's high voltage was suppressing electron emission and thus suppressing ion generation during the appropriate RF phase.

Koeth, Hanebuth, Schneider & Hoffman, Observation of Betatron Motion in the Rutgers 12-Inch Cyclotron (2006) — p. 1

Editorial note, tabletop extrapolation: The most transferable failure story in this memo: a working small machine did not automatically scale to a bigger magnet, and the leading suspect was not focusing but a source-to-dee electrostatic interaction — the dee's field suppressing filament emission at the useful RF phase, per the authors' analysis (a suggested mechanism, which their chimney redesign then acted on). Worth testing on any open-filament source sitting in the dee's fringe field.

For details beyond the scope of this document, coupled resonances between the transverse motions further limit the value of n. n values of 0.2, 0.25, 0.33, 0.5 (and others higher) need to be avoided. Since, the ions to be accelerated begin at r = 0, n = 0 and will only climb as the radius increases. If n = 0.2 needs to be avoided, then the rate at which Bz decreases must be moderated such that only near the maximum ion radius does n approach 0.2.

Koeth, Hanebuth, Schneider & Hoffman, Observation of Betatron Motion in the Rutgers 12-Inch Cyclotron (2006) — p. 2

Editorial note, tabletop extrapolation: The direct pole-tip taper criterion for a small weak-focusing machine: shape the taper so n approaches 0.2 only near maximum ion radius — under the author's stated premise of a profile whose n starts at 0 and only climbs. The resonance list (0.2, 0.25, 0.33, 0.5 and higher) is the author's claim, referred to Livingood for derivation, not a measurement from this machine; the field-index definition and 0 < n < 1 stability window are standard weak-focusing results stated here for context.

We normalized the measured field profile for the three different operating currents: 20, 30, and 40 Amperes. Each field profile, as one would expect, had a peak field at r = 0. The data was linearly scaled to bring this peak field to unity. The simultaneous plotting of these normalized profiles, as shown in Figure 2, confirms that the field index's (n's) profile does not vary with field strength, even into the beginning of the saturated régime. This generously allows for just one analysis of the field profile.

Koeth, Hanebuth, Schneider & Hoffman, Observation of Betatron Motion in the Rutgers 12-Inch Cyclotron (2006) — p. 3

Editorial note, tabletop extrapolation: Useful economy for a small-magnet builder: map the pole-tip field at a few excitations spanning the operating point, and if the normalized profiles overlay, one field analysis serves — WITHIN that tested range and magnetic history. This magnet held profile shape from 20 to 40 A, into the beginning of saturation; deeper saturation, hysteresis state or a changed excitation history can bend the profile, so remap when leaving the verified window.

The following measurements and modeling indeed confirm, at least in the assumption of azimuthal symmetry that our 12-inch magnet's field index runs from 0 to about 0.2 throughout the useful region for ion acceleration.

Koeth, Hanebuth, Schneider & Hoffman, Observation of Betatron Motion in the Rutgers 12-Inch Cyclotron (2006) — p. 3

Editorial note, tabletop extrapolation: Reference-machine geometry, not a target: on this 12-inch, maximum ion radius 5 inches sits an inch inside the 6-inch pole-tip edge, and the measured-and-modeled n runs 0 to about 0.2 across the acceleration region. Choose your own pole margin from magnetic modeling of your taper (the fringe rolls off inside the physical edge), and read 'about 0.2' as where THIS profile tops out — the design doctrine of keeping the 0.2 crossing near final radius is carried by dg-1729/dg-1835. The r = 5/6/8 inch markers are read from the Fig. 2 caption on the same page.

The profiling of the radial dependence of the magnetic field between the pole pieces was executed with a Hall probe mounted on a computer controlled motorized platform. A LabView program wrote the Hall probes value and probe's position into a text file. ... The LANL Finite Element code Possion Superfish's (PSF) [6] output was compared to our measurement. Strong agreement between the McClain & Friedman's measurement with the PSF justified the use of the computer model for further analysis, see figure 3. [3]

Koeth, Hanebuth, Schneider & Hoffman, Observation of Betatron Motion in the Rutgers 12-Inch Cyclotron (2006) — p. 3

Editorial note, tabletop extrapolation: The measure-then-validate-then-model workflow to copy with FEMM or Superfish: the model earns trust for downstream analysis only after a mapped Hall-probe profile agrees with it (here the downstream use included the field-index work of the following sections). Note the source prints "Possion Superfish" (a typo for Poisson Superfish); the quote is transcribed as printed.

