Cyclotron design rules, level 2: first-order design

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Cited in: Cyclotron Magnet Design

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

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

Editorial note, tabletop extrapolation: The cheapest field upgrade for a next machine is gap reduction - thinner chamber lids, pole pieces reaching into the chamber - before any coil or steel changes. Model the actual gain in FEMM rather than assuming 1/g.

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

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

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

Cited in: Cyclotron Magnet Design

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

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

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

The magnet consists of coils of hollow copper tubing wound on a two-ton core of mild steel. ... capable of producing a very uniform 17,000 gauss field ... tapered from 12-inch pole stems to 10-inch pole faces.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

efficiency ~ 0.98 For magnets with well designed yokes.

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

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

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

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

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

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

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

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

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

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

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

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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

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

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

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

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

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

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

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

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

calculation results and measurements differ less than 3 percent

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

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

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

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

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

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Editorial note, tabletop extrapolation: Lets the builder compute the hollow-conductor bore and pump requirement for a next machine's 5-20 kW magnet with a spreadsheet, no CFD - provided every input is converted to the source's units first: a bar-for-pascal slip in the pressure drop moves the bore answer far more than the recipe's real margin.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Editorial note, tabletop extrapolation: Directly actionable option for a next machine: targeting ~0.89 T instead of 0.59 T puts the machine on the 13.56 MHz ISM band, where used generators, amplifiers and matchboxes are plentiful. Legality rides on emissions containment rather than the band label (dg-1373's verification), and the match must still be designed for the dee's actual impedance (dg-287).

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

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

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

Ampere-Turns = 2.02 x gauss x inches gap

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Cited in: Cyclotron Vacuum Chamber Design and Sealing

Increased cross section reduces flux through yoke to 1.2T

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

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

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

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

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

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

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

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

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

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

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

Cited in: Beam Dynamics: An Interactive Laboratory

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

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

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

Cited in: Beam Dynamics: An Interactive Laboratory

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

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

Editorial note, tabletop extrapolation: Low-cost simulation path for a hobbyist - Superfish is free, SIMION is paid but widespread, and FEMM plus the playbook's Python tracker is the all-free equivalent; the appendix geometry file is a working starting template for an 8-15 cm pole magnet.

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

Loucks, Initial Results from the Houghton College Cyclotron — Houghton College thesis (2007) — p. PDF p.36 = printed p.36 (Loucks thesis Sec. 3.2 Magnet); the cited '35-36' range is correct, all figures are on 36

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

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

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

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

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

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

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

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

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

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

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

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

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

Cited in: Beam Dynamics: An Interactive Laboratory

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

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

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

Cited in: Beam Dynamics: An Interactive Laboratory

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

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

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

Cited in: Beam Dynamics: An Interactive Laboratory

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

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

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

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

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

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

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

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

Editorial note, tabletop extrapolation: Explains the positive field index (n > 0 in the site's n = -(r/B)dB/dr convention) that a flat-pole tabletop magnet already has from its natural falloff - and why a bigger gap gives more weak focusing but less field.

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

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

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

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

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

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

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

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

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

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The finished magnet forgings satisfactorily met these specifications. The chemical check analysis of the steel, well within our specifications, was: C 0.110, Mn 0.330, P 0.010, S 0.030, Si 0.015, Ni 0.060

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Editorial note, tabletop extrapolation: One-line flow-rate calculator: a 1 kW coil on a next machine needs ~0.4 gpm for a 10 C rise.

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

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

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

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

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

Editorial note, tabletop extrapolation: Turns the amp-turn number into an actual coil window size before you buy tubing or start winding.

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

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

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

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

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

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

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

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

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

Flow velocity should be high enough so that the flow is fully turbulent, Re ≳ 4000... For synchrotron radiation accelerators where beam stability depends on temperature stability, ∆T ≲ 15°C.

Tanabe, Iron Dominated Electromagnets: Design, Fabrication, Assembly and Measurements — SLAC-R-754 (2005) — p. PDF pp. 134-135 = printed pp. 134-135 (chapter section 'Coil Cooling'), as cited

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

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

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

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

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

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

Editorial note, tabletop extrapolation: Directly applicable guidance for a next machine's coil geometry.

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

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

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

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

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

Editorial note, tabletop extrapolation: Directly applicable when choosing wire gauge and supply for a next machine's coils.

C_top+bottom = 2C = 70.5 pF ... C_edge = 7.04 pF ... For a total C of: 77.5pF. Measurement of the capacitance with an L-C meter yields a value of 78.1pF. Nice agreement seen!

Koeth, Theoretical Calculations and Measurements of the DEE Voltage in the Rutgers 12 Inch Cyclotron (2005) — p. PDF 1 (page 1 of the September 2005 Koeth memo) as cited

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Editorial note, tabletop extrapolation: At ~1.3 kV and ~150 keV the reference machine's ions make ~60 turns; doubling dee voltage halves turns and dramatically relaxes both field-uniformity and vacuum (scattering) requirements.

The resonant circuit is electrically equivalent to a pair of quarter-wave coaxial transmission lines with the D's supported on the ends of the inner conductors. ... two power tubes in push-pull and two coupling loops is the more common arrangement.

Livingston & Blewett, Particle Accelerators (1962) — p. PDF pp.185-187 (printed pp.169-171)

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

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

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

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

Cited in: The Vacuum Budget of a Cyclotron

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

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

Editorial note, tabletop extrapolation: The same logic favors a drive that follows the dee on the reference machine: self-excited, or a PLL tracking the resonator - similar in spirit though not identical in dynamics, since a PLL adds its own loop behavior. Either way, mechanical drift retunes the drive instead of killing the beam.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

250 MeV protons; 17 KeV/turn: N~15,000... 250 MeV protons r=0.3m: dr/dN ~ 20 microns!

Antaya, Cyclotron Basics — MIT 8.277, Unit 10, Lecture 14 (2010) — p. 43

Editorial note, tabletop extrapolation: For the builder: 1 MeV at 2 kV per gap (2 gaps) is ~250 turns with final-orbit spacing ~0.25 mm at r = 12 cm - which is why higher dee voltage directly eases both extraction and vacuum requirements.

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

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

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

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

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

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

The dee-to-ground capacity appears as the major portion of the capacitance in the tank circuit, which must be calculated taking this into account

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

Editorial note, tabletop extrapolation: Even with a modern solid-state chain, the builder must treat dee capacitance as the resonator's dominant C when designing the matching network; the confine-the-RF-current lesson is timeless.

it is important to provide short, broad paths for current flow, especially in the ground circuits ... While the tube should be placed as close to the tank as possible, it must yet be kept away from the magnetic field

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 8-9

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

The voltages employed on the various cyclotron components are deadly; proper precautions must be taken, even during preliminary testing ... Interlock switches on the power supply covers and grounding hooks

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 9

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

the top and bottom of the chamber to bow in, which affected the capacitance of the dee and reduced the maximum voltage that the dee could withstand before flashing over.

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

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

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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

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

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

HP 33120A Function Generator - ENI 155LCRH Power Amp - LDG AT-200PC Tuner - Bird 43A RF Power Meter - Dee

Yuly et al., Modifications on the Houghton College Cyclotron (2010) — p. 12-14

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

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

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

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

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

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

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

To develop high voltages with modest RF power. The highest voltage for given power occurs when: Qloaded = 1/2 Qo

Koeth et al., The Rutgers 12-Inch Cyclotron for Students (2010) — p. 18

Editorial note, tabletop extrapolation: The one-slide justification for the builder to move from an antenna-tuner match to a true high-Q tank circuit in a next machine.

Record Input Power 2kW: 8.4 kVpeak

Koeth et al., The Rutgers 12-Inch Cyclotron for Students (2010) — p. 19

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

Gleichauf also found that the breakdown voltage was strongly dependent on the material of the insulator but independent of the material of the electrodes.

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

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

Air spaces exist in solid and liquid dielectrics... the air will have the higher stress, possibly causing sparkover through the air space... The stress in the air gap can thus be k times that in the solid.

Miley & Murali, Inertial Electrostatic Confinement (IEC) Fusion: Fundamentals and Applications (2014) — p. 116, 119

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

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

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

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

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

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

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

the quality factor of the Houghton College cyclotron was determined to be Q=16.1. The previous chamber and dee constructed in 2006 had a quality factor of 22.

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

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

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

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

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

It was believed desirable to operate at as low a frequency as possible because of the larger amount of engineering information available for oscillators in the region below 15 megacycles/sec.

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

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

This curve indicates that 96 kW of rf power is required for exciting the dees to 400 kv. ... The oscillator input was 162 kw.

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 16, 25

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

It is possible to calculate the various effects quantitatively and to predict the minimum dee voltage required to obtain a given energy in a particular cyclotron.

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 17-19

Editorial note, tabletop extrapolation: Directly applicable design step for a next machine: compute threshold voltage for the target energy and field taper before freezing the RF chain power budget.

As measured, efficiency tends to increase with dee-to-dee potential and with beam power.

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 24-26

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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

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

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

Fast pumping is required and it is desirable to use oil rather than mercury diffusion pumps as mercury seems to promote autoelectronic discharges from the electrodes.

Oliphant & Rutherford, Experiments on the Transmutation of Elements by Protons (1933) — p. 259-260

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

arc current, 3 amp; arc voltage drop, 100 volts; electron beam from exit hole, 2 amp; gas flow, 2 cm3/min at atmospheric pressure. The resonant ion beam pulled from such a source ... might be about 0.5 ma.

Livingston & Blewett, Particle Accelerators (1962) — p. 175-178

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

With no gas flow, chamber pressures of better than 1 x 10-6 mm Hg are obtained. With the deuterium gas flow from the ion source, the operating pressure is about 2 x 10-5 mm Hg.

Livingston & Blewett, Particle Accelerators (1962) — p. 198

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

Cited in: The Vacuum Budget of a Cyclotron

Operating Data of Penning Ion Sources: Arc voltage 0.3-1.3 / 1-5 kV; Ignition volt. 3 / 5 kV; Gas pressure 1-10 Pa; Gas consumption 0.2 sccm; Extraction voltage 5-25 / 5-35 kV; Anode aperture 1 x 25 / 1.5 x 25 mm; Cathode distance 10 / 6.5 cm.

Wolf (ed.), Handbook of Ion Sources (1995) — p. PDF p.101 (printed p.90), TABLE 5.5 in section 5.3.7 Operating Data

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

Cited in: The Vacuum Budget of a Cyclotron

The increase of the saturation current with temperature is very strong; a 10% change in temperature corresponds to a 10-fold increase of 20% to a 100-fold increase.

Wolf (ed.), Handbook of Ion Sources (1995) — p. 38-39

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

Most of the power put into a filament is radiated and very little is lost through the ends. Most high-temperature metals show similar radiation behavior (~20 W/cm2 at 2000 K).

Wolf (ed.), Handbook of Ion Sources (1995) — p. 39

Editorial note, tabletop extrapolation: A few cm^2 of hot filament dumps tens of watts into the reference machine's source body; the hood/chimney around the filament needs a conductive heat path to the pole or water cooling.

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

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

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

Cited in: The Vacuum Budget of a Cyclotron

the arc voltage increases with decreasing gas flow... until the discharge becomes unstable... 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. PDF p.82 (printed p.71), section 5.2.2 Characterization of the PIG Discharge

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

a moderate emission current (10-20 ma.) is observed with 200-300 volts arc bias ... an arc of 1/2 to 1 amp at 100 to 200 volts is usually satisfactory.

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. PDF p.10 (printed -11-) for the procedure; PDF p.7 (printed -8-) for the arc range - NOT PDF p.6

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

an automobile headlight filament has been used, but the breakage has been high ... perhaps .025 in. tungsten ... A .025 in. tungsten filament requires about 25 amps d.c.

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 6-7

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

A quarter-inch tube called a 'chimney' sits on top of the filament, which shields it from the electric field of the dee. Ionized hydrogen is drawn out of a small hole.

Baumgartner, The Cyclotron Kids' 2 MeV Proton Cyclotron — Cyclotrons 2013, WE1PB05 (2013) — p. 3

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

The product of pressure and distance between the electrodes (pd) is a better parameter to characterize the discharge... The voltage is mostly in the range between 300 and 1500 V, but... the current is generally in the mA range.

Miley & Murali, Inertial Electrostatic Confinement (IEC) Fusion: Fundamentals and Applications (2014) — p. 86-88

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

Cited in: The Vacuum Budget of a Cyclotron

A hysteresis effect occurs; wherein instead of retracing the path... the discharge maintains itself in the normal glow regime... at considerably lower currents... Only then does it make the transition back to the Townsend regime.

Miley & Murali, Inertial Electrostatic Confinement (IEC) Fusion: Fundamentals and Applications (2014) — p. 89-91

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

A samarium cobalt permanent magnet with a surface flux density of approximately 3 kG... The anode is fabricated by forming 0.13-mm-thick nonmagnetic stainless steel sheet metal into the shape of a cup... machined with a 6.4-mm-diameter hole on centerline.

Rovey, Ruzic & Houlahan, Simple Penning Ion Source for Laboratory Research and Development Applications (2007) — p. PDF p.1 (printed 106101-1) for the construction text; PDF p.2 (printed 106101-2) for Fig. 1 dimensions

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

The ion source is an internal cold cathode Penning Ion Gauge (PIG) source that operates in excess of 40 hours before requiring service.

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

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

For this source a Glassman High Voltage KL series high voltage supply rated at 3kV and 1A provided the necessary potential. When the plasma is established, the power supply shifts to current limited operation ... The cathode anode gap was between 0.075” (1.9 mm) and 0.150” (3.8 mm)

Forringer, Phase Space Characterization of an Internal Ion Source for Cyclotrons — MSU dissertation (2004) — p. PDF p. 29 (printed p. 19)

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

Water cooling for the cathode rod and the anode base are essential (some copper parts were melted when the ion source was run without proper cooling).

Forringer, Phase Space Characterization of an Internal Ion Source for Cyclotrons — MSU dissertation (2004) — p. 19-20

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

This puller was designed for the ion source test stand to hold 50 kV... The minimum source to puller gap is 0.196 (5.0 mm).

Forringer, Phase Space Characterization of an Internal Ion Source for Cyclotrons — MSU dissertation (2004) — p. 68, 75

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

The rate of flow required during operation is from 2 to 3 cc/min ... Electrons are accelerated from the filament into the arc chamber by a 100 to 300 volt potential, the normal arc current being 0.5 to 1.5 amperes.

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 62, 64

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

The filament is aligned to completely cover this circular defining slot. The front edge of the defining slot is placed tangent to the external plane of the arc slit.

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. PDF p. 64 = printed p. 64 (section 'The Ion Source')

Editorial note, tabletop extrapolation: Directly applicable: build a next machine's source mount with repeatable rotation/translation adjustment from outside vacuum; source-to-puller alignment is worth more beam than any power knob.

A good rule of thumb is to provide a pumping speed of at least 1 liter/sec at 10-5 mm Hg per liter of volume ... 15 to 20 min is considered a good design figure.

Livingston & Blewett, Particle Accelerators (1962) — p. 197-198

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

Cited in: The Vacuum Budget of a Cyclotron

This maximum value called the 'critical forepressure,' ranges from 25-75 Pa (0.2-0.6 Torr)... The critical forepressure should never be exceeded.

O'Hanlon, A User's Guide to Vacuum Technology, 3rd ed. (2003) — p. 232-233

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

Cited in: The Vacuum Budget of a Cyclotron

The outgassing rate of unbaked, uncleaned stainless steel is of order 10-5 Pa-m/s after 10 h of pumping... reduced by a factor of 10-100... to be suitable for high vacuum

O'Hanlon, A User's Guide to Vacuum Technology, 3rd ed. (2003) — p. 308

Editorial note, tabletop extrapolation: Multiply the next machine's internal area by 1e-5 Pa-m/s and divide by delivered pumping speed to predict the 10-hour base pressure before drilling a single hole.

Cited in: The Vacuum Budget of a Cyclotron

the molecular conductance per unit area of any structure in molecular flow has a maximum value [11.6 L/(s-cm2) for air at 22C]

O'Hanlon, A User's Guide to Vacuum Technology, 3rd ed. (2003) — p. 48-50

Editorial note, tabletop extrapolation: Sets the ceiling on what the SI100 can actually pump through the chamber port: a 4-inch (81 cm2) opening passes at most ~940 L/s, and a baffled elbow far less - size the pump port as large and short as possible.

