Magnet design rules

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

efficiency ~ 0.98 For magnets with well designed yokes.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

calculation results and measurements differ less than 3 percent

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Ampere-Turns = 2.02 x gauss x inches gap

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Increased cross section reduces flux through yoke to 1.2T

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Tabletop: This is the governing stability rule for the weak-focusing reference machine; the FEMM-derived B(r) should be checked for 0 < n < 1 over every acceleration radius, with n typically a few percent.

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

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

Tabletop: In the reference machine Qr = sqrt(1-n) sits just below 1 everywhere, so the key is field symmetry: keep the first-harmonic error (pole tilt, off-center coils) to gauss level or coherent orbit distortion grows every turn.

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

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

Tabletop: Very concrete for the reference machine: if the edge-field falloff pushes n through 0.2 near the last turns, the beam blows up vertically into the dee aperture; keep n < ~0.2 until the extraction radius or cross it fast.

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

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

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

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

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

Tabletop: A concrete shimming target: on a 0.59 T, 8-inch machine, holding the measured field to ~1e-3 of the design curve (a few gauss) keeps phase errors negligible next to the classical-cyclotron phase slip itself.

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

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

Tabletop: Sets the expected FEMM-vs-Hall-probe discrepancy for the reference machine's magnet: 1-2% mismatch is normal (unknown B-H curves, geometry error) and should be absorbed by a per-coil scale factor in the builder tool, not chased in the mesh.

the level of the magnetic field in the center is raised to an amount of a few tens to a few hundred gauss

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

Tabletop: Directly usable on a next machine: shim a small central cone so B falls gently from center outward, giving vertical focusing where n ~ 0 would otherwise leave the first turns unfocused.

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

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

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

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

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

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

For a typical conventional cyclotron (Bo ~ 1.7 T) a bump of 0.1 mT (1 G) introduces a radial gain of about 0.2 mm.

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

Tabletop: Scaled to 0.6-0.9 T and r~0.1 m, tens of gauss of first harmonic would be needed to force mm-scale separation - precession is far cheaper than brute force.

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

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

Tabletop: A next machine with R~10 cm and half-gap 1.27 cm allows only ~9 turns (needs ~17 keV/turn); shrinking the half-gap to 6-7 mm at the edge allows ~30 turns - borderline reachable with a 5-10 kV LDMOS dee.

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

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

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

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

Tabletop: The reference machine's 0.59 T and a higher-field successor's ~0.9 T are both comfortably above threshold — the PIG will ignite and run without any special field tailoring, and cyclotron field tuning won't detune the arc.

have been used in magnetic fields as high as 4.5 Tesla in the Harper Medical Cyclotron (and as low as 0.5 Tesla during low magnetic field tests in the NSCL ion source test stand)

Forringer, Phase Space Characterization of an Internal Ion Source for Cyclotrons — MSU dissertation (2004) — p. 27, 39

Tabletop: The reference machine's 0.59 T sits just inside the demonstrated envelope, and its existing turbo + 1e-6-ish base pressure meet the start requirement 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

Tabletop: General magnet practice, fully transferable - a next machine's pole/yoke/shim geometry can be optimized on a small bolt-together model before buying full-size steel.

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

Tabletop: General magnet economics, transferable - pick a next machine's coil proportions near the cost/power optimum, then adjust freely for winding or cooling convenience.

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

Tabletop: Directly applicable weak-focusing target - same n=0.2-class profile is the textbook goal for an 8-inch fixed-frequency machine's shim program.

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

Tabletop: Directly applicable - budget usable beam radius at ~90% of the 8-inch pole (r_max ~ 3.6") unless the pole is generously sized below the face.

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

Tabletop: Directly applicable - a 0.1% relative radial map (differential Hall probe or flip coil) is the entry ticket to meaningful n(r) shimming on the next machine.

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

Tabletop: Directly applicable - mil-level gap closure at 0.6 T shifts field and n(r); shim and map the next machine 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

Tabletop: Cautionary and transferable - exotic Co-Fe edge rings for the next machine's pole edge need a stability check; plain steel shims are the safe default.

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

Tabletop: Transferable principle - steel-to-steel permeability variation is real; test a next machine's shim stock from the same material lot as the poles.

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

Tabletop: Directly applicable - a few-mil pole tolerance is achievable in a good hobby/job shop and is what the field uniformity budget assumes.

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

Tabletop: Directly applicable packaging rule - make the next machine's chamber removable (or serviceable in place) without unbolting pole tips or shims.