The cyclotron magnet features flat poles with a maximum B-field of about 1T. The magnetic field can be shaped using pole-tips that are fixed on the flat poles. ... In particular, different sets of magnet pole-tips have been designed and built. ... These different magnetic configuration illustrate the main aspects of the cyclotron focusing theory: weak focusing, radial sectors (Thomas focusing) and spiral sectors (Kerst and Laslett focusing effects)

Hernalsteens, Ponter, Beaudoin, Koeth, Ruisard & Miller, Betatron Tune Characterization of the Rutgers 12-Inch Cyclotron for Different Magnetic Poles Configurations (2016) — p. 1

Editorial note, tabletop extrapolation: A strong architectural argument for an educational tabletop machine: build the magnet with flat poles and put the field shaping entirely in separate pole-tips, so focusing schemes become swappable experiments rather than a magnet rebuild. This paper documents the sets and their purpose; the mounting/interchange practice is documented in the same program's field-mapping report (lib-006), whose four pole-tip sets were mapped on this magnet.

Radial sectors pole-tips providing the so-called Thomas focusing [2] have been built but the beam could not be accelerated up to the deflector radius due to poor isochronicity. ... To successfully accelerate the beam up to the chamber's radius a new set of pole-tips was designed [5], at the same time providing additional focusing using a spiral sector design. ... An iterative design phase using a field solver and ion tracking lead to the machining of 270°spiral pole-tips

Hernalsteens, Ponter, Beaudoin, Koeth, Ruisard & Miller, Betatron Tune Characterization of the Rutgers 12-Inch Cyclotron for Different Magnetic Poles Configurations (2016) — p. 2

Editorial note, tabletop extrapolation: A documented negative result at exactly this scale: plain radial sectors on a small cyclotron can cost enough isochronism to prevent reaching full radius. If a tabletop builder wants AVF focusing, this collection's experience points to spiral sectors designed with a field solver plus tracking, not radial sectors alone. (The Archimedean-spiral / four-fold-symmetry statement is on p.1.)

The edge-focusing adds a term to νz2 depending on the "flutter" (mean square deviation of B(θ) ... where <B> is the θ-averaged axial magnetic field. ... The spiraling changes the edge crossing angles and the sector focusing contribution to the axial tune becomes ν2sector = F2 (1 + 2tan2 ε) where F is defined in Eq. 3 and ε is the spiral angle.

Hernalsteens, Ponter, Beaudoin, Koeth, Ruisard & Miller, Betatron Tune Characterization of the Rutgers 12-Inch Cyclotron for Different Magnetic Poles Configurations (2016) — p. 2

Editorial note, tabletop extrapolation: The minimum analysis needed to turn a measured or simulated AVF field map into a predicted axial tune for a tabletop machine. The quoted line reflects the PDF's text-layer rendering of typeset superscripts; the equation as set on the page is nu_sector^2 = F^2 (1 + 2 tan^2 epsilon).

Magnetic maps have been measured using a home-made magnetic measurement table and stepper motors electronics with a digital Gauss-meter. The magnetic centers of the sector focusing pole-tips are identified using a field harmonic analysis on a set of circles with different radii; indeed the non-structure harmonics are minimal at the magnetic center.

Hernalsteens, Ponter, Beaudoin, Koeth, Ruisard & Miller, Betatron Tune Characterization of the Rutgers 12-Inch Cyclotron for Different Magnetic Poles Configurations (2016) — p. 1

Editorial note, tabletop extrapolation: Answers a practical question for any tabletop AVF build: the true magnetic center of a sectored pole-tip set need not be its mechanical center, and a harmonic analysis on circles finds it — the non-structure harmonics minimize at the magnetic center. The home-made stepper table and digital gaussmeter are the hardware the Rutgers group used; the mapping accuracy and harmonic resolution a given magnet needs must be established for that magnet.

The best linear fit in the measurement range reads νa = (0.086 ± 0.001) + (0.0012 ± 0.001) · (r − 45), where r is the radius expressed in millimeters in the range 45 to 80mm. The 90 % confidence interval is also shown revealing that the measurement resolution is sufficient to confirm the observed linear trend. ... The equation of the fit of the magnetic results (in the beam based measurement range) reads νa = (0.088 ± 0.004) + (0.0015 ± 0.0002) · (r − 45).