Cited in: The Vacuum Budget of a Cyclotron

Vacuum rated to 1 x 10-8 Torr (better suited to 1 x 10-6 Torr). Temperature rating is dependent on which elastomer o-ring is used (usually 150C)

Bertolini, Accelerator Vacuum and Mechanical Engineering — USPAS course, UCRL-MI-201847 (2004) — p. 443-446

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

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

A virtual leak is a volume of trapped atmospheric gas that leaks into the vacuum vessel through holes or cracks that do not go all the way through the vessel wall. [Examples:] Unvented Screw, Two Welds in Series, Unvented Double O-rings

Bertolini, Accelerator Vacuum and Mechanical Engineering — USPAS course, UCRL-MI-201847 (2004) — p. 59-63

Editorial note, tabletop extrapolation: Every internal socket-head screw in the next machine (dee supports, ion source mounts) needs a vent hole, a slotted thread, or a vented washer; a slot machined in the O-ring groove floor serves the same purpose.

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

Face-type o-ring seals are recommended. Use as heavy a squeeze as possible... Two o-rings in series can drastically reduce permeation.

Bertolini, Accelerator Vacuum and Mechanical Engineering — USPAS course, UCRL-MI-201847 (2004) — p. 71-74

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

Cited in: Cyclotron Vacuum Chamber Design and Sealing

Seam welds are continuous, with welding only on the atmosphere side. The internal braces are stagger welded to keep virtual leaks at a minimum.

Ramler & Parker, The Argonne 60-Inch Cyclotron — ANL-5907 (1959) — p. 7

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

Cited in: Cyclotron Vacuum Chamber Design and Sealing

a preliminary vacuum of about 10^-5 mm hg should be attained; during 'bakeout' pressure should not exceed ~10^-3 mm. Operation as a cyclotron can be attempted with a pressure of 10^-4 mm or less

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 6

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

Cited in: The Vacuum Budget of a Cyclotron

a 3 inch diameter tube in the corner can extend directly downwards to a vacuum pump underneath. This design choice maximizes vacuum conductance.

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

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

an Innovac R220 diffusion pump and Kurt J Lesker TNR6XA150QF cold trap are used, which can lower the pressure to about 1e-4 Pa (1e-6 torr)

Loucks, Initial Results from the Houghton College Cyclotron — Houghton College thesis (2007) — p. 41-43

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

Cited in: The Vacuum Budget of a Cyclotron

Two 0.65 cm thick circular lids ... included a gland for a Viton O-ring for the vacuum seal. ... The chamber can be evacuated down to a final pressure of approximately 2 × 10−6 Torr

Yuly, The Houghton College Cyclotron: a Tool for Educating Undergraduates — Cyclotrons 2013, WE1PB01 (2013) — p. PDF p. 2 for the lids and Viton seal; PDF p. 3 for the 2 × 10−6 Torr

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

Cited in: Cyclotron Vacuum Chamber Design and Sealing

after the welding, the bottom plate contracted so much that it bent the whole frame out of shape... seal the bottom plate against the frame using a flat Viton ring.

Baumgartner, The Cyclotron Kids' 2 MeV Proton Cyclotron — Cyclotrons 2013, WE1PB05 (2013) — p. 2-3

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

Cited in: Cyclotron Vacuum Chamber Design and Sealing

A typical figure, used in the MIT cyclotron, is a dR of 0.15R. The deflector gap is usually tapered ... Spacings as small as 1/8 in. can be used at the entry slit, opening to 1/2 in. or greater at the exit.

Livingston & Blewett, Particle Accelerators (1962) — p. 180-181

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

304L SS, most commonly used in vacuum, a little more expensive... Joint design is critical from vacuum, metallurgical and distortion standpoints. Cleanliness is essential.

Bertolini, Accelerator Vacuum and Mechanical Engineering — USPAS course, UCRL-MI-201847 (2004) — p. 355-360

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

Cited in: Cyclotron Vacuum Chamber Design and Sealing

a lid with radius 10 centimeters and thickness of 3.5 millimeters would undergo less than 1 mm of deflection when covering a chamber with internal pressure of 1e-3 Torr

Dewan, Design and Construction of a Cyclotron Capable of Accelerating Protons to 2 MeV — MIT thesis (2007) — p. 12

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

Cited in: Cyclotron Vacuum Chamber Design and Sealing

all cyclotron components must be made of magnetically transparent materials such as aluminum, copper, or brass

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

Editorial note, tabletop extrapolation: Standard but easily violated rule: screws, feedthrough bodies, and detector hardware inside the reference machine's gap should be checked with a hand magnet before installation.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

the VTO box and obround are mounted on a motor-driven carriage which operates on a rail system. This permits the removal of the dee heads... to facilitate maintenance.

Ramler & Parker, The Argonne 60-Inch Cyclotron — ANL-5907 (1959) — p. 6-7

Editorial note, tabletop extrapolation: At tabletop scale this means: chamber slides out of the gap, dee removable through a lid, pump cart disconnectable - the difference between a research tool and a sealed monument.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

It is seen that particles are detected at about 70 kv. and the numbers increase more rapidly with increase of bombarding energy than with the lithium film.

Oliphant & Rutherford, Experiments on the Transmutation of Elements by Protons (1933) — p. 266-270

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

Cited in: Experiments by Energy Band

the ion revolution turn spacing near r = 4 inches, in a B-field of 1.0T will be just 0.04 inches, which is smaller than the 0.06 inch RF shield of the tip

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

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

The limit at the entry is set by the dr between successive turns at this radius ... it is desirable to have adjustable controls on deflector spacing and location which can be trimmed empirically.

Livingston & Blewett, Particle Accelerators (1962) — p. 181-183

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

Emergent beam intensities up to 25 per cent of the resonant beam intensity have been obtained under optimum conditions ... practical operating intensities would in this case be limited to 80 or 100 ua.

Livingston & Blewett, Particle Accelerators (1962) — p. 182

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

The separation for non-relativistic ions is dR = (R/2) (2qVo sin phi_s/T)... Eq. (15.3) implies that dR = 0.44 cm.

Humphries, Principles of Charged Particle Acceleration (1986) — p. 527

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

0.15 0.91 +/- 0.015... 0.65 218.42 +/- 0.55

Spraker et al., The 11B(p,α)8Be → α+α and the 11B(α,α)11B Reactions at Energies Below 5.4 MeV (2012) — p. 360

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

Cited in: Experiments by Energy Band

Our parameters: B=.976 T ... T=.472 MeV ... d=.291 inches ... Combining yields: Vd/d = (2T/R)(dR/(R+dR)) ... Vd = 32.531 kV

Ponter, Beam Energy Measurements with a New HV Deflection System and Ion Source Upgrades on the Rutgers 12-Inch Cyclotron (2010) — p. 6 (R and dR on 7)

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

Voltage -kV dc / Current milliamps / Pressure millitorr / Neutrons cpm: 16, 11, 18, 10 ... 25, 8.1, 14, 60 ... 31, 10.8, 13, 130. Figure 25 - Neutron readings versus other chamber parameters.

Kovalchick, Deuterium Fusion Using Inertial Electrostatic Confinement (2012) — p. PDF p.46 = printed p.46 (Kovalchick, 'Experiment 7 - Observations', Figure 25)

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

Cited in: Experiments by Energy Band

It was limited to low level output by its 22kv internal supply. 103 n/sec... a 33 kilovolt supply. 105 n/sec... currently produces in excess of 600,000 neutrons per second

Hull, Fusor: An Easy to Construct Fusion Reactor Based on Inertial Electrostatic Confinement (2009) — p. 36-39

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

Cited in: Experiments by Energy Band

Frame-by-frame analysis... revealed that ions nominally populate 40 degrees of the 360 degree RF cycle in our cyclotron.

Koeth, Undergraduate Education with the Rutgers 12-Inch Cyclotron (2015) — p. 9

Editorial note, tabletop extrapolation: Sets expectations for fast diagnostics and duty-factor arithmetic on any machine: measure your own bunch width (capacitive pickup, gated counting) and use it - 40 degrees is one measured machine's figure, not a constant.

At these energies beam intensities varied from 0.5 to 10 nA on target ... detected by eight silicon surface barrier detectors ... each detector subtending a solid angle of approximately 2.5 x 10^-4 sr.

Spraker et al., The 11B(p,α)8Be → α+α and the 11B(α,α)11B Reactions at Energies Below 5.4 MeV (2012) — p. PDF 3 (printed 359), continuing on PDF 4 (printed 360)

Editorial note, tabletop extrapolation: The single most encouraging number in the batch: professional low-energy p-B11 data at exactly the reference machine's nA beam scale. Whether nA suffices for a given measurement follows from the rate arithmetic - cross-section, solid angle, integration time (the experiments-by-energy worked examples) - not from precedent alone.

Cited in: Experiments by Energy Band

The highest proton energy obtained so far is about 160 keV, with a 3 pA peak near the correct magnetic field of 796 mT for 12.1 MHz.

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

Editorial note, tabletop extrapolation: Calibrates expectations exactly at the reference machine's operating point (~150 keV): currents fall steeply near a machine's energy limit, and the gating items the paper lists are the ordinary ones - magnet current, cooling, RF range.

Cited in: Choosing Your Machine

S/N cannot be improved by feedback. This result is generally valid, i.e. it also holds for active integrators (charge-sensitive amplifiers).

Spieler, Semiconductor Detectors Part 2 — SLUO Lectures on Detector Techniques, Lecture 7 (1998) — p. 24

Editorial note, tabletop extrapolation: For the builder: mount the preamp on the vacuum feedthrough, not at the far end of a coax run. Cable capacitance raises the series-noise term, and at alpha-spectroscopy resolutions it competes with detector leakage and shaping-time choices for the noise budget - short cable is the cheapest term to fix.

Detector capacitance may vary within a system or change with bias voltage (partially depleted semiconductor diode)... Amplifier output directly determined by signal charge, insensitive to detector capacitance

Spieler, Semiconductor Detectors Part 2 — SLUO Lectures on Detector Techniques, Lecture 7 (1998) — p. 3-8

Editorial note, tabletop extrapolation: Confirms the standard PIPS chain for the p-B11 experiment: a charge-sensitive preamp at the feedthrough - the spectroscopy-grade choice, since a plain voltage amplifier's gain rides on the diode's bias-dependent capacitance. Voltage readout keeps niche uses (fast timing, very high rate) that energy spectroscopy is not.

D-D fusion can occur in an IEC device at voltages as little as 10 kV or less, but detectable fusion generally does not occur until voltages are at least 15 kV

Kovalchick, Deuterium Fusion Using Inertial Electrostatic Confinement (2012) — p. 18

Editorial note, tabletop extrapolation: Calibrates expectations for any sub-threshold nuclear signal at home: being physically above a reaction threshold is not enough - the detectable onset sits well above it, and where it sits depends on geometry, gas pressure and loading, current, and the counting setup.

Cited in: Experiments by Energy Band · Shielding a Small Cyclotron

The amateur is limited to the middle or D-D reaction which yields a split 50:50 reaction D+D to T + Proton, D+D to He3 + neutron

Hull, Fusor: An Easy to Construct Fusion Reactor Based on Inertial Electrostatic Confinement (2009) — p. 19-20

Editorial note, tabletop extrapolation: The reference machine's p-B11 choice sidesteps this entirely. If deuterium ever runs in the cyclotron, D-D is the accessible fusion fuel in the source's US hobbyist-era framing - but licensing attaches by jurisdiction and by what the device produces (see /legal/), so verify locally rather than treating any fuel as license-free. The safety fact is the neutron branch: half of D-D reactions emit a 2.45 MeV neutron.

The grid should be made from tantalum or tungsten wire and be fusion or resistance welded.

Hull, The Farnsworth/Hirsch Fusor — The Bell Jar, Vol. 6 No. 3/4 (1997) — p. 5-8

Editorial note, tabletop extrapolation: Applies in spirit to a next machine's chimney slits, puller edges and beam stops: anything the beam or arc dwells on gets a material-and-joint choice made against its actual power density. Refractory metal with welded joints is the robust default where cooling is absent; cooled copper or graphite are engineered alternatives (dg-426, dg-939).

The project was a long and laborious one, but the efforts were well-rewarded when the first beam was obtained three years later, in the spring of 1957.

McGuire, The Iowa State University 1.5 MeV Undergraduate Cyclotron (1961) — p. 3

Editorial note, tabletop extrapolation: Schedule reality check consistent with the census: documented start-to-first-beam gaps run one to six years (the builds page's computed spread), and Iowa State's three sits mid-pack.

TOTAL: $128500. Who has >$125k to blow on a very modest strawman small particle accelerator?

Niell, Effective Scientific Equipment Procurement Strategies: Building on a Budget (2010) — p. 2-3

Editorial note, tabletop extrapolation: Calibrates a next machine's budget: every subsystem not scrounged or fabricated costs thousands new (the article's line items), which is why surplus procurement dominates documented amateur practice - the census's cost trail says the same.

Cost: Can spend no more than $400. Performance: Want to measure 40MHz sinewaves... Function: Must be in calibration, and nearly bombproof

Niell, Effective Scientific Equipment Procurement Strategies: Building on a Budget (2010) — p. 7-10

Editorial note, tabletop extrapolation: A disciplined method for the next machine's shopping list: define the B-field, vacuum and RF numbers first, then match each purchase to the cheapest vendor tier whose reliability that subsystem can tolerate - judged per purchase, not by a permanent vendor ranking.

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

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

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

Cited in: Beam Dynamics: An Interactive Laboratory

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

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

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

Cited in: Beam Dynamics: An Interactive Laboratory

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

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

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

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

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

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

The practically achievable engineering current density (the ratio of the value of the ampere-turns in the winding to the cross section of the conductor) is of the order of 5 A/mm2.

Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 15-16

Editorial note, tabletop extrapolation: First-cut sizing for a next machine's coil pack: NI / 5 A/mm^2 estimates the winding cross-section with water cooling - a starting point that still owes fill factor, cooling channels and insulation their space, and the thermal calculation is the real gate (magnet-power calculator). Air-cooled magnet wire derates well below this (dg-092).

the maximum energy gain corresponds to a system in which the RF size of the dee is close to 180 degrees or is a multiple of 180 degrees with a factor of 3, 5, 7

Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 11

Editorial note, tabletop extrapolation: The reference machine's single ~180-degree dee on h=1 is already the optimum; the formula lets the builder tool compute turns-to-energy for any future dee angle or harmonic choice.

in the presence of one accelerating dee and a voltage of 60-70 kV, protons can be accelerated in a decreasing magnetic field to an energy of 9-10 MeV

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

Editorial note, tabletop extrapolation: Sets the scale, not a law: the quoted machine class pairs 60-70 kV with 9-10 MeV, and the reference machine's ~1.3 kV dee at ~150 keV sits consistently below that line. Final energy in a classical machine is phase-budget-limited (the summed slip, dg-273), which dee voltage relieves nonlinearly - compute the budget rather than scaling proportionally.

the phase acceptance of the center, as a rule, contains the particles, the initial RF phases of which do not go beyond the range of (-90; 20)

Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 56

Editorial note, tabletop extrapolation: Explains why a large fraction of source output never accelerates: only starting phases inside a ~110-degree window of the full 360 are candidates at all - a uniform-emission estimate makes that a ~30% ceiling, before radial and axial acceptance cut further; it is not a measured capture efficiency. The builder tool should launch macroparticles across this window rather than a single reference phase.

mainly fast neutrons are generated, and the permissible flux is 30-60 neutrons/cm2 s

Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 16

Editorial note, tabletop extrapolation: At <=1 MeV protons the reference machine is below the (p,n) thresholds of its structural metals (the first structural channel, 55Mn(p,n)55Fe, opens at 1.03 MeV) and of the light targets: 7Li 1.88 MeV, 9Be 2.06 MeV, 11B 3.02 MeV, and even deuterium 3.34 MeV (NNDC QCalc, retrieved 2026-08-23) - so these neutron numbers do not set its shielding scale. They start to as soon as the machine accelerates deuterons, because D-D and Be(d,n) are exoenergetic with no threshold at all (dg-1047), or pushes protons past ~1.9 MeV on lithium; dg-1041 and dg-1047 carry the residual channels that keep a neutron survey honest below that. Read this as a scale for the case that applies, not as a clearance for the case that does not. [Corrected 2026-08-22: previously said neutron shielding is "a non-issue" for the machine; the exception clause was there, but the headline was an absolute.] [Corrected 2026-08-23: the exception clause itself was imprecise - it said the neutron channels "open far lower" for Li, Be, B or a deuterated material, but every one of those (p,n) thresholds is above 1 MeV as well; the genuinely thresholdless route is deuterons, per dg-1047. Raised by an upstream review of the source dataset.] [Corrected 2026-09-13: previously claimed 'below every (p,n) threshold'; thresholds are properties of nuclides, not of matter, and mid- and heavy-Z nuclei can sit far lower - 115In(p,n)115Sn is open at 287 keV, Coulomb-suppressed (NNDC QCalc; see the safety page's activation section) - so the claim is now scoped to the structural metals and light targets actually checked. Raised by an external site review.]

the relative radial increase is only half the relative energy increase. However, for a given cyclotron, the turn separation dr0 will double when the dee voltage is doubled.