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

Tabletop: Directly applicable - the pole-chamber geometry of an 8-inch machine forms the same parasitic cavity; copper straps pole-to-pole (or liner-to-liner) are a one-hour fix worth doing preemptively.

this shielding was found sufficiently effective, the field being cut from 140 Gauss to less than 20 Gauss.

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

Tabletop: Transferable - LDMOS amps, fans, and ferrite-cored parts near an 0.59 T magnet want a steel housing; remember the housing itself feels a large attractive force.

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

Tabletop: Fully applicable to fixed-frequency machines: map B(r) on the bench, compute n(r), and put the target/septum radius inside the n = 0.2 point; if the reference machine's beam stalls early, this is suspect number one.

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

Tabletop: Budget a next machine's energy at the n = 0.2 radius, not the pole edge; shaving the pole-edge shims to push n = 0.2 outward buys more usable energy than chasing radius into the fringe.

Mag. field, k-gauss 14 - 19

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

Tabletop: The reference machine's 0.59 T is a factor 2-3 below the entire historical population; pushing a next machine's magnet toward 1.2-1.5 T multiplies energy 4-6x at fixed pole radius and is how every real small machine reached MeV.

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

Tabletop: Extrapolating down, an 8-in-pole machine wants ~0.5-1 ton of iron - hobby-crane scale; it also warns that every inch of extra 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

Tabletop: Sanity template for a next machine on 8-in poles: expect ~1.0-1.4 in gap, ~0.5-0.8 in dee aperture, and plan energy at a 3.2-3.6 in beam radius, not at the pole edge.

Field drop-off 3-4 %

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

Tabletop: Directly transferable target for shimming the reference machine's 0.59 T field: a measured 2-4% drop across the usable radius, smooth and monotonic, is what the entire fixed-frequency population converged on.

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

Tabletop: The builder can trim B to match a fixed RF (or vice versa) and expect the shim profile to survive, as long as the iron is not driven into locally different saturation - measure n(r) at both ends of the intended current range.

Air-cooled coils. Iron ore blocks for shielding

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

Tabletop: Supports keeping a next machine's coils air-cooled with duty-cycle management instead of plumbing water - two real machines at 12.5-16 kG did exactly that.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

It 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

Tabletop: Two transfers: verify a next machine's field map with the chamber assembled and pumped (pole deflection under vacuum load is a real 1950s worry that proved negligible for them — measure once to confirm); and note 0.03% first harmonic as what a carefully shimmed classical machine actually achieved — consistent with the ~5 G field target for a next machine.

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

Tabletop: 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

Tabletop: Deliberately-saturating iron as a field-programming element is a trick FEMM models well — for a next machine's central plug or shim stack, a piece sized to saturate at the main operating point gives low-field correction "for free" without trim windings.

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

Tabletop: A measured 1960s tolerance to calibrate the next machine's 5 G / 5-deg-RF-phase target against: an AVF machine accelerating hundreds of turns lived with 15 G deviation. A classical few-tens-of-turns tabletop machine tolerates proportionally more — the phase-slip integral, not the gauss number, is what to check in the tracker.

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

Tabletop: Validates the classical-cyclotron instinct for a next machine: a small positive field bump at center (field falling with radius from turn one) focuses the turns that the z-distribution studies (ORNL 22-inch) show carry all the loss; give away a little phase to get it. Empirically checkable on the reference machine with shim washers at the pole center.

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

Tabletop: The 1966 proof that a next machine's compute-first pipeline (field map -> tracker -> build) is sound — if the field is measured carefully and the tracker is honest, first beam on the first pump-down is a reasonable expectation, not luck. Also a period example of commissioning on H2+ rather than protons for shielding reasons.

This region, called the "gap," should have a diameter about nine times as great as its axial dimension.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 6

Tabletop: 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

Tabletop: Gives the next machine's FEMM loop a quantitative target - compute gap-flux/pole-flux efficiency for each candidate tip and expect ~0.5-0.65, not the naive 1.0; large shortfalls flag leakage-wasting geometry.

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

Tabletop: On 8-in poles the difference between 92% and 96% usable radius is ~9% in energy (B^2R^2); the groove-plus-raised-edge profile is cheap to try in FEMM and on the real shims. NYO-780 pp.9-10 reached the same ~96% figure experimentally - cite both.