Hernalsteens, Ponter, Beaudoin, Koeth, Ruisard & Miller, Betatron Tune Characterization of the Rutgers 12-Inch Cyclotron for Different Magnetic Poles Configurations (2016) — p. 3

Editorial note, tabletop extrapolation: A validated model-versus-measurement pair for a weak-focusing machine in the target class: this machine's field map predicted its beam's axial tune within the measurement errors. For THIS field the fits put νz ≈ 0.09–0.13 over 45–80 mm (n ≈ 0.008–0.02) — comfortably below the n = 0.2 Walkinshaw coupling band that this collection's weak-focusing rules treat as the ceiling (dg-003, dg-138); another machine's margin comes from its own n(r), not these numbers. The printed slope uncertainty (±0.001 on a slope of 0.0012) is nearly as large as the value and looks like a source misprint given the stated 90% confidence in the trend.

The 12-inch cyclotron was tuned up for D+ ions, with the RF system tuned to 7.150MHz, for an average magnetic field set to 0.96T (by setting the top coil to 29.007Amps and bottom coil to 29.121 amps) with the AKG270 spiral poletips.[1] The ion source used the largest rectangular aperture chimney (hence lowest pressure differential), the Mass Flow Controller was set to 0.230 scc/m for an operating pressure of 3E-6 Torr, the ion source was run with a 10mA arc discharge current – all of these parameters balanced for optimal operating point.

Koeth, Gilde & Moroch, Measurement of Neutron Diffusion Time from Fast Pulsed Systems (draft, 2020) — p. 1

Editorial note, tabletop extrapolation: The most fully specified deuteron operating point in this collection — but treat it as recorded settings, not a validated matched pair: 7.150 MHz and 0.96 T are not mutually consistent with f = qB/2πm_d (7.150 MHz corresponds to ≈0.94 T; 0.96 T to ≈7.32 MHz, about 2% apart), and the draft does not say which number was measured against what. Reconcile against a field map or frequency counter before using the pair as a tune recipe. The slightly different top and bottom coil currents are reported settings; the draft does not state their purpose. Draft report.

The 12-inch diameter H-frame iron core magnet provides a nominally 1 Tesla vertical field in the 2-inch magnetic gap. … Interchangeable iron pole tips allow for application of various focusing schemes. … The Rutgers 12” Cyclotron (Fig. 1) is a 1.2 MeV particle accelerator dedicated to student education and exploration.

Ruisard, Hine, Koeth & Rosenberg, The Rutgers Cyclotron: Placing Student's Careers on Target — WE1PB02, Proceedings of Cyclotrons2013 (2013) — p. 1

Editorial note, tabletop extrapolation: PDF p.1 = printed p.291. The closest published match to the 8–12 inch class: same pole-diameter band, H-frame topology, a NOMINAL 1 T across a 2-inch gap, interchangeable tips, and a 1.2 MeV rating. Read the parameter set as an existence proof for the class, with one conversion warning: 1 T is roughly double a 0.5–0.6 T amateur magnet, so this machine's energies do not transfer to a weaker field at the same radius (E ∝ B²r²).

This solution only delivered a few nanoamps of current at the outer edge of the chamber.

Ruisard, Hine, Koeth & Rosenberg, The Rutgers Cyclotron: Placing Student's Careers on Target — WE1PB02, Proceedings of Cyclotrons2013 (2013) — p. 2

Editorial note, tabletop extrapolation: PDF p.2 = printed p.292 (the "dramatically increase deliverable beam current" phrase is on p.1). The easiest thing to machine — flat, parallel, precision-ground poles — is a documented failure mode at this scale: with a purely vertical field there is no axial restoring force, and this machine delivered only a few nanoamps to the chamber edge until a slight radial taper was cut. What another machine gets from flat poles depends on its own alignment, apertures and source; the transferable instruction is to evaluate axial tune and transmission from your own field map, expecting roughly this fate without a gradient.

Coupling resonances further restrict 0 < n < 0.2. In the existing tips, n = 0.2 occurs beyond the deflector radius.

Ruisard, Hine, Koeth & Rosenberg, The Rutgers Cyclotron: Placing Student's Careers on Target — WE1PB02, Proceedings of Cyclotrons2013 (2013) — p. 2

Editorial note, tabletop extrapolation: PDF p.2 = printed p.292. The pole-tip acceptance criterion under the ideal azimuthally-symmetric weak-focusing model (νr = √(1−n), νz = √n, so νr = 2νz at n = 0.2): do not just satisfy 0 < n < 1 — shape the taper so n stays under 0.2 out to the last useful radius, as this machine's tips do (n = 0.2 beyond the deflector radius). Confirm on the actual field map with a tune or tracking analysis; azimuthal variation, fringes and errors move the real resonance picture.