Kleeven & Zaremba, Cyclotrons: Magnetic Design and Beam Dynamics — CAS 2015, arXiv:1804.08961 (2018) — p. 44

Editorial note, tabletop extrapolation: The reference machine (~150 keV, 2.6 keV/turn, r ~ 9.6 cm) gets ~0.8 mm/turn. A 10 kV dee at the same radius scales it by the ratio of per-turn energy gains - computed from the actual voltage convention and gap count: 10 kV peak with two crossings at good phase is ~20 keV/turn, ~6 mm; one effective crossing or poor phase halves it or worse.

for a final energy of T = 30 MeV, dT = 100 keV, and an extraction radius of 0.5 m, we find dr = 0.83 mm. This is a rather small number, e.g. when compared with a radial beam width of for instance 4 mm.

Botman & Hagedoorn, Extraction from Cyclotrons — CAS, CERN 96-02 (1996) — p. 6

Editorial note, tabletop extrapolation: Small machines fare better because dr/R scales as dT/T: a 350 keV next machine at 10-20 keV per turn carries a fractional turn separation 9-17x this 30 MeV machine's. Its beam width does not shrink in proportion, though - so the separation-vs-width comparison still needs the machine's own numbers (dg-495).

when a coherent oscillation amplitude x of 3 mm has been built up ... and acceleration takes place until vr = 0.8, the maximum turn separation due to precession is 3.8 mm.

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

Editorial note, tabletop extrapolation: A deliberate few-mm coherent amplitude (source off-centering is one way to seed it), plus letting nu_r fall toward 0.8 in the fringe, can multiply turn spacing severalfold - IF the precession phase is arranged so the separation appears at the septum azimuth. It is a designed, tracked orbit-dynamics move, not a free effect.

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

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

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

Cited in: Beam Dynamics: An Interactive Laboratory

An angle kick of typically 50 to 100 mrad is provided. The inner electrode, septum, is at earth potential. At the entrance it has a thickness of a few tenths of a mm, increasing to several mm at the exit.

Botman & Hagedoorn, Extraction from Cyclotrons — CAS, CERN 96-02 (1996) — p. 14

Editorial note, tabletop extrapolation: At 350 keV a 100 mrad kick over 10 cm of arc needs E = theta*(2T/q)/L = 7 kV/cm - about 3.5 kV across a 5 mm gap. At nanoamp beams the septum's heat load is negligible whatever fraction it intercepts: 1 nA of 350 keV beam carries only 0.35 mW in total.

a criterion for the product of electric field E and potential V for a cyclotron deflector in order to avoid electric discharges: VE < 1.5 104 (kV)2/cm. The maximum sustainable voltage in a magnetic field is 20-30% lower.

Botman & Hagedoorn, Extraction from Cyclotrons — CAS, CERN 96-02 (1996) — p. 14

Editorial note, tabletop extrapolation: A 3-5 kV, 5-10 kV/cm tabletop deflector sits orders of magnitude below this bulk-discharge criterion - so at tabletop scale the practical ceiling comes from feedthrough, surface and edge-radius engineering (dg-353, dg-297, dg-295), not from the Smith-Grunder product.

At HV edges, electric field lines become so dense that breakdown becomes a major concern. Aluminum=290 kV/inch ... We settled on a minimum radius of R=.1875 inches ... Emax=170 kV/inch

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

Editorial note, tabletop extrapolation: Direct amateur precedent: a 1 T / 472 keV university tabletop deflector ran at 28-32 kV. A lower-energy machine needs proportionally less deflector voltage (scaling roughly with beam energy at similar geometry - a 150 keV-class machine perhaps a third, not a tenth), and the edge-field formula stays the design check: generous radii reduce peak field, they do not make sparking impossible - finish and conditioning still rule (dg-295, dg-353).

For DR = 0.1R: Va = 47,000 volts ... A typical figure, used in the MIT cyclotron, is a DR of 0.15R. ... The deflector gap is usually tapered.

Livingston & Blewett, Particle Accelerators (1962) — p. 163-166

Editorial note, tabletop extrapolation: Scaling by 2T: a next machine at 350 keV needs about 1/45 of MIT's voltage at the same normalized geometry - roughly 1-2 kV across a proportionally scaled entry gap - rising if a faster peel (larger DR) or a larger gap is wanted. Compute with the formula for the actual geometry (dg-590's worked example).

Emergent beam intensities up to 25 per cent of the resonant beam intensity have been obtained under optimum conditions; ... practical operating intensities would in this case be limited to 80 or 100 [micro]a.

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

Editorial note, tabletop extrapolation: Plan a next machine's deflector attempt around the classical rungs - tens of percent at best, and that under optimum tuning: with nA internal beam, 0.1-0.25 nA external is still a countable, PIXE-usable beam. The upper rungs belong to machine classes a tabletop deflector does not reach.

This results in a phase acceptance of only a few degrees for the typical case of a few hundred turns.

Baartman, Cyclotrons: Why/How Are Their Dynamics Different? — JINST 18 T03005 (2023) — p. 10

Editorial note, tabletop extrapolation: Do not chase single-turn extraction on a small machine: accept multi-turn with spread of order the turn energy gain (~20 keV at a 10 kV dee - the simple-picture floor; turn overlap and precession can widen it), which PIXE tolerates. (Spread and dB/B detail: botman pp.11-14.)

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

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

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

the negative hydrogen ion beam simply passes a thin carbon foil (e.g. pyrolytic graphite, typically 50 to 200 ug/cm2), which strips off the electrons.

Botman & Hagedoorn, Extraction from Cyclotrons — CAS, CERN 96-02 (1996) — p. 3-4

Editorial note, tabletop extrapolation: At sub-MeV a 50 ug/cm2 foil costs ~10 keV of energy and some scattering. The septum, HV and turn-separation problems genuinely disappear - replaced by the H- problems: an internal H- source, and the 1e-6 Torr-class vacuum that gas stripping of the fragile H- demands (dg-599).

the cross section of H- interactions with the gas molecules is maximal for the energy range (0.1 - 300) keV of the beam in the central region.

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

Editorial note, tabletop extrapolation: A next machine's H- variant spends its whole life at the cross-section peak. Run the loss arithmetic explicitly through T = exp(-n*sigma*L) with measured H- detachment cross-sections - the 1e-15 cm2 class near the peak; fetch sigma(E) for the actual gas mix when designing. At that scale ~25 m of spiral at 1e-6 Torr loses of order 5-10%, and 1e-5 Torr costs most of the beam: vacuum, not physics, decides this option. (70 MeV data: cyclotron_vacuum_model p.3.)

Cited in: The Vacuum Budget of a Cyclotron

the cold cathode PIG source with arc voltages above 1 kV and currents between 0.5 and 5 A, and the hot cathode PIG source with arc voltages below 1 kV and currents between 1 and 50 A

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

Editorial note, tabletop extrapolation: The reference machine's source at tens-to-hundreds of mA sits BELOW the handbook's canonical cold-cathode band, which starts at 0.5 A - closer to a glow regime than the tabulated arcs. The design consequence stands regardless: if the discharge crosses into a self-heated, negative-slope mode (AMIT reported a transition near 250 mA on their source), only a stiff current source holds it - so build the arc supply as a current source from the start.

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

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

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

the ion current density at the cathodes is five to ten times the density at the anode surface ... The total extracted current of a PIG ion source is proportional to the arc current (Figure 5.6), and for extraction through the anode, about 10 to 100 (mA/cm2)/A

Wolf (ed.), Handbook of Ion Sources (1995) — p. 82-83

Editorial note, tabletop extrapolation: Sizing arithmetic for the chimney slit: a 0.5 x 5 mm slit (0.025 cm^2) at 100 mA arc predicts ~25-250 uA available at the slit — consistent with Forringer's measured 230-590 uA at 50-150 mA through a 0.5 mm slit.

Gas consumption (sccm) 0.2 [hot cath.] / 0.2 [cold cath.] / 0.2-0.6 [heated cath.] (Table 5.5; verified against page image)

Wolf (ed.), Handbook of Ion Sources (1995) — p. 101

Editorial note, tabletop extrapolation: The headline for the reference machine is the gas line - full-size accelerator PIGs run on 0.2-0.6 sccm, and its own hydrogen feed is a 1-sccm-full-scale mass-flow controller, so what the chimney buys is not less gas but gas confined where the ionization happens. Dimensions scale down for a 36 mm pole gap (its chimney will be shorter than the 6.5-10 cm cathode spacings listed, which are for big-gap machines).

An arc is struck by raising the arc voltage to about 3 kV and increasing the gas pressure ... is stabilized by the arc supply current regulator or ballast series resistor ... Arc currents are 1-15 amps for dc sources and higher for pulsed sources. Arc voltages are 300-2000 volts.

Clark, Ion Sources for Cyclotrons — Cyclotrons '81, Caen (1981) — p. 3

Editorial note, tabletop extrapolation: Spec the arc supply for ~3 kV compliance even though running voltage is ~0.3-2 kV, and automate the sequence - gas up, strike, gas down, current-regulate - with the boost magnitude and timing tuned on the machine rather than copied.

Source extraction voltage is 10-30 kV dc for external sources, with the anode being biased positive. For internal sources, the anode is usually grounded and 30-100 kV of rf voltage is used for extraction

Clark, Ion Sources for Cyclotrons — Cyclotrons '81, Caen (1981) — p. PDF p.3 (printed p.233 of the 9th Int. Conf. on Cyclotrons proceedings)

Editorial note, tabletop extrapolation: The reference machine extracts with its few-kV dee - far below the surveyed machines. Compensating with a small source-puller gap follows Child-Langmuir-like scaling (I ~ V^1.5/d^2 in the planar model - a guide in this geometry, not a law): documented small gaps run 2.3-2.9 mm (Siemens, K100 - dg-624), and expect proportionally lower current than published microamp figures until measured.

The cathode anode gap was between 0.075" (1.9 mm) and 0.150" (3.8 mm), and is not a critical parameter for the source's operation.

Forringer, Phase Space Characterization of an Internal Ion Source for Cyclotrons — MSU dissertation (2004) — p. 29

Editorial note, tabletop extrapolation: Generous tolerance on the AXIAL gap - that part of the chimney stack-up doesn't need precision. Concentricity and slit alignment are separate tolerances with their own tighter demands, and the cooling warning stands at any arc power: provide a conduction path sized for continuous arc wattage, or plumb water.

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

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

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

The chimney is centered at (0.000,0.000) and the puller is centered at (0.021,0.000). The minimum gap between the chimney and the puller is 2.9 mm while the gap at the source opening is 3.0 mm, meaning that the beam does not see the peak electric field. [K100 geometry]

Forringer, Phase Space Characterization of an Internal Ion Source for Cyclotrons — MSU dissertation (2004) — p. 78, 85

Editorial note, tabletop extrapolation: Gap sets extraction field at fixed voltage, so at a few kV on the dee the chimney-puller gap must shrink below these machines' values to recover useful gradient - but there is no constant-kV-per-mm law to size it by (dg-419): pick a gap, then verify holdoff on the bench with the actual electrodes, finish and RF. The K100's deliberate 0.5 mm center offset - trading peak field at the beam for extraction optics - is the transferable design idea.

the properly aligned configuration produces significantly more secondary emission electrons ... with the anode rotation angles from -0.2 to -1.5 degree, more than 50% H- beam can be extracted through pullers

Mu et al., Simulation of Electron Behavior in PIG Ion Source for 9 MeV Cyclotron (2015) — p. 4-6

Editorial note, tabletop extrapolation: Two different tolerance classes: build the chimney concentric (pin the cathode discs to the bore, machine in one setup), and provide an external rotational adjustment of the source stalk with sub-degree feel for slit-to-puller aiming. The KIRAMS optimum spanned about a degree, so an adjustment range of a few degrees around nominal is the class to design for - the actual optimum is found on the machine, not inherited.

The inclusion of a chimney placed on top of the existing design will permit the thermionic electrons to travel to the median plane, thereby generating ions in the entire column. A small aperture, 1/16 of an inch in diameter, opening towards the DEE permits ions to be drawn into the accelerating field.

Koeth, Rutgers 12 Inch Cyclotron Ion Source Studies: Part I (2006) — p. 2-3

Editorial note, tabletop extrapolation: The half-step option: chimney-over-filament keeps the reference machine's existing filament supply and adds gas confinement plus a defined 1.6 mm emission aperture. Injection matching to the first orbit remains its own design question (aperture position, puller, phase - dg-348), not an automatic property; a PIG chimney gets the same geometry benefits and deletes the filament, at the price of a new arc supply (dg-383).

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

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

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

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

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

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

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

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

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

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

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

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

Cited in: Cyclotron Vacuum Chamber Design and Sealing

It is supported on insulating columns, making it possible to provide a DC bias.

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

Editorial note, tabletop extrapolation: A DC-isolated dee mount costs little at design time and provides the discharge-control knob the era's reports repeatedly reach for (dg-320, dg-680, dg-805). A kilovolt-class bias means the mount and its feed are HV-insulated by design, not as an afterthought.

A density of 200 pounds per cubic foot was obtained with a 28 day crushing strength of 3,000 pounds per square inch and a water content of 10 percent. ... All removable shielding blocks were stacked in two vertical layers to that no straight-through cracks remained.

Creutz, Design and Construction of Synchro-Cyclotron — NYO-780 (1950) — p. PDF 43 (printed p. 38), Section VIII - SHIELDING

Editorial note, tabletop extrapolation: Transferable - stagger any shielding blocks on a next machine (concrete, water, borated PE) so seams never line up with the beam plane.

Cited in: Shielding a Small Cyclotron

they cannot be opened without turning off the cyclotron oscillator or reducing the magnetic field from its resonance value.

Creutz, Design and Construction of Synchro-Cyclotron — NYO-780 (1950) — p. 44

Editorial note, tabletop extrapolation: Directly applicable: interlocking RF-enable to the enclosure door is the cheap, classic scheme. Prefer the oscillator-off condition as the gate - an off-resonance field reduces acceleration but leaves RF and high voltage energized, so field detuning alone is not a conservative personnel interlock.

Cited in: Shielding a Small Cyclotron

a .080" gap between copper or copper-plated surfaces having a reasonable polish would hold a maximum of 50 kilovolts at 13 mc at a pressure of about 5 x 10-6 mm.

MacKenzie et al., Design of the Radio-Frequency System for the 184-inch Cyclotron — UCRL-64 (1948) — p. 13

Editorial note, tabletop extrapolation: Directly applicable breakdown data for setting a next machine's dee-to-liner and puller gaps at 5-13 kV - with the derate compared in FIELD, not voltage (the two units had different gaps), and remembering vacuum RF hold-off does not scale as fixed kV-per-gap: bench-verify the actual geometry (dg-419).

For reasons of convenience, a quarter scale was chosen. The resonant frequency is then increased fourfold and all inductances and capacitances are reduced by a factor of four.

MacKenzie et al., Design of the Radio-Frequency System for the 184-inch Cyclotron — UCRL-64 (1948) — p. 14

Editorial note, tabletop extrapolation: Transferable method: prototype a next machine's resonator at reduced scale with a VNA - remembering effective dee capacitance is not the static value, which is exactly what the model run is for.

The evident discrepancy in transmission line length was eventually traced to a cumulative error of about two inches in various small errors in model dimensions.

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

Editorial note, tabletop extrapolation: Directly applicable: give a next machine's resonant line or tank a deliberate tuning range - trombone section, tuning vane, trimmer capacitor - instead of trusting calculated dimensions to land the frequency.

All discharges were eliminated by cutting down the available volume by means of perforated shields around the sides of the dee, by adding a grounded dummy dee and by applying a negative bias to the dee.

MacKenzie et al., Design of the Radio-Frequency System for the 184-inch Cyclotron — UCRL-64 (1948) — p. 23

Editorial note, tabletop extrapolation: Directly applicable - the 1948 combination that cleared THAT machine's discharges: reduced free volume (perforated shields preserve pumping speed), a grounded dummy dee, and negative dee bias. On a new machine, apply the elements as diagnosis suggests (dg-1273's discrimination between multipactor and gas discharge) rather than as one obligatory bundle - though all three are cheap to design in from the start.

It would produce 15 kv peak volts on the dee at 10 me and 9 kv at 20 me with 6 kw input. It averages around 70%.

MacKenzie & Waithman, R.F. System for Frequency Modulated Cyclotron — MDDC-1045 (1946) — p. 4

Editorial note, tabletop extrapolation: A benchmark near the reference machine's 9 MHz - and transferring it runs through the resonator parameters: scale by the actual dee capacitance and Q via dg-313's formula, not by watts-per-kV alone.

The upper and lower frequency limits can be varied together about 6% by a tuning vane which varies the impedance of the transmission line. It is a movable copper sheet with flexible end connections.