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

Tabletop: Directly the next machine's shim program - FEMM replaces some iterations, but finite permeability and saturation mean the last passes happen on the bench with a probe map, exactly as NYO-780 (p.7) did with its bolt-together model magnets. Cite both.

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

Tabletop: Handy closed-form sanity check for any center-cone or button shim on the next machine before FEMM - saturated iron adds field like a permanent magnet of strength Bs/4pi, independent of excitation.

The resistance of the coil is proportional to its mean circumference ... the coil should be as small as is consistent with a reasonable power requirement.

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

Tabletop: 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

Tabletop: This collection's only explicit dollar-optimization of magnet proportions - rerun Eq. 114 with 2026 unit costs (scrap steel, surplus copper, $/kWh over expected machine life) to place a next machine's coil proportions. NYO-780 p.8 did the equivalent sweep by model; cite both.

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

Tabletop: Licence to trade a few percent of cost-optimality for access, cooling clearance, or stock material sizes - the optimum is a plateau, not a peak. 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

Tabletop: A 1952 statement of the plan's own doctrine - cost models are gated on real operating data, so freeze the estimate, build, and revise with actuals rather than polishing the spreadsheet.

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

Tabletop: Two cautions in one - shave the computed OD, and treat big-machine coil proportions (including TID-454's own x~1.4) as non-transferable to an 8-12 in machine without redoing the optimization at that scale.

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

Tabletop: When sizing a surplus supply for the next machine's coil (or the number of turns for a given supply), pick turns so the coil's hot resistance sits at the supply's V_max/I_max corner.

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

Tabletop: 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

Tabletop: For a next machine's steel shopping - spend on clean low-carbon (1006/1008) pole and pole-base stock, accept structural mystery steel in the return yoke, and size the pole base to run near but not into the knee (~1.8-2.1 T).

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

Tabletop: 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.

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

Tabletop: 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 rather than absolute B(r), and supply drift drops out of the shim iteration.

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

Tabletop: SCALE-SCOPED (megagauss context) but the scaling itself is exact and explains amateur economics - it is why small bore air-core inserts and compact analyzing magnets are feasible while whole-machine air-core fields are not.

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

Tabletop: Locates amateur work far below the exotic regime - for sub-kG correction coils, steering windings and test solenoids, wind the simple thing; sophistication buys nothing until iron saturates and fields climb an order of magnitude.

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

Tabletop: Marginal for the cyclotron itself, but the right doctrine for any air-core uniform-field fixture - probe-calibration coils, a beamline corrector, or a small synchrotron's reference field - when tens of gauss or more are wanted continuously.

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

Tabletop: Explains an observation class on the reference machine: probe current can look tolerant of field/frequency error while the beam's phase (and thus its energy at radius) shifts underneath — reinforcing ORNL-1347's rule that current on target is not evidence the energy is what B-rho says. Phase self-selection also broadens resonance-tuning curves; do not read their width as the true stability margin.

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

Tabletop: Scale-free requirements-hierarchy discipline; the same three hard requirements (isochronism/weak-focusing law, focusing, power) apply verbatim to any cyclotron magnet trade.

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

Tabletop: Directly scale-free: machined iron holds tolerance far better than wound copper at any size, and 'shim if necessary' should be a scheduled step, not a failure mode.

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

Tabletop: 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

Tabletop: Scale-free budgeting rule (from the Analogue, a 42-gauss machine): spend regulation money in proportion to field contribution — main coil tightly regulated, trim/harmonic coils on cheap trimmed sources.

Gap tolerance +/- 0.004 in.

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

Tabletop: 810-MeV provenance: this is the spec for a 53-ft isochronous magnet with 4-in beam aperture; the transferable content is the relative-tolerance framing (fraction of gap), consistent with the next machine's 5 G / 5-deg-phase field-error budget, not the absolute mils.

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

Tabletop: A zero-cost magnet diagnostic for the reference machine or a next machine - enameled wire and a bench supply locate both the magnetic median plane (which need not be the geometric midplane) and the field center before any Hall-probe mapping campaign.

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

Tabletop: Direct pole-scale match to the reference machine (8-in. poles) - an eighth-inch median-plane and quarter-inch centering tolerance were good enough for a working ORNL test machine; ornl-1345's B-sweep species analysis on this same machine presumed exactly this alignment quality.