As predicted via simulation, phase slippage at standard DEE voltage (8 kV) was so severe that ions were not delivered to the deflector.

Ruisard, Hine, Koeth & Rosenberg, The Rutgers Cyclotron: Placing Student's Careers on Target — WE1PB02, Proceedings of Cyclotrons2013 (2013) — p. 2

Editorial note, tabletop extrapolation: PDF p.2 = printed p.292. A cautionary data point for anyone tempted by straight radial-sector AVF tips: on this machine the phase slippage was fatal at 8 kV on the dee — and, holding the same field-frequency mismatch and final radius, a machine with LESS energy gain per turn takes more turns and accumulates more slip, so a low-voltage build should expect this failure mode to bite harder, not softer. Check isochronism in the tracker before cutting sectored steel (the spiral redesign that followed is dg-1745's story).

This form is convenient for sectors defined by an Archimedean spiral, r = aθ^(1/n), for which tan ξ = dθ/dr.

Ruisard, Hine, Koeth & Rosenberg, The Rutgers Cyclotron: Placing Student's Careers on Target — WE1PB02, Proceedings of Cyclotrons2013 (2013) — p. 3

Editorial note, tabletop extrapolation: PDF p.3 = printed p.293 (the exponent 1/n is printed as a superscript; the quote transcribes it inline). The design equation for trading spiral tightness against vertical tune before cutting steel — with one correction applied: as printed, tan ξ = dθ/dr is not dimensionless; the standard edge-angle relation is tan ξ = r·dθ/dr, which for the stated Archimedean spiral evaluates to nθ. The flutter and approximation conventions are the paper's; verify against Livingood (its own ref [10]) before using the tune expression numerically.

Fourteen pole piece conceptions were modeled during the semester long project. … After examining field profiles and particle motion, the original design was adjusted or discarded, and a new design analyzed identically. Due to the short project duration (1 semester), each of the 3 students established competency in one program and worked as a team in interpreting results.

Ruisard, Hine, Koeth & Rosenberg, The Rutgers Cyclotron: Placing Student's Careers on Target — WE1PB02, Proceedings of Cyclotrons2013 (2013) — p. 3

Editorial note, tabletop extrapolation: PDF p.3 = printed p.293. The transferable part is the loop and its discipline: CAD → field solver → profile/flutter inspection → tracking → adjust or discard, then re-analyse identically — with the labour split so nobody had to master every tool. Fourteen concepts in one semester is what three students at a university managed with that structure; treat it as an existence proof of the loop's throughput, not an amateur productivity quota.

The ideal average field profile decreases with radial distance from the center before flattening out at larger radii … This is necessary to provide weak focusing at the central region, where flutter is negligible. High flutter values were also desirable, to increase the vertical tune.

Ruisard, Hine, Koeth & Rosenberg, The Rutgers Cyclotron: Placing Student's Careers on Target — WE1PB02, Proceedings of Cyclotrons2013 (2013) — p. 3

Editorial note, tabletop extrapolation: PDF p.3 = printed p.293. The most useful shaping rule in this paper for a small AVF attempt: flutter is essentially zero on axis, so the central region must still weak-focus — the falling inner profile is not optional — and the flat outer region approximates isochronism only in the low-energy nonrelativistic sense (exact fixed-frequency isochronism wants the orbit-averaged field rising as γ; immaterial at this machine's energies, material by 20 MeV). Fig. 4 shows the resulting bump-plus-flat profile for the chosen 270-degree spiral, whose caption marks the isochronous region.

This configuration demonstrated a reasonably flat profile, with a variation of ~4% from 1.5 out to 4 inches

Ruisard, Hine, Koeth & Rosenberg, The Rutgers Cyclotron: Placing Student's Careers on Target — WE1PB02, Proceedings of Cyclotrons2013 (2013) — p. 3

Editorial note, tabletop extrapolation: PDF p.3 = printed p.293. A reference AVF geometry at exactly tabletop scale — four sectors, Archimedean, 270 degrees of sweep, ~4% average-field flatness over the 1.5–4 inch working annulus on THIS 12-inch magnet. The same spiral cut for a different gap, excitation or yoke will not reproduce the flatness; re-run the 3-D model and map the result (the paper's own loop, dg-1788). SUSPECTED SOURCE MISPRINT: Fig. 4's x-axis is labelled "radius [mm]" but runs 0–6, which is inches on a 12-inch (6-inch-radius) pole; read it as inches, consistent with the text's own "1.5 out to 4 inches".