MacKenzie & Waithman, R.F. System for Frequency Modulated Cyclotron — MDDC-1045 (1946) — p. 5

Editorial note, tabletop extrapolation: Directly applicable to a fixed-frequency machine: a vane gives few-percent trim to land the dee resonance on the magnet's cyclotron frequency. The range you get depends on your line's geometry - size the vane by calculation and keep a fallback adjustment (dg-665's trombone/trimmer).

Above this voltage, which is in the neighborhood of 500 volts, the discharge is rapidly extinguished as electrons can no longer oscillate. However, the discharge is usually intense enough, even at 10-5 mm of Hg to prevent the voltage from building up to this extinction value. Such a discharge can be eliminated by a sweeping field obtained in any manner. The sweeping field was obtained on the 37-inch cyclotron by biasing the dee, transmission line, and condenser stator parts a few hundred volts positive.

MacKenzie & Waithman, R.F. System for Frequency Modulated Cyclotron — MDDC-1045 (1946) — p. 12

Editorial note, tabletop extrapolation: The single most relevant discharge fact for the reference machine: its ~1.3 kV dee lives just above this regime, and the 5-13 kV upgrade must punch through it during every start - plan for a bias supply on the dee from day one, and note the source's polarity (positive on the 37-inch; dg-320's machine used negative - both worked, because any sweeping field defeats the resonance).

At 20 megacycles the space between electrodes which will allow an electron to reach an energy around 30 volts in 5 cm. There are very few paths, along the magnetic field, in the neighborhood of the dee that are greater than this, so no trouble has occurred in this region. In the rotary condenser however, most of the paths are of the order of 20 cm. Electrons oscillating in this space can reach efficient ionizing energies long before their amplitude becomes equal to the distance between electrodes.

MacKenzie & Waithman, R.F. System for Frequency Modulated Cyclotron — MDDC-1045 (1946) — p. 12

Editorial note, tabletop extrapolation: Directly applicable geometry rule - at 9 MHz electron oscillation amplitudes are larger still, so keep open RF-exposed volumes and along-field gaps in the next machine's chamber small or shielded.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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

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

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

Cited in: Beam Dynamics: An Interactive Laboratory

It must be kept in mind for systems having low accelerating voltages similar to the 184-inch cyclotron, that the ions will rapidly increase the amplitude of their vertical oscillations at the point where n = 0.2.

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

Editorial note, tabletop extrapolation: The reference machine's few-kV dee means many turns near any resonance radius - the slow-crossing regime the quote warns about. Keep n below 0.2 over the whole usable radius (the mapped check, dg-138), and give the dee aperture real margin over the expected radial oscillation amplitude.

Cited in: Beam Dynamics: An Interactive Laboratory

Mag. field, k-gauss 14 - 19

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

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

Dee-to-dee, kv 10 - 18 ... Internal Beam, Stable, ua 100

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

Editorial note, tabletop extrapolation: Proof that low dee voltage works at small radius: ISSP is the existence proof for a sub-MeV goal on a ~10 kV-class dee. Dee voltage buys turn count, phase budget and survival - the energy ceiling stays with B*r (dg-026) - and the field profile must keep the extra turns focused.

Oscillator tube one 8T11R ... Osc. input, max 10 kw ... Osc. output, max 6 kw ... Oscillator tube one, RCA 899A ... Osc. input, max 12 kw ... Oscillator tube 3Q 260E (S.T.C.) ... Osc. output, max 50 kw

Howard, Cyclotrons and High-Energy Accelerators, 1958 — ORNL-2644 (1958) — p. PDF 106 (printed -99-) as cited for BNL; ISSP on PDF 60 (printed -53-), Stanford on PDF 166 (printed -161-), ANU on PDF 26 (printed -19-)

Editorial note, tabletop extrapolation: Those kilowatts bought tens-of-kV dees at high Q, not beam power. A few-kV tabletop dee's budget comes from the resonator formula instead (dg-313: tens of watts dissipated, so a 100 W-1 kW amplifier class with margin) - and the census's plain self-excited oscillators show that sophisticated drive chains are not a prerequisite for running a cyclotron.

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

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

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

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

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

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

Field drop-off 3-4 %

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

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

Cited in: Beam Dynamics: An Interactive Laboratory

Internal Beam, Stable, ua 1000-2000 ... External Beam, Stable, 800 ua; 100 ua focused on target 15 ft from machine

Howard, Cyclotrons and High-Energy Accelerators, 1958 — ORNL-2644 (1958) — p. 107

Editorial note, tabletop extrapolation: If the reference machine sees nA, the gap to the historical uA-mA norm lives in source output and center-region transmission, not physics limits - and extraction cost most census machines most of their beam, so budget a next machine's external current pessimistically.

Ion source, type hooded arc, tungsten filament

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

Editorial note, tabletop extrapolation: Population-level evidence that the hooded filament arc is the proven route to 100 uA-class internal beams at this scale - evidence of practice, not proof a cold-cathode PIG cannot compete (PIGs run cyclotrons too, dg-383): the choice trades filament fragility against arc-supply simplicity and delivered current.

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

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

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

Air-cooled coils. Iron ore blocks for shielding

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

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

Construction started 1940. Completion date July 1941 ... Total cost $5000 initial, $5000 improvements.

Howard, Cyclotrons and High-Energy Accelerators, 1958 — ORNL-2644 (1958) — p. 166

Editorial note, tabletop extrapolation: Scope calibration: small teams on small budgets built working 2-4 MeV, 16-27 inch machines in this era. A next machine at the few-hundred-keV scale on 8-in-class iron - dg-697's K ~ 48*(B*r)^2 gives about 0.35 MeV at 1 T on an 8-in pole's usable radius - is historically a modest, well-precedented project.

a Phillips-Ion-Gauge-type discharge can start in the magnetic field inside the vacuum tank near the positive transmission line

Osterlund & Smythe, A Cyclotron Power-Amplifier RF System Using a 4CW50,000C/8350 Tetrode — COO-535-543 (1963) — p. 5

Editorial note, tabletop extrapolation: Very relevant at higher dee voltage on the reference machine or a next machine: crossed E and B in vacuum is exactly a PIG geometry - it is how the gauge and the source work - so route DC-carrying feedlines, bias leads and probe wires out of the field region or shield them. This failure mode is designed out at layout time.

If this is done at the rate of 10 megacycles per second, the power requirement would be 20 megawatts!

Goodman, A Square-Wave Cyclotron Oscillator — ORNL-2403 (1958) — p. 13

Editorial note, tabletop extrapolation: The cleanest back-of-envelope argument in this collection for why dee voltage is bought with Q, not amplifier watts - scale it to a next machine (7-9.5 kV on tens of pF at 6.78 MHz) to show why a few hundred LDMOS watts suffice only through a good resonator.

It was somewhat difficult to get both the phase and the amplitude of the third harmonic adjusted correctly; however no serious attempt was made to develop a good self-excited driving system.

Goodman, A Square-Wave Cyclotron Oscillator — ORNL-2403 (1958) — p. 25

Editorial note, tabletop extrapolation: Mirrors the next machine's decision already leaning MOPA: independent control of each degree of freedom is the argument, and a DDS + LDMOS chain is the modern form - while the self-excited literature (dg-1367, dg-254) holds the other seat. This source records a difficulty, not a verdict.

Cited in: Driving the Dee: RF Coupling

for equal probability of sparking with given materials, the product of gap voltage and cathode gradient is a constant.

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

Editorial note, tabletop extrapolation: For a next machine's deflector the trade falls out of a chosen VE number: a 3-mm gap at VE = 1.5e4 (kV)^2/cm predicts ~67 kV at ~220 kV/cm - far beyond tabletop needs (dg-590's few kV), which is the real point: tabletop deflectors sit deep inside the bulk-breakdown envelope, and surface/edge engineering rules instead (dg-591).

In order to provide an adequate margin for day-to-day operation, a design value of 1.5 X 10^4 should be used.

Smith & Grunder, Electrical Design of Electrostatic Deflectors for Sector-Focused Cyclotrons — UCRL-10654 (1963) — p. 33

Editorial note, tabletop extrapolation: The most quotable deflector design number in the collection: design to VE = 1.5e4 (kV)^2/cm and treat the tested 2.25e4 as commissioning margin - as the source machine practiced. Transfer it as a starting point under the usual conditions (electrode material, finish, conditioning - dg-353, dg-295), and verify on the actual electrodes.

it stores only 2-1/2 joules and, at most, this is distributed among 1200 diodes. ... There is so little energy in a spark from this rectifier that it will not puncture even a piece of 5-mil aluminum foil.

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

Editorial note, tabletop extrapolation: The governing philosophy for a next machine's deflector supply: limit the energy delivered per spark rather than trying to prevent sparks - low stored energy is an equipment-survival property, and a sub-joule store at 50-100 kV is achievable. It is not a personnel-safety property: such a supply remains dangerous to people, and in human contact the supply's follow-on current adds to the stored energy. Personnel protection stays with enclosure, interlocks, grounding and discharge practice (dg-522, dg-654).

The extraction requirements, simply stated, are: (a) The precession must be arrested (b) Sufficient gain per turn must be obtained (c) Losses owing to axial blowup must be minimized.

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

Editorial note, tabletop extrapolation: The cleanest checklist in this collection for what a next machine's precessional-assist extraction must accomplish - phase-lock the precession to place orbit maxima at the septum azimuth, then count gain-per-turn against septum thickness. Machine-class independent.

The possibility of changing the electrical frequency and gradient to match operating conditions eliminates difficulties arising in magnetic extraction systems for variable-energy machines.

Stubbins, Radiofrequency System for Extracting Particles from a Cyclotron — UCRL-8578 (1958) — p. 4

Editorial note, tabletop extrapolation: Supports the next machine's plan-of-record (electrostatic deflector, no fixed magnetic channel) in spirit: an educational machine running several field/energy points wants extraction strength on a knob. A plain electrostatic deflector carries the voltage knob - not the source system's frequency knob - and that adjustability is exactly what a fixed B-bump lacks.

The alignment of the source with the magnetic field is extremely critical, as was expected, and makes it necessary to provide for external adjustments of the ion source.

Howard (ed.), Electromagnetic Research Division Quarterly, period ending 30 June 1952 — ORNL-1345 (1952) — p. 10

Editorial note, tabletop extrapolation: Strong design input for a next machine: budget at least one externally accessible source degree of freedom (rotation or z) - both ORNL machines provided it after finding the optimum unreachable blind. Adjustment under beam is the convenient form; adjust-then-pump iterations reach the same optimum, slower.

A negative voltage bias, 1 to 2 kv, is applied to the dees in order to sweep out any ions that may be formed while oscillation is being established.

Howard (ed.), Electromagnetic Research Division Quarterly, period ending 30 June 1952 — ORNL-1345 (1952) — p. 9

Editorial note, tabletop extrapolation: Transferable as a startup practice: a bias supply that sweeps ions out during RF ramp-up is the classical cure for start-up loading (dg-320, dg-680 - polarity differs by machine and both worked). What voltage a small machine needs is found at the machine; the 63-inch's 2-4% of dee voltage is the documented anchor, not a scaling law.

In dc tests the output of the source, measured after the beam had passed through a 180 deg path in the magnetic field, was: 8 ma of N+, 2 ma of N++, and 2 ma of N+++.

Howard (ed.), Electromagnetic Research Division Quarterly, period ending 30 June 1952 — ORNL-1345 (1952) — p. 24

Editorial note, tabletop extrapolation: The 180-degree bend uses the cyclotron's own field as a mass spectrometer with the RF off — on the reference machine this is precisely the source-species test geometry: source + static field + offset collector measures the H+/H2+/H3+ mix directly before any acceleration studies.

the ion source position is limited to a maximum radius of 2.5 inches. This forces operation at comparatively low dee voltages (20-30 kv) in order to center the orbits.

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

Editorial note, tabletop extrapolation: The design logic transfers directly to a next machine's central-region layout: pick dee voltage and source-puller radius TOGETHER from the first-orbit geometry. It also cuts the other way for the reference machine's 5-13 kV upgrade: raising dee voltage moves the optimum source position outward — re-scan source position after the RF upgrade.

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

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

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

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

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

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

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

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

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

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

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

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

In a high-current low-voltage coil, insulation is required only to maintain mechanical separation of the conductors.

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

Editorial note, tabletop extrapolation: What transfers is the architecture - few turns of heavy conductor at high current, direct cooling through generous passages - which beats many-turn fine-wire coils on space factor and pumping pressure. The bare-minimum insulation standard does not transfer: a modern coil wants verified turn-to-turn and ground insulation against inductive transients (dg-218's dump events), abrasion, thermal aging and coolant exposure, cheap as modern materials make it.

A second type of coil which is more attractive, when the coil must be wound at the cyclotron site, is a flat-wound helix.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 26

Editorial note, tabletop extrapolation: Directly a garage-scale construction technique: cut flat copper sectors, stack into a helix, join into a continuous conductor - no winding mandrel needed. The joints are the engineering: braze for permanent low-resistance splices, bolt only with designed contact pressure and area (the report's joint-sizing criterion: scan re-read queued for the number), and place cooling per the report's tube arrangement.

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

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

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

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

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

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

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

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

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

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

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

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

Cited in: Choosing Your Machine

S = 400 A^2/OL liters/sec ... For convenience of calculation the value 400 is used rather than 403; the results are hardly affected since the formula is only an approximation.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 144-145

Editorial note, tabletop extrapolation: The workhorse formula for long, odd-shaped passages in a cyclotron - annular gaps around the dee, slots, duct runs - where circular-tube handbook formulas fail. Its own conditions ride along: LONG ducts in molecular flow, and 'only an approximation' by the source's own words; short apertures, bends and abrupt area changes take end corrections or the orifice forms (dg-839), and a complex dee cavity is a network of elements, not one duct.

Cited in: The Vacuum Budget of a Cyclotron

For an orifice small relative to the area surrounding it, S = 75A. For an orifice large relative to the area surrounding it, S = 75A Abar/(Abar - A).

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 145

Editorial note, tabletop extrapolation: With the duct rule this covers most of a chamber conductance budget: baffle holes, dee mouths and constrictions become orifice or short-duct elements in a network. Finite-thickness holes transmit less than the zero-thickness 75A form - they are short ducts; interpolate or use transmission-probability tables - and series elements combine only approximately, so the budget is an estimate the pumpdown curve then checks.

Cited in: The Vacuum Budget of a Cyclotron

the term "resistance" is used there to indicate the reciprocal of the conductance. The use of resistance presents perhaps a clearer picture through the use of an electrical analog.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 132

Editorial note, tabletop extrapolation: The report's method in one sentence - their 32-in pumps' 13,700 l/s collapsed to 8,300 l/s effective inside the dee (air; the report's own worked numbers). The size of that collapse is the reason to budget from the source outward, not the pump inward - compute the conductance chain for the actual geometry rather than assuming any fixed fraction survives.

Cited in: The Vacuum Budget of a Cyclotron

Thus the 32-in. pumps will handle almost twice as much gas as the 20-in. pumps, and the decision to use 32-in. pumps is an obvious one.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 135-137

Editorial note, tabletop extrapolation: The right way to evaluate a diff-pump upgrade for a next machine - work in throughput (torr-l/s) at the pressure the source needs, with the MFC's known gas feed as the load, instead of comparing nameplate l/s.

Cited in: The Vacuum Budget of a Cyclotron

If 200 ml/hr is considered as a maximum rate of gas injection, this results in ... 0.042 liter-mm/sec.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 136

Editorial note, tabletop extrapolation: The same arithmetic the builder runs with the MFC: a 0.1-1 sccm hydrogen feed is 1.3e-3 to 1.3e-2 torr-l/s; divide by the honest effective speed FOR HYDROGEN at the chamber, then add the pump ultimate and the outgassing floor, to predict running pressure before touching hardware. The formula assumes the source feed dominates the incremental load - the flow-on/off test verifies that (dg-370).

Cited in: The Vacuum Budget of a Cyclotron

Fig. 6.3-Typical characteristics of three-fourths scale model ... 150-kw input, 27.5-kw plate dissipation per tube ... The fairly low efficiency, 27 per cent, indicates that it would be desirable to go to six type-880 tubes in the final model

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. PDF p.162 (unnumbered chapter opener, Technical Report No. 6) for the quoted text; the figure is on PDF p.167 = printed p.167

Editorial note, tabletop extrapolation: The transferable method rule - prototype the next machine's dee/stem/liner as a cheap scale model (or full-scale mockup, given the small size) and measure resonance, Q and parasitics before final fabrication; NYO-780 p.29ff records the same practice. Cite both.

a careful choice of materials of construction, for example, using as much aluminum as possible and very little stainless steel, should reduce the radiation problem significantly.

Boom, Toth & Zucker, Residual Radiation of the LRL 184-inch Cyclotron — ORNL-3158 (1961) — p. 18

Editorial note, tabletop extrapolation: ENERGY SCOPE: a 730-MeV machine's recommendation. At the reference machine's sub-MeV proton operation the spallation and (p,xn) channels behind it are closed, so bulk structural activation does not drive material choice at that scale - with the standing exceptions: thresholdless capture on some nuclides, light-element targets, and any deuteron operation. The drawing-board principle bites the moment a machine crosses into open-channel territory.