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

Tabletop: The reference machine's H-frame magnet is the analogous asset: energy upgrades (gap, shims, dees, rf power) can be staged around the same 757-lb iron for years, exactly as ORNL staged 1.5 -> 5 MeV -> (proposed) 48-in. heavy ions around one magnet line. Rename footnote: PDF p. 17.

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

Tabletop: 86-inch numbers, but the trick scales - a few-turn half-wrap trim coil on a next machine's pole gives a first-harmonic/gradient control for orbit centering and effective-energy variation that FEMM can model directly; also a candidate cheap "variable-energy" feature for an educational machine.

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

Tabletop: 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 every millimeter given to voltage clearance is field (B ~ 1/gap) taken from energy. Decide dee voltage and gap in the same trade study.

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

Tabletop: 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, scaled up in radius and voltage. Use it to sanity-check B-f consistency and to see what 100 kV (vs the reference machine's ~0.8 kV) buys in radius terms.

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

Tabletop: For a next machine's shim development (5 G ~ 5 deg rf phase target): 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 against an uncharacterized pole error. 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

Tabletop: Calibrates expectations for a next machine - 5e-4 base-field uniformity is what sustained professional effort actually bought on 44-in. poles; set the shim budget assuming the ground pole delivers ~0.05% and the final trim to the 5-G target comes from shims, not from more grinding.

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

Tabletop: 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. ORNL judged these features worth 14.4 tons of model.

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

Tabletop: 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

Tabletop: DIRECT method (not numbers) - measure the real beam first, then stack two explicit margins. A next machine's envelope must come from its own extraction simulations/measurements; the 50%-then-round-up discipline is what prevents an undersized bore discovered after winding.

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

Tabletop: DIRECT money-saver, stated as an explicit lesson-learned footnote in 1954 and standard practice ever since. A next machine's quads (if built) can use round stock or FEMM-checked circular-arc tips; spend the FEMM time on end effects, not profile exactness.

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

Tabletop: DIRECT - for short quads the fringe extension is a first-order effect, not a correction. Modern practice: l_eff = l_phys + ~aperture radius; get it from the FEMM/tracker pipeline per magnet, and expect focal errors of tens of percent if ignored.

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

Tabletop: DIRECT - at a next machine's rigidity, transport-quad fields are hundreds of gauss at most, so air-cooled random-wound coils on unsaturated iron are the default. OCR trap - the text layer renders the B^1/2 exponent as B^2; page image verified B^1/2.

the coils in each unit are connected in series since otherwise we would have extreme difficulty in maintaining uniform gradients.

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

Tabletop: DIRECT wiring doctrine for any home-built multipole - gradient symmetry comes from forced equal current, not matched resistances. The 20% ampere-turn margin and the use-the-wire-you-have coil design (surplus

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

Tabletop: 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

Tabletop: DIRECT - the 0.4-gap effective-boundary shift is the same magnitude modern codes assign (FINT*gap); for a next machine's analyzer designed in FEMM the rule is a sanity check that the simulated effective edge sits ~0.4 gap outside the steel.

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

Tabletop: 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

Tabletop: SCALE-HONEST: geometry is energy-independent (it fixes E/E0 ratios, not E), so a palm-sized R ~ 5-10 cm version at a few hundred gauss would broad-range-analyze a next machine's ~170 keV protons identically - a compelling teaching-lab focal-plane instrument. The 5-ton, 14-kG original is MeV-class; copy the optics, not the iron.

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

Tabletop: 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

Tabletop: DIRECT pairing of two ideas the reference machine already half-uses - (1) an error that scales rigidly with excitation is absorbed by end-to-end calibration; (2) loss of NMR (or Hall-linearity) signal quality is itself a diagnostic of entering saturation. Worth writing into the next machine's field-mapping procedure.

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

Tabletop: DIRECT construction pattern for any next-machine analyzer or spectrograph - poles-as-chamber eliminates the gap-wasting separate tank (the alternative Bromley rejected for his condenser on machining/gasketing grounds, nyo-3823 p.6). The anti-scattering baffles and the tenth-mil spacer discipline are the details that make emulsion-grade spectra possible.

The radial spacing of the table entrys is interpreted as increased by the factor 64/8.75 corresponding to the ratio of pole diameters

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

Tabletop: The historical analog of the CadQuery->FEMM->field-map pipeline, plus two habits worth copying — symmetrize and smooth measured maps before tracking, and document every cleanup applied to the field the tracker actually ate.