Difference analysis reveals a 14% variation between simulation and measurement. However, the discrepancy is <1% within the ion region.

Ruisard, Hine, Koeth & Rosenberg, The Rutgers Cyclotron: Placing Student's Careers on Target — WE1PB02, Proceedings of Cyclotrons2013 (2013) — p. 4

Editorial note, tabletop extrapolation: PDF p.4 = printed p.294. A rare model-versus-measurement pair at tabletop scale, and the lesson is the split: a 14% global mismatch coexists with sub-1% agreement where the beam lives. Score a FEMM/Elmer validation over the ion region so a usable model is not condemned by its periphery — but keep the full-aperture residual map and read it: where the big errors sit (and whether they are fringe, boundary or saturation artifacts) matters for extraction and for trusting the model's edges.

The geometric center was identified using an FFT-based analysis that maximizes the fourth harmonic and minimizes all others.

Ruisard, Hine, Koeth & Rosenberg, The Rutgers Cyclotron: Placing Student's Careers on Target — WE1PB02, Proceedings of Cyclotrons2013 (2013) — p. 4

Editorial note, tabletop extrapolation: PDF p.4 = printed p.294. A purely computational alignment method for anyone with a mapped field: for an N-sector pole, choose the origin that concentrates power in the N-fold symmetric harmonics (N and its multiples are legitimate structure; everything else is error or mis-centering). It removes the guesswork from registering a hand-built mapper's frame to the pole — then cross-check against mechanical registration and, once beam exists, closed-orbit behaviour, since a construction error can put the symmetry center away from the orbit center.

Multiple off-center stable orbits were found at particle energy 250 keV (nominal r=2.75”). … In Fig. 7, four stable fixed points can be seen surrounding the central fixed point. … The off-center islands quickly disappear at higher energies, and seem to have little effect on particle motion/stability during acceleration.

Ruisard, Hine, Koeth & Rosenberg, The Rutgers Cyclotron: Placing Student's Careers on Target — WE1PB02, Proceedings of Cyclotrons2013 (2013) — p. 4

Editorial note, tabletop extrapolation: PDF p.4 = printed p.294. Warns an AVF builder that a low-sector-count spiral geometry can grow parasitic off-center equilibrium orbits at intermediate energy (four of them here at 250 keV, matching the four-fold symmetry). The source's own hedged report: the islands "quickly disappear at higher energies, and seem to have little effect" during acceleration. Practical consequence: a beam that looks mis-steered at mid-radius may be sitting on an island — check with turn-by-turn tracking rather than assuming detrapping is clean.

A 30 AWG 7 cm radius wire loop was energized with 2.5 amps and placed in the magnetic gap … Four additional orbits were found at higher radii, beyond the four seen in simulation. These are likely lower energy equilibria, as the wire loop technique does not strictly correlate circumference to ion orbit energy (due to an additional degree of freedom, tension).

Ruisard, Hine, Koeth & Rosenberg, The Rutgers Cyclotron: Placing Student's Careers on Target — WE1PB02, Proceedings of Cyclotrons2013 (2013) — p. 4

Editorial note, tabletop extrapolation: PDF p.4 = printed p.294. An almost free diagnostic: hookup wire, a couple of amps and an acrylic spacer reveal a pole-tip set's equilibrium-orbit structure with no vacuum, RF or source. Run it as the controlled demonstration it was: 2.5 A through 30 AWG dissipates about 0.9 W in the fine wire, so use a fused, current-limited low-voltage supply, keep the duty short, secure the (nonmagnetic) leads, and keep hands clear while energized. Carry the authors' own caveat with the method: wire tension is an uncontrolled degree of freedom, so a loop's circumference does not map cleanly onto a beam energy — they found four MORE orbits than simulation predicted for exactly that reason.

The cyclotron facility has already secured an H-frame 19-inch magnet, a special General Electric magnet delivered to Rutgers in 1947 … and operated for 35 years for NMR research before retirement to storage.[13] Upon acquisition, the venerable magnet coils were in need of refurbishing and are currently awaiting new copper windings. … Future plans include the assembly of a second generation 19-inch educational cyclotron.

Ruisard, Hine, Koeth & Rosenberg, The Rutgers Cyclotron: Placing Student's Careers on Target — WE1PB02, Proceedings of Cyclotrons2013 (2013) — p. 5

Editorial note, tabletop extrapolation: PDF p.5 = printed p.295. One documented acquisition route: a decommissioned 1947 GE NMR electromagnet, secured for a planned second-generation educational machine — with the coils needing refurbishment as part of the price. It also records the scale step this program judged worth taking from a proven 12-inch: 19 inches, not 30. Before buying any surplus magnet of that vintage, inspect winding insulation, cooling passages, resistance and field quality; rewinding is a real possibility, not a certainty. This was a plan in 2013; the paper reports no beam from the 19-inch machine.