Cited in: Shielding a Small Cyclotron

Targets and their assemblies normally emit about 100 to 500 r/hr 5 minutes after bombardment ... The intensity of radiation by the exit strip averages about 10,000 r/hr, and the deflector about 500 r/hr.

McWalters et al., Radiation Exposures of Personnel at the 60-inch Cyclotron — UCRL-8276 (1958) — p. internal-target and external-target figures on PDF p. 10 as cited; deflector/exit-strip figures on PDF p. 15 (section 'Maintenance')

Editorial note, tabletop extrapolation: ENERGY SCOPE: these are 10-24 MeV activation levels. The design ordering survives: whatever intercepts full beam (probe tip, Faraday cup, target holder) concentrates the consequences. On a sub-MeV machine that is heat and sputtering today - and activation joins the list via thresholdless capture on some materials, light-element targets, or any deuteron operation, growing first at these same components if energy climbs.

Cited in: Shielding a Small Cyclotron

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

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

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

conceived as an experimental device to examine the practicability of isochronous acceleration ... to reveal any unexpected phenomena ... and finally, to demonstrate the feasibility of a high efficiency beam extraction system.

Oak Ridge National Laboratory, A Proposal for the Mc² Isochronous Cyclotron — ORNL-3540 (1963) — p. 263

Editorial note, tabletop extrapolation: The three-purpose charter is scale-free for any model or prototype a program chooses to build; whether to build one at all is a cost-versus-risk call - FEMM plus the tracker is the tabletop program's cheap analogue. The keV-electron stand-in trick itself needs more than matched T/mc^2 to be faithful (rigidity and geometry must scale together).

Cited in: Choosing Your Machine

All suffer from one or more of the following defects: excessive space requirements, lack of terminal space, lack of terminal auxiliary power, and lack of flexibility for future uses.

Oak Ridge National Laboratory, A Proposal for the Mc² Isochronous Cyclotron — ORNL-3540 (1963) — p. 149

Editorial note, tabletop extrapolation: Their injector shoot-out (tandem vs open-terminal vs pressurized vs Van de Graaff) models the documentation style for any subsystem selection in mark2_design_notes open decisions.

Cited in: Choosing Your Machine

Six- and eight-sector machines are free from strong essential resonances ... also, the symmetry easily permits four accelerating gaps per revolution, a situation well suited to rf cavities.

Oak Ridge National Laboratory, A Proposal for the Mc² Isochronous Cyclotron — ORNL-3540 (1963) — p. 266-267

Editorial note, tabletop extrapolation: 810-MeV specifics (vr climbing to 2, spiral sectors) do not scale down; the method — list resonances crossed by your vr/vz trajectory before fixing N, then let RF layout break ties — applies to any AVF design.

Representatives of the steel industry were consulted to determine the size of forging of the required shapes that could be practicably produced.

Oak Ridge National Laboratory, A Proposal for the Mc² Isochronous Cyclotron — ORNL-3540 (1963) — p. 136

Editorial note, tabletop extrapolation: Scale-free: for a next machine this reads 'call the waterjet/plate supplier before freezing the pole drawing' — same move as TID-454's cost-driven magnet design.

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

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

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

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

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

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

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

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

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

The cost of the magnet would be increased unreasonably if a gap suitably large for conventional dees were provided. For this reason, a system for acceleration with vertically oriented resonant cavities was adopted.

Oak Ridge National Laboratory, A Proposal for the Mc² Isochronous Cyclotron — ORNL-3540 (1963) — p. 145

Editorial note, tabletop extrapolation: The specific topology (vertical TEM cavities) is 810-MeV-only; the transfer is the coupling: every inch of dee clearance is bought with magnet cost, so dee-gap and magnet-gap must be traded as one system, as in a next machine's gap decision.

chosen for the final design since this is the ordinary coaxial cavity and is more amenable to design ... was chosen as a compromise between voltage-holding ability and transit-time effects.

Oak Ridge National Laboratory, A Proposal for the Mc² Isochronous Cyclotron — ORNL-3540 (1963) — p. 174-176

Editorial note, tabletop extrapolation: Scale-free method: a dee-stem system is likewise a transmission line with machine-fixed dimensions and a few free ones - when sizing the planned higher-voltage dee (the 5-13 kV upgrade), name each free spacing's compromise pair in the design notes the way the source names theirs.

Checking of the model dimensions revealed a construction error of several percent in the spacing near the median plane ... a resonant frequency of 151.3 Mc/s was calculated for the model; this is within 4% of the measured value.

Oak Ridge National Laboratory, A Proposal for the Mc² Isochronous Cyclotron — ORNL-3540 (1963) — p. 177

Editorial note, tabletop extrapolation: Scale-free double duty: a bench mock-up of a next machine's dee/stem before the LDMOS amplifier arrives certifies the calculation and catches build errors - and while it sits on the bench, sweeping for higher-order modes and measuring Q are nearly free additions (dg-664).

Computed power loss in cavity 500 kW; Beam power 160 kW; Contingency 200 kW; total 860 kW

Oak Ridge National Laboratory, A Proposal for the Mc² Isochronous Cyclotron — ORNL-3540 (1963) — p. 180

Editorial note, tabletop extrapolation: The kilowatts are 810-MeV numbers; the structure sizes the planned 100-500 W LDMOS chain honestly - compute the resonator loss (dg-313), add beam and coupling loads, then carry contingency as a NAMED line of the source's ~30% class instead of hiding margin inside each estimate.

Thus, when a spark occurs in the cavity a large resistive load is reflected to the plates of the power amplifier and the tube plate current would decrease.

Oak Ridge National Laboratory, A Proposal for the Mc² Isochronous Cyclotron — ORNL-3540 (1963) — p. 182-183

Editorial note, tabletop extrapolation: Scale-free fault-mode-first design: dees spark at every scale, so choose a next machine's amplifier coupling for arc behavior, not just matched-condition efficiency - establish what YOUR coupling does to the device when the load arcs (some couplings raise device stress instead), then layer the protection accordingly (dg-338, dg-679). Directly relevant to protecting an LDMOS pallet.

The net speed of these pumps was assumed to be 25% of the speed at the mouth of the pump, because of the usual losses in baffles and valves.

Oak Ridge National Laboratory, A Proposal for the Mc² Isochronous Cyclotron — ORNL-3540 (1963) — p. 158

Editorial note, tabletop extrapolation: Scale-free in structure, not numbers: size from the outgassing load, compute the actual duct and baffle conductances (1/S_eff = 1/S_mouth + 1/C - the vacuum deep dive's budget method), and treat handbook outgassing rates as early-time bounds. The 25% is what THEIR plumbing cost them; the reference machine's SI100 stack has its own conductance chain to compute.

Cited in: The Vacuum Budget of a Cyclotron

electric fields are relatively ineffective at high particle velocities, but the force on an ion due to a magnetic field is proportional to velocity.

Oak Ridge National Laboratory, A Proposal for the Mc² Isochronous Cyclotron — ORNL-3540 (1963) — p. 151

Editorial note, tabletop extrapolation: At 150 keV protons (v ~ 5.4e6 m/s) the comparison runs strongly toward electrostatic: modest septum fields equal coil fields that are awkward to engineer at that scale, which is why documented small machines extract electrostatically. Run the B = E/v arithmetic before copying any big-machine magnetic-channel scheme - the crossover is a computation, not a law.

Historically, the shielding initially provided for high-energy accelerators has later proved to be inadequate ... The experiment areas are now too small in almost every installation.

Oak Ridge National Laboratory, A Proposal for the Mc² Isochronous Cyclotron — ORNL-3540 (1963) — p. 184

Editorial note, tabletop extrapolation: Scale-free planning doctrine, and this collection's first design-stage statement of it: leave physical room (and structural capacity) to add shielding around a next machine before the first neutron is made.

Cited in: Shielding a Small Cyclotron

we have designed the shielding so that the limits for general population are observed in the regularly inhabited work areas adjoining the accelerator and experiment rooms.

Oak Ridge National Laboratory, A Proposal for the Mc² Isochronous Cyclotron — ORNL-3540 (1963) — p. 186

Editorial note, tabletop extrapolation: Directly transferable posture for a residential-basement machine: the family upstairs is 'general population', so design to the CURRENT public limit at occupied locations - in the US today 1 mSv (0.1 rem) per year, fifty times below occupational and five times stricter than the source's era ratio - and take the numbers from the jurisdiction's own regulations (/legal/), not from a 1965 report.

Cited in: Shielding a Small Cyclotron

we have neglected both the secondary production and target attenuation; this results in a conservative estimate still within the precision of other data.

Oak Ridge National Laboratory, A Proposal for the Mc² Isochronous Cyclotron — ORNL-3540 (1963) — p. 189

Editorial note, tabletop extrapolation: Scale-free methodology (their 810-MeV cascade physics is not): carry the same per-step bookkeeping on a next machine's estimate. The quote's specific lesson: omissions can run in opposite directions and partially cancel, so direction is tracked per step, never assumed - and the net conservatism is only as good as the input data's precision.

Cited in: Shielding a Small Cyclotron

The thickness of shielding required for a high energy accelerator is established chiefly by the cascade nucleons ... The evaporation particles must be taken into account, however, in determining the activation of materials

Oak Ridge National Laboratory, A Proposal for the Mc² Isochronous Cyclotron — ORNL-3540 (1963) — p. 186-188

Editorial note, tabletop extrapolation: The sort-by-question habit is the transferable part: identify which radiation component sets shield thickness and which sets activation and surface dose for YOUR source term. For a D-D-capable machine that is fast-neutron moderation for thickness, with capture gammas and nuclide-specific activation as separate questions carrying their own data - not a clean analogue of the source's cascade/evaporation split, which is high-energy physics.

Cited in: Shielding a Small Cyclotron

The estimate of $0.35 per pound for the finished magnet appears reasonable when compared with the unit price of $0.26 per pound paid for another large magnet at the Laboratory.

Oak Ridge National Laboratory, A Proposal for the Mc² Isochronous Cyclotron — ORNL-3540 (1963) — p. 245

Editorial note, tabletop extrapolation: Scale-free estimating hygiene: their App. F traces $11.5M to named suppliers; a next machine's BOM should likewise tie each line to a quote, a catalog page, or a reference machine receipt — and explain deltas ('more complex machining, more waste metal').

Provisions have been made in all plans to make the addition of the medical facility as simple and as economical as possible ... The cost of the medical facility is not included in the initial cost of the project

Oak Ridge National Laboratory, A Proposal for the Mc² Isochronous Cyclotron — ORNL-3540 (1963) — p. 22

Editorial note, tabletop extrapolation: Scale-free scoping discipline for the business plan: design the educational-machine baseline with hooks for upgrades (extraction port, shielding growth, second station) without loading their cost onto gate-one.

A very effective adjustable beam deflector has been developed; under the best conditions, 38% of a 1000 ua internal beam has been deflected.

Howard (ed.), Electromagnetic Research Division Quarterly, period ending 31 December 1951 — ORNL-1269 (1952) — p. 40

Editorial note, tabletop extrapolation: Sets expectations for any future extraction gate: design the septum/deflector with in-vacuum adjustability - the quoted 'very effective' unit was fully adjustable and even so extracted 38% at BEST. Tens of percent is the documented ballpark for classical deflectors (dg-496, dg-595); define success for your machine before the attempt, and account for where the undeflected majority goes (dg-260).

Since the dee voltage in the experimental unit was limited to 10 kv, application of injection potentials of over 10 kv resulted in deceleration of ions between the accelerating electrode and the dee.

Howard (ed.), Electromagnetic Research Division Quarterly, period ending 31 December 1951 — ORNL-1269 (1952) — p. 47

Editorial note, tabletop extrapolation: Any source-bias or puller experiment must check the same ordering in ITS geometry: a dc extraction potential that overtops what the RF gap can supply runs the first gap backward. The check is signed potentials and timing at the actual gap - the source's inequality is that machine's instance of it, not a universal bound.

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

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

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

The extreme radioactivity induced in type 304 stainless steel makes its use undesirable, the use of an aluminum alloy is now being investigated.

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

Editorial note, tabletop extrapolation: At sub-MeV energies on ordinary structural metals activation is small where it occurs at all - thresholdless capture and deuteron operation are the exceptions - and the selection logic transfers whole: thermal adequacy is not the whole selection. Prefer aluminum or graphite for probes, septa and slits anywhere protons above a few MeV are contemplated, and let the licensing story inherit the same reasoning.

Cited in: Shielding a Small Cyclotron

such a cyclotron is feasible, that an energy definition of less than +/-10 kev could be achieved, and that deflected beams would be in the range of 1 to 10 ua

Howard (ed.), Electromagnetic Research Division Semiannual, period ending 20 March 1953 — ORNL-1531 (1953) — p. 19

Editorial note, tabletop extrapolation: Direct prior art for the plan's educational variable-energy concept: vary energy with field/frequency plus a movable target (cf. the 44-inch spacer), and buy energy DEFINITION with a simple analyzed beamline - accepting the current it costs - rather than machine perfection.

Since this circuit depends upon the electrical characteristics of the resonant dee system, it cannot be designed until these characteristics are determined.

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

Editorial note, tabletop extrapolation: The template for the reference machine's LDMOS upgrade - freeze the amplifier and dee-resonator designs, but specify the matching/coupling network only after measuring the real dee system's f0, Q, and shunt impedance on the bench. Ordering the coupling parts first is the classic mistake this rule prevents.

The whole dee system is insulated from ground so that a bias potential may be applied to control ion loading.

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

Editorial note, tabletop extrapolation: The reference machine already uses dee bias; the design rule for a next machine is to make bias a first-class requirement - insulate the dee-stem support (see the ornl-1884 cantilever-on-insulators execution) rather than retrofitting isolation later.

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

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

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

Dees were simulated by a capacitor connected from the end of each dee stem to ground... Other circuit components were selected to have approximately the same values as those in a full-scale operation.

Howard (ed.), Electronuclear Research Division Semiannual, period ending 20 September 1953 — ORNL-1663 (1954) — p. PDF p. 19 as cited (printed p. 10, section 'VARIABLE-ENERGY HEAVY-PARTICLE CYCLOTRON')

Editorial note, tabletop extrapolation: A bench-scale dee-stem mockup (pipe sections plus padding capacitors) lets the next machine's oscillator/coupling scheme be raced against alternatives for pocket change - the same measure-on-model philosophy as the deferred filament-coupling rule, one report earlier in hardware form.

The liner, dees, and dee-stem housing are being fabricated by an outside contractor. The faceplates, dee stems, ion source, target probe, and vacuum system were fabricated locally

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

Editorial note, tabletop extrapolation: The three-report arc remains this collection's cleanest outsourcing story: the contracted brazed, water-cooled vacuum parts were where the delays landed - one program's experience, and a fair prior. For a next machine: buy simple machining, keep leak-integrity parts in-house or design them repairable.

Cited in: The Vacuum Budget of a Cyclotron

All other components of the present 44-in. cyclotron, oscillator, dee system, vacuum system, ion source, target-probe, and power supplies, would be utilized.

Howard (ed.), Electronuclear Research Division Semiannual, period ending 20 September 1954 — ORNL-1795 (1954) — p. 23

Editorial note, tabletop extrapolation: A strong argument for clean interfaces between a next machine's subsystems: ORNL could contemplate a new machine class for the price of iron and a tank because everything else was JUDGED reusable - the judgment is the quote's; the adaptation cost of the reuse is not on this card. Design interfaces so the same judgment could be true of your machine.

Dee-to-dee r-f voltage (design), kv 200; Threshold voltage for N5+, kv 110 (Table 3, condensed)

Howard (ed.), Electronuclear Research Division Semiannual, period ending 20 March 1955 — ORNL-1884 (1955) — p. 20

Editorial note, tabletop extrapolation: Margin philosophy consistent with the 63-inch's 75-vs-60 kV acceptance hold (ornl-1339): documented machines bought well over threshold. For the LDMOS upgrade, compute the threshold dee voltage for the intended turn count and buy real headroom - documented precedents cluster around 1.3-2x. What the margin purchases (orbit count, loading headroom, species reach) is the editorial reading, not the table's statement.

Being mostly below ground level, the room will be easy to shield. Placing the room at the basement floor level will make it convenient to transfer heavy equipment.

Howard (ed.), Electronuclear Research Division Semiannual, period ending 20 March 1955 — ORNL-1884 (1955) — p. 21

Editorial note, tabletop extrapolation: Directly relevant to the facility question for any MeV-class educational machine: below-grade siting was the study's shielding strategy, and siting beside existing utilities and controls was a cost line they weighed as seriously as the magnet. Earth shields in the directions it actually covers, by its actual thickness, density and moisture - it does not blanket-replace engineered shielding, and the uncovered directions, the roof, and every penetration still get the full design treatment (see the shielding deep dive).