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

Tabletop: Cuts both ways at reference-machine and next-machine scale — shim asymmetries of tens of gauss are dynamically significant near nu_r = 1 (center and full radius), yet a deliberate few-turn bump coil is a powerful, cheap orbit-steering experiment.

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

Tabletop: Directly transferable design-process pattern for any pole/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 instead of a target field profile.

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

Tabletop: 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

Tabletop: A model-calibration pattern the FEMM-based pipeline should copy — one deliberate known-geometry measurement (a wire loop, a known coil) in the actual gap pins the permeability/saturation assumptions the whole field model rests on.

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

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

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

a magnetic mirror built into the upper end of the arc hood by the simple insertion of a steel bearing ball 1/8" in diameter.

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

Tabletop: DIRECT and nearly free for any filament hooded source running in the main field: a bearing ball is stock hardware and the hood already exists. This is the halfway house between a plain filament arc and a cold-cathode PIG — same electron-reuse physics, no second cathode, no separate supply.

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

Tabletop: An honest negative result from 1961 that still stands: the electron injection angle into the mirror (set by filament orientation relative to B) decides whether electrons are inside or outside the loss cone. Plan the mirror experiment as an A/B test with the glow diagnostic, and try filament orientation as a variable 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

Tabletop: 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

Tabletop: The general move — translate a beam-geometry tolerance into a measurable dH/dx budget via the curl-free midplane relation — is machine-independent and gives a field-map pass/fail number before any tracking is run.

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

Tabletop: Same arithmetic every H-frame designer runs today (corroborates the ampere-turn sizing in Wouters and Zickler's CAS magnet notes); the 85-95% efficiency band is a sanity check on any FEMM excitation result for an unsaturated return frame.

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

Tabletop: 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

Tabletop: Brackets the usual 1.5-2.5 A/mm^2 air-cooled small-magnet guidance from the modern side (Zickler/Tanabe territory) with 1940s operating experience; a passively cooled tabletop coil should sit at or below the bus-bar figure.

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

Tabletop: 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.

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

Tabletop: Directly relevant to removable pole caps and bolt-on shim plates on a small H-frame — the retention hardware must react a lateral load, not only the axial pull normally computed from B^2/2mu0.

Force between pole faces (lb) = 1/1.735 X (kilogauss)^2 X area (sq in.)

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 31

Tabletop: 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.

it is desirable to keep the driving coils as close to the air gaps as possible in order to reduce spreading and bowing of the field and to keep the largest possible fraction of the gap area usable.

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

Tabletop: 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.

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

Tabletop: 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 an integrator, provided the flip is a true reversal.

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

Tabletop: The classical answer to shimming with a wandering surplus supply — map relative structure differentially and pin the absolute scale with occasional flips; a modern two-channel Hall differential measurement inherits the same immunity.

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

Tabletop: Zero-cost qualitative diagnostics for a home lab — a filing map locates stray-field lobes and leakage paths before any probe survey, and the discharge-follows-field trick is a natural cross-check in a machine that already runs a plasma source.

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

Tabletop: 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

Tabletop: The mesh-refinement decision in physical form — coarse resolution for excitation/force/leakage questions, fine resolution only for the ppm-level uniformity region; spending fine-model effort on questions the coarse model already answers is waste in either medium.

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

Tabletop: A ready-made deliverables checklist for a simulation campaign on a new magnet — a FEMM study that produces these five plots plus a member-by-member flux audit has done what the 1944 model program did, in the same order.

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

Tabletop: A two-point excitation scan (measured or simulated) separating "efficiency constant" from "efficiency dropping" localizes saturation onset without any interior probe — directly usable on an H-frame by comparing measured B vs I against the linear NI prediction at two currents.

In the neighborhood of 10,000 to 15,000 gauss the flux density is good, yet the yokes are not overloaded to the extent that the permeability of the steel drops excessively.

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

Tabletop: 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

Tabletop: Gives this collection a quantitative "too far": mu ~ 100-150 at the working point is the failure territory, and the audit must use the actual steel''s curve — the same reason a FEMM model of an H-frame is only as good as the 1010/1018 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

Tabletop: The general pattern — a boundary cell needs measured, adjustable over-excitation (or shimming), and a two-point measurement plus linear extrapolation converges in one iteration — applies to any edge-compensation knob: outer-radius shim thickness, trim turns near a yoke window, or a correction-coil ampere-turn setting.