We find that operating below the nominal magnetic field increased the turn-to-turn phase slippage.

Gonski, Burcher, Lazarov, Krutzler, Koeth & Beaudoin, A Novel Optical Method for Measuring Beam Phase and Width in the Rutgers 12-Inch Cyclotron — WE1PB04, Proceedings of Cyclotrons2013 (2013) — p. 2

Editorial note, tabletop extrapolation: PDF p.2 = printed p.300 (the linear fit is Fig. 5, PDF p.3 / printed p.301). Practical tuning guidance: on this machine, field trim and RF phase budget were one knob, with an approximately linear response over the measured 0.498–0.566 T and a definite sign — below nominal costs phase. On another machine, run the same local field scan (or a trajectory model) to get the slope and sign; the linearity is an observation over this range, not a law.

during the experiment, current to the magnet was not continuously increased so as to follow the hysteresis loop.

Gonski, Burcher, Lazarov, Krutzler, Koeth & Beaudoin, A Novel Optical Method for Measuring Beam Phase and Width in the Rutgers 12-Inch Cyclotron — WE1PB04, Proceedings of Cyclotrons2013 (2013) — p. 3

Editorial note, tabletop extrapolation: PDF p.3 = printed p.301. A direct warning for any iron-cored tabletop magnet: the search procedure an operator naturally uses (find resonance, then step up and down) is exactly what breaks hysteresis reproducibility, and Rutgers name it as a contributor to their error bars. The primary remedy is procedural — pre-cycle the magnet and approach every setpoint from the same direction; a calibrated Hall probe (or NMR where homogeneity permits) then verifies the field at the radii that matter, rather than substituting for the discipline.

the pole tips can be up to 1-inch thick and are easily removable – to date, we have four sets of pole tips and one of each set is shown in Fig. 2. They consist of two weak focusing (one “good” and one intentionally “bad” for educational purposes), a radial sector AVF and a spiral sector AVF, all with a maximum central axial field, Bz(r=0), of 1.2 Tesla.

Koeth, Beam Physics Demonstrations with the Rutgers 12-Inch Cyclotron — WEPPT025, Proceedings of Cyclotrons2013 (2013) — p. 1

Editorial note, tabletop extrapolation: PDF p.1 = printed p.369 (the four sets are photographed in Fig. 2). The key architectural decision for a tabletop machine intended to be experimented on: make the pole tips removable and the same magnet becomes four different machines. Budget the geometry honestly — tips up to 1 inch THICK EACH sit inside the magnet opening, and the clear beam gap that remains is a separate design number this paper does not state. 1.2 T central is the stated ceiling with tips installed, versus the "nominally 1 Tesla" working figure quoted elsewhere in this collection.

The magnet’s upper and lower coils are independently energized for intentional field imbalance so as to shift the median plane. … Figure 6 shows three standard radial-draw beam images: the left frame top/bottom coil at 17/12 amps, the middle frame at 14.5/14.5 amps, and the right frame at 12/17 amps.

Koeth, Beam Physics Demonstrations with the Rutgers 12-Inch Cyclotron — WEPPT025, Proceedings of Cyclotrons2013 (2013) — p. 3

Editorial note, tabletop extrapolation: PDF p.3 = printed p.371 (design intent on PDF p.1 / printed p.369). A genuinely cheap axial-steering mechanism for a small machine: energize the two coils independently and trim the median plane. On this machine a 5 A top-to-bottom imbalance about the 14.5/14.5 A balance point still brought beam to the periphery — a demonstration that the knob has useful range, with transmission, centering and beam quality at each setting still to be measured on any machine that copies it.

Values of n=0.2, 0.36, 0.5 (and others yet higher) need to be avoided.

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

Editorial note, tabletop extrapolation: PDF p.2 = printed p.370. The explicit forbidden-n list a weak-focusing pole-tip designer rarely sees written down: inside 0 < n < 1, the taper must also avoid 0.2 (Qx = 2Qz), 0.36 and 0.5. A well-chosen profile keeps n below 0.2 for nearly the whole acceleration (the source's own following prescription); the design questions are where n(r) crosses what, and how fast — compute or map n(r) rather than assuming which resonances are in play.