Cited in: Choosing Your Machine · Shielding a Small Cyclotron

Plans are being made for an electron-model accelerator to be used in assessing the importance of imperfection resonances and the feasibility of their penetration.

Howard (ed.), Electronuclear Research Division Semiannual, period ending 20 March 1955 — ORNL-1884 (1955) — p. 35

Editorial note, tabletop extrapolation: A historical instance of risk-ordered development: when the open question is orbit dynamics, a cheap electron model is one way to attack it before proton iron is bought - scaled properly (dg-892's rigidity caveat). The tabletop program's equivalent instruments are the tracker and measured field maps.

The major components have been assembled and vacuum-tested (see Fig. 5).

Howard (ed.), Electronuclear Research Division Semiannual, period ending 20 March 1955 — ORNL-1884 (1955) — p. 19

Editorial note, tabletop extrapolation: Schedule realism, one datapoint thick: a professional division with machine shops took about two years from revision concept to vacuum-tested assembly, with outsourced fabrication the long pole (dg-951). A home program's periods stretch and compress differently; the census's one-to-six-year first-beam spread is the wider base rate.

in order to produce a suitable object for the analyzing magnet, we introduce a second magnet whose sole function is to focus as much of the beam as possible on a precision slit.

Bromley & Bruner, The Design of a Focusing and Analyzing System for the 27-inch Cyclotron Beam — NYO-3823 (1954) — p. 4

Editorial note, tabletop extrapolation: DIRECT for any ANALYZED external line on a next machine - the canonical two-stage architecture: a condenser focuses as much beam as possible onto a precision slit, and that illuminated slit becomes the analyzer's cleanly defined object. Lines that only transport or irradiate skip the apparatus; the slit's shielding is the companion rule (dg-966).

A considerable amount of undesirable radiation will be produced by that part of the beam intercepted by the slit system. ... it is also desirable that the analyzer image distance be large, in order to reduce the angular spread of the beam at the image point. ... [placing the condenser farther from] the cyclotron port ... required larger condenser pole pieces in order to accommodate the horizontally spreading beam.

Bromley & Bruner, The Design of a Focusing and Analyzing System for the 27-inch Cyclotron Beam — NYO-3823 (1954) — p. 5

Editorial note, tabletop extrapolation: DIRECT and cheap to honor at layout time, nearly impossible later: treat every defining aperture as a place where beam power - and therefore radiation - concentrates. At 150-170 keV the intercepted beam makes mostly heat plus thick-target bremsstrahlung whose X-ray yield climbs steeply with voltage, so the slit belongs with the shielded, surveyed components, wherever the survey ranks it that day.

Cited in: Shielding a Small Cyclotron

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

the problem of obtaining a pulsed beam usually does not arise, because the beam of a conventional cyclotron is already naturally bunched.

Fulbright et al., A Fast Neutron Time of Flight System for Use with Cyclotrons — NYO-9360 (1962) — p. 6

Editorial note, tabletop extrapolation: DIRECT and foundational for the experiment catalog: the reference machine at 9 MHz delivers phase-bunched beam at the RF period - a measurable, teachable property and the enabling fact for gated counting. 'Usually' is operative: time-of-flight at fine resolution, or experiments needing low repetition rate, can still require pulse selection or extra bunching - check bunch width and period against the experiment's timing demands.

the pulses are obtained in a way which makes them insensitive to beam current changes, and b) all reference pulses are smooth and identical in shape.

Fulbright et al., A Fast Neutron Time of Flight System for Use with Cyclotrons — NYO-9360 (1962) — p. 6

Editorial note, tabletop extrapolation: The most directly transferable finding here: the machine's RF is a free, stable timing fiducial at any scale - clock gated counting and TOF off a capacitive sniff of the dee. A fiducial is not a beam-arrival timestamp: beam phase relative to the RF moves with field tuning, loading and cable delays, so calibrate the offset against a real beam signal - and re-calibrate after retuning - before treating RF zero-crossings as beam time.

Performance of the model is considered sufficiently satisfactory to proceed with the full scale design and construction based on the model dimensions.

Anderson, Half-Scale Model Tests on the Three Quarter Wave R.F. System — UCRL-31 (1947) — p. 16

Editorial note, tabletop extrapolation: A next machine's dee/stem/tank is already benchtop-sized, so the transferable form is the mockup itself — a cheap RF-only copy (no vacuum) of the dee-liner geometry, swept with a VNA before the vacuum parts are machined. Same lineage as UCRL-64 and MDDC-1045 already in this collection.

Cited in: Choosing Your Machine

These were the capacity presented to the dee by the dummy dee, the minimum capacity of the rotor, and the inductance at the throat of the dee.

Anderson, Half-Scale Model Tests on the Three Quarter Wave R.F. System — UCRL-31 (1947) — p. 10

Editorial note, tabletop extrapolation: Direct checklist for why a tank on the reference machine or a next machine does not resonate where the lumped-element estimate says — dummy-dee proximity, feedthrough/trimmer minimum C, and stem-to-dee transition inductance are the three knobs.

volts per turn substantially lower than the designed 280 kev/turn would result in sharp reduction of both extraction efficiency and optical quality.

Blosser & Gordon, Computational Study of a Resonant Extraction System for a 3-Sector Cyclotron — MSUCP-9 (1961) — p. 45

Editorial note, tabletop extrapolation: The quantitative ancestor of 'dee volts buy extraction': the reference machine's uncalibrated ~1.3 kV dee is one reason it is internal-beam-only, and a next machine's 5-13 kV target is what would make an extraction scheme thinkable - thinkable, not feasible, until the turn separation (delta_r ~ r*delta_E/2E), phase width, septum clearance, tune and bump design are actually computed.

beams entering the extraction region approximately centered on the equilibrium orbit behave as well or better than beams entering with substantial displacement.

Blosser & Gordon, Computational Study of a Resonant Extraction System for a 3-Sector Cyclotron — MSUCP-9 (1961) — p. 45

Editorial note, tabletop extrapolation: The project-level lesson for a next machine — run the cheap simulation before committing hardware to any orbit-dynamics intuition, including intuitions published by people as good as Blosser and Gordon.

Table 1. k/h = 0.1: at x/h = 0, E/(V0/h) = 0.99388 [values verified against page image]

Beal, Computation of Electric Field and Potential of an Idealized Dee Geometry — MSUCP-12 (1961) — p. 11

Editorial note, tabletop extrapolation: Sets the ceiling on CENTERLINE gap field for a dee redesign: with a 1-inch aperture (h = 0.5 in) and 2.5 kV dee-to-dummy, the median-plane peak cannot exceed ~2 kV/cm however tight the gap. Two cautions: local surface fields at electrode edges run above the centerline value - breakdown cares about those (dg-353) - and widening the aperture trades centerline field for beam height by the table's factors, not one-for-one at every k/h.

Table 1, k/h = 2.0: E/(V0/h) = 0.37823 at x/h = 0, maximum 0.38966 at x/h = 1.2 [verified against page image]

Beal, Computation of Electric Field and Potential of an Idealized Dee Geometry — MSUCP-12 (1961) — p. 16

Editorial note, tabletop extrapolation: Kills the tempting E = V_dee/gap for FIELD estimates on a next machine's geometry, where gap and aperture are the same order (k/h ~ 1) and neither limiting approximation holds - use the formulas or tables for the profile. Energy gain is a different question: absent transit-time effects the work across the gap is q*V0 whatever the profile; the profile changes transit-time factors and where field concentrates - and the surface fields at electrode edges, which the breakdown margin actually cares about (dg-353, dg-1028).

The bremsstrahlung is approximately inversally proportional to the M2 where M is the mass of the incident particle. It is therefore usually insignificant for heavy particles.

Martin (ed.), Accelerator Radiation Protection — AD-755510 / USA-NLABS-TR-73-7, US Army Natick Laboratories (1972) — p. 30

Editorial note, tabletop extrapolation: Supports the program's standing model that dee-voltage electrons, not the proton beam's own bremsstrahlung, dominate the X-ray hazard on a sub-MeV proton cyclotron. Dominant is not sole: characteristic X-rays and any nuclear gammas from targets keep their own lines in the survey plan.

If we assume that the ion current "I" results in a reverse directed electron current of magnitude 0.2*I that is accelerated through 1/3 the terminal voltage we would usually get a very considerable x-ray production.

Martin (ed.), Accelerator Radiation Protection — AD-755510 / USA-NLABS-TR-73-7, US Army Natick Laboratories (1972) — p. 31

Editorial note, tabletop extrapolation: Use this only as the lesson that stray-electron X-rays exist wherever there is RF voltage and vacuum, never as a ceiling. For a next machine's hazard analysis, plan around at least the peak-to-peak dee voltage as the electron impact energy - a planning floor, not a physical ceiling, since multi-transit RF processes can exceed single-gap figures - and let the measured X-ray endpoint from the survey be the authority the analysis answers to.

As a rough estimate we offer that shielding which is required at 90 deg from the beam axis of an electron accelerator, with the same beam current and energy.

Martin (ed.), Accelerator Radiation Protection — AD-755510 / USA-NLABS-TR-73-7, US Army Natick Laboratories (1972) — p. 31

Editorial note, tabletop extrapolation: The conservative sizing pattern for a product-machine enclosure: bound the ion machine by an equivalent electron accelerator at the same current and at the maximum electron energy credible in the machine (at least peak dee-to-ground; dg-1036), then read the required thickness from electron-accelerator shielding data at that energy and verify by survey. The reference machine's chamber walls stopping its soft X-rays is a measured fact about ~10 kV operation, not a rule to inherit.

Because of the Coulomb barrier, proton cross sections for nuclear interaction are negligible below about 0.1 MeV. In light nuclei there are some exceptions which are of little interest here.

Martin (ed.), Accelerator Radiation Protection — AD-755510 / USA-NLABS-TR-73-7, US Army Natick Laboratories (1972) — p. 48

Editorial note, tabletop extrapolation: Closes the neutron question for the reference machine at ~150 keV-class energies EXCEPT via the light-nuclei exceptions the chapter waves off - and the exceptions differ in kind: the deliberate 11B(p,alpha) target yields charged alphas and gammas, not neutrons directly (the indirect path to check is secondary (alpha,n) on nearby low-Z materials); deuterium contamination is the direct neutron path, D(d,n) being thresholdless (see Ch. IV rule).

For light and low-intermediate nuclei, (p,n) thresholds are of the order of an MeV. Neutron emission becomes the dominant reaction when the incident particle energy exceeds the threshold by about 1 MeV.

Martin (ed.), Accelerator Radiation Protection — AD-755510 / USA-NLABS-TR-73-7, US Army Natick Laboratories (1972) — p. 48

Editorial note, tabletop extrapolation: The threshold-audit pattern for every machine energy bump: list materials the beam can strike, look up (p,n) thresholds, and confirm E_beam sits below them. At 170 keV (a next machine) every (p,n) channel on stable nuclei is closed, but the margin is not uniform: the lowest known stable-target threshold, 115In(p,n)115Sn at ~287 keV, leaves only ~120 keV, while the common structural metals and light targets sit >600 keV away (first structural channel 55Mn(p,n)55Fe at 1.03 MeV; 7Li(p,n) at 1.88 MeV). The audit must be redone on any energy bump, against the materials actually present, not a generic list. [Corrected 2026-09-13: previously claimed every stable-nucleus channel closed 'by >600 keV of margin'; that figure held for the structural metals and light targets but not for mid-Z nuclides like 115In (NNDC QCalc; see the safety page's activation section). Raised by an external site review alongside the dg-581 correction.]

it is a fairly accurate rule of thumb that for energies of interest here, the facility generally contains adequate neutron shielding in the process. The more serious neutron shielding problem occurs when the X- and gamma ray hazard is exceeded by the neutron hazard. Proton and deuteron accelerators are cases in point.

Martin (ed.), Accelerator Radiation Protection — AD-755510 / USA-NLABS-TR-73-7, US Army Natick Laboratories (1972) — p. 57

Editorial note, tabletop extrapolation: For any future neutron-capable operation (a deuterium species test, or a >1.9 MeV machine) the caveat is the operative part: an X-ray shield does not automatically cover the neutron hazard, and the source names proton and deuteron machines as exactly the case where neutrons dominate. The source's physics points to hydrogenous material (concrete, HDPE) rather than lead for the neutron component, but sizing it is a separate design problem - worked from the actual source term and verified by survey - not settled in advance by this rule of thumb.

Experimental removal cross sections are roughly three-quarters of the total cross section for 8 MeV neutrons. For hydrogen this fraction is somewhat larger. [Table III-7B] Ordinary Concrete 0.0942 ... Barytes Concrete 0.0945

Martin (ed.), Accelerator Radiation Protection — AD-755510 / USA-NLABS-TR-73-7, US Army Natick Laboratories (1972) — p. PDF 58 (printed 49) for the quote; PDF 57 (printed 48) for the exponential/reactor framing; PDF 60 (printed 51) for the concrete coefficient in Table III-7B

Editorial note, tabletop extrapolation: The one-line neutron shield ESTIMATOR for contingency planning - a D-D source term attenuates ~10x per 24 cm of concrete at the chapter's coefficient - used with its conditions: the coefficient is energy-derived (8 MeV; 2.45 MeV D-D neutrons remove differently), hydrogen content matters, and the chapter's own safety factors ride along. An estimate to verify by survey, never a design allowable.

shall not exceed 5 rems multiplied by the number of years beyond 18. The dose in per calendar quarter shall not exceed 3 rems.

Martin (ed.), Accelerator Radiation Protection — AD-755510 / USA-NLABS-TR-73-7, US Army Natick Laboratories (1972) — p. 116

Editorial note, tabletop extrapolation: CAUTION — HISTORICAL NUMBERS, superseded by 10 CFR 20 / NCRP 116 (5 rem/yr occupational, 100 mrem/yr public, age-proration abolished). Keep for reading-era context and for the still-valid design pattern: public-tier limits ~10-50x below occupational drive product-machine enclosure design, since customers are "general population."

Cyclotron positive ions 50-200 usec ... Microstructure at RF frequencies

Martin (ed.), Accelerator Radiation Protection — AD-755510 / USA-NLABS-TR-73-7, US Army Natick Laboratories (1972) — p. 123

Editorial note, tabletop extrapolation: The reference machine runs CW-RF but a beam bunched at 9 MHz; any future pulsed-RF operation (LDMOS duty-cycling) puts the machine squarely in this table — recheck every survey instrument's pulse response before trusting it.

the second term in the equation above becomes zero and the number of counts per second, as is expected, becomes the radiation source pulse rate.

Martin (ed.), Accelerator Radiation Protection — AD-755510 / USA-NLABS-TR-73-7, US Army Natick Laboratories (1972) — p. 134

Editorial note, tabletop extrapolation: THE classic accelerator-survey trap, and the reason the program's survey doctrine prefers current-mode ion chambers over GM counters for any pulsed operation: a counter reading 60 cps at a 60 Hz pulse rate is reporting its saturation value, not a dose rate. The saturation reading appears when the field is strong; a weak pulsed field reads below the pulse rate, so equality with the pulse rate is the alarm signature.

They obtained an accuracy of +-10% in measuring dose equivalent of neutrons over the range 0.04 to 10 MeV.

Martin (ed.), Accelerator Radiation Protection — AD-755510 / USA-NLABS-TR-73-7, US Army Natick Laboratories (1972) — p. 127

Editorial note, tabletop extrapolation: Justifies planning on one moderated rem meter as the primary neutron instrument for a D-D-class source term (2.45 MeV sits mid-band). Its band is not everything: moderated and scattered fields extend below 40 keV where response rolls off, so corners and maze mouths get checked against the instrument's stated energy response - and the calibration must be current.

The most common cause of serious radiation exposures associated with accelerators, has been accidental (and sometimes intentional) entrance into the normally shielded target cell.

Martin (ed.), Accelerator Radiation Protection — AD-755510 / USA-NLABS-TR-73-7, US Army Natick Laboratories (1972) — p. 144

Editorial note, tabletop extrapolation: The product-machine posture in one line: an educational cyclotron IS the 'small shielded box with an interlocked lid' (Ch. I's phrase). Lid switch + beam-off interlock + machine-on light is the historically identified starting set for this machine class - not a sufficiency proof: fail-safe wiring (opening kills beam; no automatic restart on re-closing), periodic interlock function tests, and the access and bypass rules (dg-654, dg-1074) complete the design.

Naturally no "line of sight" path for radiation would be permitted yet it is also necessary that the scatter path through the maze be considered.