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

Tabletop: 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 — a modest face sheet decouples interior steel economies from gap-field quality.

the forces calculated on the basis of the average over the entire region will be lower than the true force.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 144

Tabletop: 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

Tabletop: Governs any shim pack, pole-cap seat, or chamber-lid-under-pole arrangement: a deliberately larger uniform standoff can beat a smaller irregular one, because +/-50% of a big gap passes where +/-50% of a tiny gap is unmachinable.

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

Tabletop: The historical calibration point for any predict-then-verify magnet pipeline: a faithful scaled model (same-steel/same-B then; validated FEM now) lands within a few per cent on global quantities and errs conservative when the prototype''s iron is better than the model''s — but the trust was EARNED by one full validation campaign, not assumed.

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

Tabletop: A 1944 warning that survives every FEMM run: analysis predicts the as-built field well but predicts CHANGES to an as-built field only if the change is modeled exactly as executed. Plan shimming as measure-cut-measure iterations, and keep shim stock adjustable.

a check on the positions of the tanks in this quadrant showed that some of them had moved as much as 2.5 in. out of the gaps.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 190

Tabletop: 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 invisible at the symmetric position and largest just when the part has already started to walk.

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

Tabletop: Three habits for a home lab: repeat-trace to certify a mapping method, calibrate the current METER (it is usually the accuracy floor of a B-vs-I curve), and normalize survey data to a monitor reading so supply drift cancels out of shape maps.

Apparently the control of the magnetic properties in the manufacture of steel is rather uncertain.

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (c. 1950) — p. 14

Tabletop: 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 (c. 1950) — p. 14

Tabletop: 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 (c. 1950) — p. 17

Tabletop: 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 (c. 1950) — p. 18

Tabletop: The transferable rule is identity of 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, not a library curve for its nominal grade.

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 (c. 1950) — p. 19

Tabletop: 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, and remember the yoke-steel trick — outer return-path steel raises gap field without touching pole-gap geometry.

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 (c. 1950) — p. 26

Tabletop: DIRECT — the differential trick ports to modern probes; two matched Hall/NMR channels read as a difference kill supply drift and thermal drift, the dominant error sources in a garage field survey. Same scheme reused on the full magnet with 28-turn, 0.607-cm-mean-radius coils (PDF p.30).

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 (c. 1950) — p. 29

Tabletop: DIRECT physics — the n = 0.4 exit target and monotonic ~1% interior droop are the same numbers this collection's Wouters and Livingston rules give, here as an as-built spec that produced a working field. A FEMM shim study should adopt criteria (1)-(5) as its objective function.

with this shim design a reduction of the exciting current produced a minimum in the radial dependence, which is an objectionable feature.

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (c. 1950) — p. 30

Tabletop: 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 (c. 1950) — p. 30

Tabletop: Any ferromagnetic chamber lid or pole-integrated cover on a tabletop machine sees magnetic clamping comparable to or exceeding vacuum load — check both cases (energized/de-energized) for deflection, and expect assembly/disassembly forces. Stray field at the RF tube/amplifier is likewise a real design input for a compact machine.

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 (c. 1950) — p. 33

Tabletop: 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 (c. 1950) — p. 33

Tabletop: A central field bump gives axial focusing in the first turns, where small machines lose most of their beam. A machined center button is one of the cheapest beam-current experiments available to the reference machine or a next machine — the no-minimum constraint is the part that takes care.

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 accomodate water lines

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (c. 1950) — p. 33

Tabletop: DIRECT — an H-frame yoke is item (1) by construction. Keep fasteners, liner screws, and cooling-line reliefs symmetric in the pole region, or place them where the survey says 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 (c. 1950) — p. 41

Tabletop: DIRECT — thousandths of pole tilt are visible in a tabletop field survey and in beam behavior. Shim the measured field, not the dial indicator; calibrate shim sensitivity from the first iteration and extrapolate; and expect a floor because every local correction spreads.

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 (c. 1950) — p. 42

Tabletop: Sets a realistic bar — a carefully shimmed iron magnet holds azimuthal variation to ~a few parts in 10^4 over the working radii, and the spec that matters is at ~80% radius, not at the pole edge.

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 (c. 1950) — p. 42

Tabletop: DIRECT physics: a displaced/dished magnetic median plane steers the circulating beam into a dee lid at small gap heights. A tabletop analog of the dip needle (or vertical probe-pair difference) belongs in the survey plan; and keep deliberate shimming mirror-symmetric about the midplane unless correcting the median surface is the goal. Needle details PDF p.44, map Fig. 3.13 p.45.