Since the ions begin their spiral journey at r=0 necessarily n also starts at 0, and will only climb as the radius increases; if n=0.2 is to be avoided (Qx=2Qz), then the rate at which Bz decreases must be moderated such that n=0.2 only near the final ion radius.

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

Editorial note, tabletop extrapolation: PDF p.2 = printed p.370. The actionable pole-taper prescription for a small weak-focusing machine, on the source's own premise that n starts at 0 and climbs with radius: moderate the fall-off so n = 0.2 arrives only near the final radius. A taper aggressive enough to buy strong axial focusing early reaches the coupling resonance early, and time spent near it with any driving asymmetry risks resonant amplitude growth — Rutgers built a deliberately bad pole set to demonstrate exactly that (dg-1841).

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

Koeth, Beam Physics Demonstrations with the Rutgers 12-Inch Cyclotron — WEPPT025, Proceedings of Cyclotrons2013 (2013) — p. 3

Editorial note, tabletop extrapolation: PDF p.3 = printed p.371. The inverse of a design rule and the most instructive demonstration here: a taper whose n = 0.2 point lands at 3.5 inches instead of near the 5-inch dee edge converted a working configuration into one that grows axial displacement — and in the reported simulation and experiment the growth fed on a 3 mm chamber-to-magnet offset (the difference resonance bounds axial amplitude by the initial radial offset). What transfers is the mechanism and the method — locate n = 0.2 on the measured map, track orbits through it — not a fabrication tolerance or a universal seed threshold.

The most accessible magnet was a Varian V-3400 NMR magnet. It is of the typical H-frame design. Slight modifications were made to utilize the V-3400. Mounting the magnet sideways on a table created a horizontal gap at a reasonable work height. New pole tips were machined from 1020 rolled steel into cylinders, maximizing the diameter. The poles are nine inches in diameter and create a gap of 2.1875 inches. The maximum field obtainable from this geometry is 1.2 Tesla.

Koeth, The Construction and Operation of a Nine Inch Cyclotron (undated scan; the machine ran 1995–1999) — p. 1

Editorial note, tabletop extrapolation: Directly on point for an 8-12 inch tabletop machine. Two transferable moves: a surplus NMR/analytical H-frame magnet is a viable starting core, and re-orienting it so the gap is horizontal turns a vertical-gap instrument into a bench cyclotron with a flat median plane at working height. The 9 in pole / 2.1875 in gap pair (gap ~24% of pole diameter) is a concrete usable aspect ratio at this scale.

For reasons that will be discussed later the operating frequency is 13.56+0.03 MHz. Using the cyclotron frequency relationship: f = qB/2(pi)m a magnetic field of 0.889 Tesla was determined to be the operating field value. This was a welcome operating value, as the magnet need only be run at 70 percent of its maximum values, reducing the chance of coil failure by pressing the tolerances.

Koeth, The Construction and Operation of a Nine Inch Cyclotron (undated scan; the machine ran 1995–1999) — p. 1

Editorial note, tabletop extrapolation: A builder who inherits a fixed RF frequency (13.56 MHz here — a standard ISM frequency with cheap surplus hardware) can invert the design order and let the magnet operating point follow. Computed: 0.889 T is 74.1% of the 1.2 T ceiling — the author's "70 percent" is his rounding — and he treated the margin as a reliability choice for his coils; what margin buys on another magnet is a thermal/insulation/cooling question to check, not a free good. The quote's "+" before 0.03 MHz is a plus-or-minus sign the scan renders as a plus with an underline.

The magnet weighs 1780 pounds, it requires 40 volts at 168 amps, 7Kilowatts, to produce the maximum field of 1.2 Tesla. Only 28 volts at 114 amps, 3.2 kW, is required at the operating value of 0.889 Tesla. Water cooling is used to remove the heat generated by the coils, the inlet pressure is approximately 38 PSI and flow rate is no less than 4 GPM. The pressure is controlled with an inline pressure regulator and the flow rate is monitored with an impeller driven magnetic pick-up digital flow meter.

Koeth, The Construction and Operation of a Nine Inch Cyclotron (undated scan; the machine ran 1995–1999) — p. 1

Editorial note, tabletop extrapolation: The most useful sizing datum in the document: backing off from 1.2 T to the 0.889 T operating point cut coil dissipation from 6.7 kW (40 V × 168 A; the author's "7Kilowatts" is rounding) to 3.19 kW — a factor of about 2.1 — while still requiring monitored water cooling (38 PSI, ≥4 GPM, flow meter). The shape of the lesson transfers (field costs quadratic-ish power near saturation; margin is cheap to buy by backing off), the numbers belong to this 1780-pound magnet.

in six thousand or 2 gauss. Practically though, the field control was less than the theoretical as variations in cooling water temperature would change the resistance of the coils. The DC power system being voltage regulated then caused changes in the magnet current and of course the magnetic field.