Martin (ed.), Accelerator Radiation Protection — AD-755510 / USA-NLABS-TR-73-7, US Army Natick Laboratories (1972) — p. 145

Editorial note, tabletop extrapolation: The audit rule for every feedthrough, window and joint in an enclosure: check sight-lines from the X-ray source point (the dee gap) outward, then bound the one-bounce leakage with the albedo rules (dg-1068). Geometry creates the streaming problem; material still sets what each bounce and wall costs, so both enter the estimate.

it should never be convenient for an operator or an experimentor to remake an open interlock without someone actually going to the position of the break and, if the hazard no longer exists, reestablishing the interlock.

Martin (ed.), Accelerator Radiation Protection — AD-755510 / USA-NLABS-TR-73-7, US Army Natick Laboratories (1972) — p. 149

Editorial note, tabletop extrapolation: Design requirement for the product controller: a tripped lid/door input must latch and require a local (at-the-lid) action plus console reset — a firmware-only "clear fault" button recreates the exact failure mode this rule exists to prevent.

a fail-safe design may typically use a complete path or presence of a signal to permit accelerator operation and an open circuit or loss of signal to disable operation.

Martin (ed.), Accelerator Radiation Protection — AD-755510 / USA-NLABS-TR-73-7, US Army Natick Laboratories (1972) — p. 152

Editorial note, tabletop extrapolation: The normally-energized interlock-loop architecture: a series loop holding the RF/HV enable relay closed puts breaks, unplugs and power loss on the safe side. One loop is the architecture, not the whole chain - channels that must be independent stay independent (dg-1074), the loop gets exercised periodically (dg-1110), and any trip thresholds (a beam-current ceiling included) come from the machine's own hazard analysis.

For interlocks, however, the loss of operating time must be preferred to the loss of safety.

Martin (ed.), Accelerator Radiation Protection — AD-755510 / USA-NLABS-TR-73-7, US Army Natick Laboratories (1972) — p. 153

Editorial note, tabletop extrapolation: Two concrete requirements: (1) an FMEA-style enumeration of interlock failure modes with each shown to land safe; (2) latched annunciation: the controller must remember a mid-run lid opening even if reclosed, until deliberately reset.

A person overlooked during the search before lockup must be able to positively defeat the beam instead of ineffectively shutting down some unassociated apparatus.

Martin (ed.), Accelerator Radiation Protection — AD-755510 / USA-NLABS-TR-73-7, US Army Natick Laboratories (1972) — p. 153

Editorial note, tabletop extrapolation: In-enclosure e-stop requirement for any walk-in product installation; even for benchtop machines the classroom master kill must cut the actual hazard (RF+HV+source), not merely the controller, and the no-blame-for-pressing norm belongs in the curriculum.

Human safety should not be entrusted to one or more persons following a written routine. ... Even mechanized systems become routine after a time and hence may lose their effectiveness.

Martin (ed.), Accelerator Radiation Protection — AD-755510 / USA-NLABS-TR-73-7, US Army Natick Laboratories (1972) — p. 155

Editorial note, tabletop extrapolation: The strongest possible source endorsement for the program's hardware-interlock- over-procedure stance (procedures complement, never replace, the interlock chain), plus a curriculum idea: occasionally rotate the interlock test scenario so student operators never go through the motions.

There can be no substitute for the vigilance of personnel. Automatic devices, interlocks and remote area monitoring systems are essential but insufficient to do the job without personnel training.

Martin (ed.), Accelerator Radiation Protection — AD-755510 / USA-NLABS-TR-73-7, US Army Natick Laboratories (1972) — p. 17

Editorial note, tabletop extrapolation: The counterweight to over-trusting the product machines' interlock chains — the curriculum's radiation-safety module is a safety SYSTEM component, not documentation overhead.

it may be necessary for the operations staff to act as the health physics staff as well. Though less then ideal, this condition will frequently be a "way of life". Under these conditions it is of paramount importance to define responsibilities and priorities.

Martin (ed.), Accelerator Radiation Protection — AD-755510 / USA-NLABS-TR-73-7, US Army Natick Laboratories (1972) — p. 19

Editorial note, tabletop extrapolation: A 1972 acknowledgement, with conditions, of the small-facility reality in which one person wears both the operator and radiation-safety hats. The conditions transfer to any teaching installation - the documentation names the RSO-equivalent role and its decision rights - and the arrangement itself must clear the jurisdiction's requirements: registered machines commonly require a named, qualified RSO (/legal/), which written role definitions support but do not replace.

The threshold for (gamma,n) reactions are of sufficient magnitude to make the production of 13N and 15O of concern only to electron accelerators of energies in excess of 15-20 MeV.

Martin (ed.), Accelerator Radiation Protection — AD-755510 / USA-NLABS-TR-73-7, US Army Natick Laboratories (1972) — p. 176

Editorial note, tabletop extrapolation: Scopes air activation out of every current and planned program machine - all far below even the 10.6 MeV threshold - so the air-handling design concentrates on ozone (dg-1085). When a reviewer asks, cite the actual thresholds alongside the manual's concern line rather than conflating them.

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

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

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

first evaluated using the Smith-Garren formula, checked at critical places, especially at larger r, by exact orbit motion computer solutions.

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

Editorial note, tabletop extrapolation: Exactly the field-solver-plus-orbit-tracker pipeline an amateur design can run. The Nevis precedent: spend the expensive tracking where the cheap formulae are least trustworthy - large radius and the extraction region on their machine - and anywhere else the smooth approximation visibly strains.

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

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

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

alerted by the ORNL studies of observed beam loss in the ORIC cyclotron to try to avoid

Rainwater et al., The Columbia University Nevis Synchrocyclotron Major Modification — NEVIS-189 / R-774 / CU-295 (1971) — p. 4

Editorial note, tabletop extrapolation: Method transfers directly — a tune plot should carry resonance lines sourced from operating-experience literature, not just textbook theory; a weak-focusing tabletop crosses fewer lines but the audit habit is the point.

a half-wave resonator permits the rotating capacitors to be located outside the main vacuum chamber for good shielding from both the magnetic field and radiation

Rainwater et al., The Columbia University Nevis Synchrocyclotron Major Modification — NEVIS-189 / R-774 / CU-295 (1971) — p. 10

Editorial note, tabletop extrapolation: The placement principle transfers: keep variable capacitors, trimmers and drive mechanisms of a next machine's tank outside the pole gap and chamber, where field, beam spray and pumpdown cannot reach them - where the geometry allows it.

The design has used a 1/2 scale model, in conjunction with detailed computer calculations, to establish all parameters which can be varied

Rainwater et al., The Columbia University Nevis Synchrocyclotron Major Modification — NEVIS-189 / R-774 / CU-295 (1971) — p. 9

Editorial note, tabletop extrapolation: At tabletop size the "scale model" is the full-size mockup on the bench — cold-test a next machine's dee/stem with a VNA before power exists; the mode-spectrum audit transfers verbatim.

The dee resonator will be dc floating so a negative bias of amount sufficient to control multipacting can be applied.

Rainwater et al., The Columbia University Nevis Synchrocyclotron Major Modification — NEVIS-189 / R-774 / CU-295 (1971) — p. 10

Editorial note, tabletop extrapolation: Directly relevant at a next machine's planned 5-13 kV dees, where multipactor bands are widest: a 1971 operating-lab remedy with a concrete magnitude to scale from. Bias works by breaking the multipactor resonance condition; what trajectories do in detail depends on the local fields, so 'sufficient to control' is found empirically - exactly as Nevis wrote it.

Since the underground beam stop is aimed away from the experimental areas, this greatly eases shielding, and subsequent background problems

Rainwater et al., The Columbia University Nevis Synchrocyclotron Major Modification — NEVIS-189 / R-774 / CU-295 (1971) — p. 3

Editorial note, tabletop extrapolation: Direction-dependence of secondary radiation is universal even though the 550-MeV numbers are not: orient any future target station and Faraday-cup dump so the forward cone points at mass, not people. The specific takeoff angles and bend counts are per-facility physics rather than constants - lay out first, then let the survey confirm the geometry did what was expected.

The trend seems to be toward more elaborate systems which utilize solid state devices, fail-safe circuitry and self-checking circuits.

Ohnesorge & Butler, Recent Trends in Particle Accelerator Radiation Safety — CONF-741040-6, Oak Ridge National Laboratory (1974) — p. 2

Editorial note, tabletop extrapolation: Directly actionable for the next machine and the tiny controls spec: an amateur interlock chain (door, HV, RF-enable, radiation monitor) should be fail-safe and self-testing. Those properties come from the circuit design, not the device family - solid-state parts can fail shorted - so the design proves de-energize-to-safe behavior and exercises each channel periodically. What was state of practice in 1974 is trivially cheap in 2026.

fixes the half-value thicknesses of ordinary concrete for neutrons from cyclotron targets at approximately 10 cm

Ohnesorge & Butler, Recent Trends in Particle Accelerator Radiation Safety — CONF-741040-6, Oak Ridge National Laboratory (1974) — p. 3

Editorial note, tabletop extrapolation: The corpus's first literal shielding number for MeV-class cyclotron neutrons. The reference machine's proton operation sits below its (p,n) thresholds and makes none - deuteron operation is the standing exception (D-D is thresholdless) - and this ~10 cm HVT is the sizing constant the moment any machine or D-beam work crosses into neutron production; it was measured for cyclotron-target spectra, so re-check it for a materially different spectrum.

the As Low As Practicable philosophy can be adopted and put into practice only where there is a firm commitment by management to do so

Ohnesorge & Butler, Recent Trends in Particle Accelerator Radiation Safety — CONF-741040-6, Oak Ridge National Laboratory (1974) — p. 3

Editorial note, tabletop extrapolation: The governing philosophy any licensing narrative must speak fluently - in its modern wording (ALARA), since the terms are not interchangeable in a regulatory context. For the home program it means shielding and interlock decisions justified as 'as low as reasonably achievable', not 'under the limit'.

one should seek substances which combine high density with low atomic number. Among convenient and practical materials none would seem better than concrete.

Moyer, Hildebrand, Knable, Parmley & York, Character of the Radiation Field and Shielding at the 184-Inch Cyclotron — AECD-2149, UC Radiation Laboratory (1947) — p. 5

Editorial note, tabletop extrapolation: The shadow-effect argument is a >100 MeV argument. At low energy the conclusion usually still favors hydrogenous materials - elastic scattering on hydrogen dominates moderation - but merit depends on the objective: moderation, capture, dose, or secondary-gamma control (hydrogenous shields buy moderation with 2.2 MeV capture photons, dg-1329). Concrete, water and polyethylene win per dollar for neutron MODERATION, with the gamma bill accounted separately.

Besides the neutron beam cone from the probe there was found to be a general spray of neutrons due to the deuteron beam grazing the interior of the dee.

Moyer, Hildebrand, Knable, Parmley & York, Character of the Radiation Field and Shielding at the 184-Inch Cyclotron — AECD-2149, UC Radiation Laboratory (1947) — p. 2

Editorial note, tabletop extrapolation: Wherever beam is lost - dee edges, septum, probe stalk, chamber wall - is a candidate source, and a survey plan that only looks downstream of the target can miss most of the emission solid angle. Moyer's spray was found by surveying: that is the lesson.

dimensions can be calculated fairly exactly whereas in the system shown in Figure 5 one must depend on model tests (which are safer anyway).

MacKenzie, Preliminary Report on the “Three Quarter Wave” R.F. System for Frequency Modulated Cyclotrons — AECD-1850, University of California (1947) — p. 6

Editorial note, tabletop extrapolation: Transmission-line formulas ignore end effects, bends, and support hardware; for any resonator whose geometry is not a textbook line, a cheap model measurement outranks the calculation it checks.

The 1/2 scale model uses about 400 watts input to the oscillator at 48 megacycles and 600 watts input at 18 megacycles to produce 1500 volts on the dee.

MacKenzie, Preliminary Report on the “Three Quarter Wave” R.F. System for Frequency Modulated Cyclotrons — AECD-1850, University of California (1947) — p. 16

Editorial note, tabletop extrapolation: Dee power scales as voltage squared: measure watts-per-volt-squared on the bench and the amplifier requirement for any target voltage falls out. Mind the quantity - the model figures are OSCILLATOR INPUT, so the scaled 28-42 kW carries the model oscillator's efficiency inside it: separate wall loss from drive-chain overhead when budgeting a modern amplifier (dg-313, dg-316), and budget for joint quality and surface material shifting Q.

In a typical charged particle experiment 100 na of beam loses 43 keV in a W = 380 ugm/cm2 PbCl2 salt target

Thomas & Karasek (eds.), Proceedings of the Fourth Annual Conference of the Nuclear Target Development Society — ANL/PHY/MSD-76-1, Argonne National Laboratory (1975) — p. 238

Editorial note, tabletop extrapolation: A 1 uA, 170 keV proton beam fully stopped in an internal target deposits 0.17 W — forty times Corwin's example — into whatever spot the beam makes; the entire current limit of a thin uncooled target follows from this one number and the two removal channels (radiation, conduction) he works out next.

the target appears transparent and all of the radiating surface of a solid may not be present in a thin film.

Thomas & Karasek (eds.), Proceedings of the Fourth Annual Conference of the Nuclear Target Development Society — ANL/PHY/MSD-76-1, Argonne National Laboratory (1975) — p. 238

Editorial note, tabletop extrapolation: Radiation is the only cooling channel a self-supporting foil in vacuum really has at the spot: solving Corwin's equation for a stopped 0.17 W beam on a 0.03 cm2 spot with e = 0.1 gives roughly 1200 C equilibrium - above most evaporated films' damage points and hot enough to anneal or evaporate many (boron itself melts higher, but its substrate and adhesion rarely survive) - which is why the spot is enlarged or the film backed (dg-1160).

so a metal target could conduct the heat away with a 12 C rise in temperature.

Thomas & Karasek (eds.), Proceedings of the Fourth Annual Conference of the Nuclear Target Development Society — ANL/PHY/MSD-76-1, Argonne National Laboratory (1975) — p. 238

Editorial note, tabletop extrapolation: The 100x conductivity gap between salts/insulating compounds and metals is the single biggest lever on target survival: a boron film on a thick copper or silver backing is conduction-cooled through the backing, while the same film self-supported is radiation-only (dg-1159). Thickness enters linearly, so doubling film thickness halves the rise at fixed power.

Rolling is by far the most conservative process with regard to material loss in preparing thin targets. ... The vacuum evaporation process is very inefficient and frequently evaporation efficiencies of only 1% are obtained.

Thomas & Karasek (eds.), Proceedings of the Fourth Annual Conference of the Nuclear Target Development Society — ANL/PHY/MSD-76-1, Argonne National Laboratory (1975) — p. PDF p.18 (printed p.3) for Table 1's boron row; the efficiency sentence spans PDF p.17 (printed p.2) and PDF p.23 (printed p.8), the table intervening

Editorial note, tabletop extrapolation: The boron row of Table 1 is the direct answer for a B target: evaporation is the only listed route — 20-250 ug/cm2 self-supporting, 10-1000 ug/cm2 on a metal backing (boron is too brittle to roll). For thin-film evaporation recipes themselves cross-cite ORNL-3021; this table tells you which recipe book to open.

With a proton beam, targetry is just no problem. One can obtain very nice high-resolution results.

Thomas & Karasek (eds.), Proceedings of the Fourth Annual Conference of the Nuclear Target Development Society — ANL/PHY/MSD-76-1, Argonne National Laboratory (1975) — p. 158

Editorial note, tabletop extrapolation: Direct license for a proton machine: target thickness and uniformity tolerances that dominate heavy-ion work are second-order for protons, so a thick-ish imperfect boron layer costs beam-energy definition, not feasibility. When tempted by heavier beams, budget with the Z^2-at-equal-velocity scaling and check real stopping tables (SRIM/NIST-class) at low energy, where effective-charge effects bend the simple law.

If the beam is focused to an area of about 0.2 cm2, the resulting specific energy depositions amounts to 1 kW/cm2.

International Nuclear Target Development Society Workshop — ANL/PHY-84-2, Argonne National Laboratory (1983) — p. 29

Editorial note, tabletop extrapolation: The reference machine at ~3 nA / ~150 keV deposits ~0.5 mW - no realistic solid target is troubled by half a milliwatt. Rerun the two-line arithmetic at every upgrade, using the energy LOST IN the target rather than incident beam power where targets are thin: a 10 uA / 1 MeV machine puts up to 10 W into a mm-scale spot, which is rotating-target or water-cooled-backing territory.

in cyclotrons using a simple dee system as the tank circuit difficulties are encountered in getting the oscillator to break into full oscillation.

Fulbright, The Sparker, a Device to Overcome the Multipactor Difficulty in Starting the Oscillator of a Cyclotron — NYO-9359, University of Rochester (1961) — p. 2

Editorial note, tabletop extrapolation: DIRECT: this names the exact configuration of the reference machine - a simple dee system as the tank circuit - and matches its documented pattern of RF amplifiers failing to bring the dee to voltage. Multipactor loading in the ~100 V band is the report's named mechanism and a testable CANDIDATE cause, not a confirmed diagnosis: the bias and drive-through cures (dg-1274) double as the discriminating experiments.

multipactor loading, which occurs with voltages of the order of a hundred, cannot build up sufficiently to prevent the rise of voltage through the multipactor region.