Koeth, The Construction and Operation of a Nine Inch Cyclotron (undated scan; the machine ran 1995–1999) — p. 2

Editorial note, tabletop extrapolation: A cautionary rule with a number attached: the DAC chain promised 2-gauss setability (one part in six thousand), and the VOLTAGE-regulated supply handed that away to the chiller — cooling-water temperature moved coil resistance, hence current, hence field. Current regulation removes that specific path; hysteresis, yoke temperature, ripple and calibration remain, so a claimed field stability is demonstrated by measurement (or closed on a Hall/NMR probe), never promised by the DAC's step size. (The sentence begins on p.1: "...theoretically the magnetic field could be adjusted to one part..."; "Telsa" is a source typo.)

A precision shunt of 1.00 mOhm was inserted into the magnet DC power lead, a 5 digit Keithly DVM measured the voltage drop across the shunt. A Bell 620 Hall Effect Gaussmeter measured the field, while another Keithly DVM measured the 620's recorder output. The Hall Effect probe was located centered, flat against the surface of the bottom pole piece. An HP85 HPIB based computer was employed to slowly ramp the magnetic field while, while reading the values of the two meters. … The data was then recorded to an IBM PC disk via an RS232 link.

Koeth, The Construction and Operation of a Nine Inch Cyclotron (undated scan; the machine ran 1995–1999) — p. 2

Editorial note, tabletop extrapolation: A cheap, reproducible B-versus-I measurement arrangement: precision shunt + DVM for current, Hall gaussmeter read at its recorder output by a second DVM, a computer ramping slowly and logging both. Two craft details worth copying: the probe flat against a pole face is a REPEATABLE mechanical reference (one point, though — median-plane mapping is a separate job, dg-1683-class), and slow single-direction ramps respect hysteresis. Add probe calibration and an uncertainty estimate before calling the curve a calibration. (Spellings as printed: "Keithly", doubled "while".)

Uniformity of the magnetic field is extremely precise. The surfaces of the two poles are parallel with 0.001 inches. As will be seen later, the poles and yoke are slightly deflected due to the extreme pull of the electromagnetic force at high fields. No shimming of the magnetic field to increase the beam current has been attempted yet, however there are future plans to do so.

Koeth, The Construction and Operation of a Nine Inch Cyclotron (undated scan; the machine ran 1995–1999) — p. 2

Editorial note, tabletop extrapolation: What the reference machine did: pole faces parallel within 0.001 inch, no shimming attempted (a stated future plan), and beam achieved — an existence proof that this machine's field, as machined, sufficed for its ~184 keV operation. It is one machine's outcome, not a tolerance spec: map the assembled field under excitation (including the deflection under magnetic load the author himself flags, dg-1862) and let beam-dynamics requirements decide whether machining or shims are owed.

the magnet poles must be attracting one another under the tremendous force, thereby squeezing the lids on the vacuum chamber. The inward movement of the lids would decrease the distance between the DEE and the lids creating an increase in chamber capacitance, thereby bringing down fr. The distance of movement was calculated from the change in frequency. Just using the approximation for a parallel plate capacitor the distance the gap decreased was on the order of 7 nanometers. The attractive force between the two poles was also estimated, at 1 Tesla the attractive force is approximately 16,000 N which the equivalent of placing a 3,500 pound mass on the top yoke. … Under such forces it is reasonable to imagine deflection on the order of 70 Angstroms.

Koeth, The Construction and Operation of a Nine Inch Cyclotron (undated scan; the machine ran 1995–1999) — p. 5

Editorial note, tabletop extrapolation: The most surprising transferable failure mode in the document, appearing when the chamber is shimmed snugly between the poles: Fig. 8 shows the tank fr flat at ~13.559 MHz from 0.17-0.67 T then falling to ~13.551 MHz near 1.0-1.07 T — an ~8 kHz walk, comparable to this RF source's 10 kHz tuning step. Expect the tank to move during a magnet ramp and either retune per field point or decouple the lids from the pole faces. The 16,000 N checks against B²A/2μ₀ for a 9-inch pole at 1 T (computed, ≈16,300 N); the attribution of the shift to lid motion is the author's interpretation, consistent between his frequency-derived 7 nm and force-based plausibility argument.