Fulbright, The Sparker, a Device to Overcome the Multipactor Difficulty in Starting the Oscillator of a Cyclotron — NYO-9359, University of Rochester (1961) — p. 2

Editorial note, tabletop extrapolation: The decision menu for any machine that stalls in the multipactor band: bias, drive-through, or impulse shock. On a small machine the driven start maps to an external exciter ahead of the power stage; the bias cure maps to a DC offset on an insulated dee (dg-320, dg-805), with the magnitude found empirically.

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

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

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

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

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

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

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

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

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

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

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

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

Two experimental models had values of 0.37 and 0.30, but in both cases it was necessary to use conductor sizes which were available but not specifically designed for the job.

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

Editorial note, tabletop extrapolation: Amateur coils are usually wound from whatever magnet wire is available: budget a pessimistic 0.3-0.4 space factor when sizing the coil window, and read handbook ~0.5 figures as purpose-designed-conductor numbers.

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

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

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

Cited in: Choosing Your Machine

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

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

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

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

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

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

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

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

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

Cited in: Choosing Your Machine

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

It is designed so as to take maximum advantage of naturally occurring shielding of a small ravine.

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (1951) — p. 5

Editorial note, tabletop extrapolation: The siting lesson transfers even if the scale does not: cheap mass - earth berms, water, basement corners - is legitimate shielding MATERIAL for a D-D-capable machine, once treated as engineering rather than slogan: effectiveness depends on composition, thickness, geometry and the capture gammas that moderation produces (hydrogenous media slow neutrons well, then emit 2.2 MeV capture photons), so earth and water get designed and surveyed like any shield (see the shielding deep dive). Spec detail: PDF p.128.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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

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

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

Aluminum was chosen over stainless steel because of its short half-life property.

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (1951) — p. 46

Editorial note, tabletop extrapolation: DIRECT for any machine that will make neutrons: aluminum's dominant activation products are short-lived compared with stainless steel's cobalt-trace Co-60 (years) - the report's reasoning - though aluminum is not activation-proof: fast neutrons make 24Na (15 h) and alloying elements add their own products, so 'short half-life' is comparative, never absolute. Choose the beam-facing metal for the machine you hope it becomes; TIG-welded aluminum is proven UHV-adequate practice from 1951.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

Installation of the copper tank liners, R. F. loops and loop insulators approximately tripled the interior surface area

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (1951) — p. 53

Editorial note, tabletop extrapolation: DIRECT: every liner, loop and insulator added to a chamber is outgassing area, and UW's base pressure roughly doubled when their additions tripled the surface. Base pressure follows total outgassing over delivered speed (P ~ sum(q_i*A_i)/S_eff), so area is the usual driver - materials and cleaning move the q's. The variac experiment (heater power vs measured speed) remains the way to find a surplus diffusion pump's real optimum.

Cited in: The Vacuum Budget of a Cyclotron

upon considering the approximations necessarily made in this type of analysis, the figure of 150 kw maximum r-f power was selected.

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (1951) — p. 75

Editorial note, tabletop extrapolation: DIRECT scaling method for the LDMOS upgrade: measure the dee system's Q and C, compute watts per kV from P = V^2/(4QX) (equivalently V^2/(2*R_shunt)), then add margin for what the lumped model misses - beam loading, coupling loss, arcs, duty cycle. UW's own practice sized 150 kW against a ~52 kW computed requirement, roughly 3x, 'upon considering the approximations'; let your margin come from your own unknowns inventory, with theirs as the precedent.

This method should be easiest of the methods used to assure oscillation at the proper frequency with the dees operating 180 degrees out of phase.

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (1951) — p. 76

Editorial note, tabletop extrapolation: For a one-dee-plus-dummy machine the mode problem collapses. For any driven system, verify which resonance the amplifier locks to - a network-analyzer sweep plus a phase comparison between dee pickups distinguishes the modes - because the wrong one accelerates nothing.

Electron oscillations in the vicinity of the dees and dee stems at low r-f voltages tend to absorb energy and prevent the oscillations from building up.

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (1951) — p. 75

Editorial note, tabletop extrapolation: The corpus's driven-start cure (mddc-1045 tickler; nyo-9359's catalogue) as a 1951 DESIGN feature rather than a retrofit, including the half-frequency/doubler isolation trick that spares a changeover switch. Directly relevant to the reference machine's dee-voltage buildup pathology: any LDMOS drive chain is inherently a driven start, but only if it can push watts through the multipactor loading band without foldback or protection tripping - and that band's voltage is geometry-, frequency-, pressure- and surface-dependent, so measure it on the actual dee. [Note revised 2026-08-23: the earlier note quoted '~100 V' for the band as if it were a design constant.]

there are many uncertainties in the exact determination of the constants of the equivalent circuit ... the calculated values ... serve well as a guide

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (1951) — p. 82

Editorial note, tabletop extrapolation: A tabletop resonator IS the scale model — build the dee/stem mockup on the bench, measure f and Q before committing to vacuum hardware, and trust lumped calculations as guides not gospel. Berkeley used the same quarter-scale method on the 88-inch (ucrl-9435), which also confirms the Q-degradation-at-joints lesson (ornl-2648).

Machining work will begin after the oscillator is operating and an internal beam produced.

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (1951) — p. 116

Editorial note, tabletop extrapolation: The commissioning-order lesson as an explicit 1951 schedule decision: internal beam first, extraction hardware behind it. A sensible default for a next machine - the probe and its lock as first-beam hardware, extraction machining held until the internal beam teaches you the real orbit - a default, not a law.

(b) the multipactoring problem, common in the field of particle accelerators, rarely occurs in other industrial applications

Smith, The RCA 6949 as a Self-Excited Cyclotron Oscillator — UCRL-9435, Lawrence Radiation Laboratory (1960) — p. 7

Editorial note, tabletop extrapolation: The checklist for adapting any industrial or ham RF gear (an LDMOS pallet included) to a cyclotron: add spark protection, add a multipactor start plan, and only then worry about power. Fixed-frequency tabletop machines are spared only (c).

The threshold of secondary emission is about 150 electron volts for most surfaces; consequently, multipactoring becomes possible when the voltage across the dees reaches this value.

Smith, The RCA 6949 as a Self-Excited Cyclotron Oscillator — UCRL-9435, Lawrence Radiation Laboratory (1960) — p. 4

Editorial note, tabletop extrapolation: DIRECT: a small machine's dee voltage passes through the ~100-150 V-class region on every start - whether multipactor actually lights there depends on the gap-frequency resonance and the surfaces' secondary yields, which is why some machines never see it. Completes this collection's cure set: mddc-1045 (bias + tickler), nyo-9359 (impulse start), ucrl-64 (volume reduction + bias).

Vacuum switches connected in the three-phase, 16.6 kv ac lines feeding the rectifier ... open within 10 msec plus the time to the first current zero ... In this service it will open the anode circuit within 10 usec of a fault.

Smith, The RCA 6949 as a Self-Excited Cyclotron Oscillator — UCRL-9435, Lawrence Radiation Laboratory (1960) — p. PDF p. 6 (printed -6-) for the layer arrangement; PDF p. 7 (printed -7-) for the regulation and termination items

Editorial note, tabletop extrapolation: The modern translation, mapped by FUNCTION rather than spec-for-spec: an LDMOS drain supply wants a fast electronic disconnect (the hard-tube modulator's descendant), a slower breaker layer, and snubbing on the dc feed - each layer rated against the actual stored energies and fault modes of the build (dg-330, dg-679, dg-1371).

In this type of system the resonator is the frequency-determining element of the system; hence it is called a self-excited oscillator.

Smith, The RCA 6949 as a Self-Excited Cyclotron Oscillator — UCRL-9435, Lawrence Radiation Laboratory (1960) — p. 4

Editorial note, tabletop extrapolation: The live architecture decision for a next machine. An LDMOS chain driven by a synthesizer is a MOPA — it inherits ornl-2403's virtues (frequency authority, instrumentation) AND the self-excited literature's start-up disease (nyo-9359): the synthesizer holds frequency while multipactor holds the dee at zero. Smith's phase-discipline logic (feedback phase correct across the whole operating range) is the checklist item either way. High-SWR argument p.6.

Cited in: Driving the Dee: RF Coupling

At the maximum particle energy, the beam requires 60 kw of power.

Smith, The RCA 6949 as a Self-Excited Cyclotron Oscillator — UCRL-9435, Lawrence Radiation Laboratory (1960) — p. 5

Editorial note, tabletop extrapolation: The four-line budget is the right form at any scale. A tabletop version: watts of copper loss (dg-313), a beam line computed from ITS current and energy - 1 nA at 500 keV is 0.5 mW, 10 uA at 1 MeV is 10 W, small only until the source improves - a stray-ion line that follows source gas and RF (measurable as the loading difference with the source on vs off), and a misc line that is mostly coupling and radiation.

For accelerator applications, a tube should have a sufficiently heavy grid to absorb several joules of energy in an area determined by the cross section of the spark.

Smith, The RCA 6949 as a Self-Excited Cyclotron Oscillator — UCRL-9435, Lawrence Radiation Laboratory (1960) — p. 6

Editorial note, tabletop extrapolation: The solid-state translation: LDMOS devices have finite ESD, avalanche and mismatch ratings rather than a tube grid's joules of thermal mass, so the ruggedness must live in the coupling network - series blocking, clamping, fast drive-cut (dg-338, dg-758). A dee-side fault arrives first at the OUTPUT network, which is where the protection belongs.

Bevor man an den Nachbau eines Zyklotrons geht, muss man sich darüber im Klaren sein, was man benötigt. ... Bei den fünf Teilsystemen handelt es sich im einzelnen um das Magnet-System, das das Führungsfeld liefert, das Beschleunigungs-System, das für die Hochspannung sorgt, das Ionen-System, verantwortlich für die Produktion der Ionen, das Vakuum-System, das das erforderliche Vakuum zur Verfügung stellt, und schließlich das Detektor-System, das die beschleunigten Teilchen registriert. ... Die Vorgaben in den grünen Kreisen sind zum einen gerätespezifische Größen. Dazu gehören: der Radius der Magnetpole rp und der maximale Bahnradius ... das Nenn-Saugvermögen SN des Pumpstands [tr.: before building a cyclotron one must be clear what is needed; the five subsystems are the magnet system supplying the guide field, the acceleration system providing the high voltage, the ion system producing the ions, the vacuum system, and the detector system registering the accelerated particles; the givens in the green circles are device-specific quantities - the pole radius, the maximum orbit radius, the pump stand's nominal pumping speed - the calculated quantities in blue circles]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 27-29

Editorial note, tabletop extrapolation: A small machine has few free parameters; listing which are fixed by hardware (pole radius, pump) and which are design choices (B, gap, U0, species) keeps the sizing chain consistent and exposes circular dependencies early.

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

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

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

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

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

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

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

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

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

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

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

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

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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

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

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

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

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

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

Aus Gründen der Spannungsfestigkeit der Durchführung ist U0 ≤ 3000 V [tr.: because of the feedthrough voltage rating, U0 <= 3000 V]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 42

Editorial note, tabletop extrapolation: A 5-15 kV dee upgrade is an insulation-coordination problem across the WHOLE RF path - feedthrough, stem supports, matching capacitors, connectors, plus contamination and conditioning state - with the feedthrough a frequent but not guaranteed weakest link. Specify every element for peak RF plus any DC bias, in vacuum, with tracking margin.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

Diese beträgt nach aktuellen Messungen ca. 330 kΩ [tr.: according to current measurements this is about 330 kOhm]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 42, 44

Editorial note, tabletop extrapolation: The scaling explains why a 100-500 W amplifier class suits a 5-13 kV dee - sized with margin: P_source >= U0^2/(2*R_p*eta) with measured end-to-end efficiency eta (matchbox, feedline and base-load losses all sit between amplifier and dee), and the larger dee's own R_p measured, not borrowed from this machine.

Der verwendete Transceiver, ein ICOM M 600, liefert in der Betriebsart H3E eine sinusförmige Spannung (Amplitude ≈ 70 V) im Frequenzbereich von 0,5–35 MHz mit einer abgegebenen Leistung von ungefähr 45 W an 50 Ω Ausgangsimpedanz. ... Das Widerstandsnetzwerk der Eingangsstufe stellt dabei eine Grundlast für den Transceiver dar. Dieser würde sonst [...] abschalten [tr.: the transceiver used, an ICOM M 600, delivers in H3E mode a sinusoidal voltage (amplitude ~70 V) over 0.5-35 MHz with about 45 W into 50 ohm output impedance ... the input resistor network is a base load; otherwise the transceiver shuts down]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 44-45

Editorial note, tabletop extrapolation: The load-requirement lesson generalizes as a check, not a law: characterize the chosen amplifier's required load, mismatch tolerance and protection behavior (an LDMOS deck without foldback dies where the ICOM merely shuts down), and budget a dummy-load fraction plus a VSWR interlock so a detuned dee - a plasma flash, say - cannot damage the final stage.

Da ein Dee wie die Vakuumkammer selbst auf Masse liegt, kann dieses Dee verkürzt werden [tr.: since one dee is at ground like the chamber, it can be shortened]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 46

Editorial note, tabletop extrapolation: Single-dee-plus-dummy gives half the energy gain per turn of an ideal push-pull pair at the same per-electrode amplitude, in exchange for one feedthrough and one resonator - a trade that favors simplicity on most small builds; state the amplitude convention whenever quoting the factor of two.

Bei der Dimensionierung des Dummy-Dees stellt sich natürlich die Frage nach der Tiefe und der Größe des Beschleunigungsspalts gap. Aus Plausibilitätsgründen wurde jeweils ein Maß von 20 mm gewählt. [tr.: in dimensioning the dummy dee the question arises of its depth and the size of the accelerating gap; on plausibility grounds 20 mm was chosen for each]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 46

Editorial note, tabletop extrapolation: A wide gap simplifies the source mount (the chimney sits inside it) at the cost of transit-time factor; choose the gap from the transit calculation - T = sin(x)/x with x = omega*g/(2v) over the actual injection and orbit velocities - rather than adopting either 20 mm or any other fixed number.

Bei einem Druck von p = 10−6 mbar [...] würden die H2+-Ionen (im Mittel) also erst nach mehr als 123 m auf ein Stickstoff-Molekül treffen [tr.: at 1e-6 mbar H2+ travels more than 123 m between collisions]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 50

Editorial note, tabletop extrapolation: The table is a historical order-of-magnitude estimate with two labeled limitations: a hydrogen-FED machine's residual gas is mostly H2 (measure it - an RGA settles it), and the loss process that matters for beam survival is charge exchange, whose energy-dependent cross-section must come from evaluated data (dg-460), not hard spheres. Use lambda_loss(E) = 1/sum_j n_j*sigma_loss,j(E) over the actual partial pressures.

Für 16 Beschleunigungen wären 2,76 m Weglänge erforderlich, die mit 3 m knapp erreicht werden [tr.: 16 accelerations need 2.76 m of path, barely reached with 3 m]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 54-55

Editorial note, tabletop extrapolation: Recomputed: r1 = 17.5 mm, sum sqrt(i) for i=1..16 = 44.47, giving 2.45 m of arcs plus 16*0.02 = 0.32 m of gap = 2.76 m. Caution: the bitmap Table 6.2 lists 2.44 m and 1.27 m, i.e. arcs only without the k*gap term; use the text figure.

für einen Volumenstrom von ca. 0,14 ml/min sich ein Enddruck pE = 4,0 · 10−5 mbar einstellt [tr.: at about 0.14 ml/min a final pressure of 4.0e-5 mbar establishes itself]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 51-53

Editorial note, tabletop extrapolation: The one-line balance is the first thing to validate against the gauge on a new machine - at several MFC settings, with the background term measured separately (feed off) and the flow convention of the actual controller pinned down before trusting any prediction.

Allerdings darf für S nicht das Nennsaugvermögen SN = 28 l/s der Turbomolekularpumpe für Wasserstoff angesetzt werden [tr.: the nominal 28 l/s hydrogen speed of the turbo must not be used for S]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 52, 82-83

Editorial note, tabletop extrapolation: The lesson is the calculation, not a flange size: compute each line's conductance for each gas that matters and pick the port from the required chamber speed - short and fat wins, and mounting the pump directly on the chamber removes the term entirely. The 39/75% figures are this installation's; other lines and gases differ.

Damit erhält man letztlich als Berechnungsformel für den Rohr-Strömungsleitwert: GL = π/12 v̄ D³/L [tr.: the working formula for tube conductance]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 82-83

Editorial note, tabletop extrapolation: The D^3 dependence means a DN63 line has ~4x the conductance of DN40 at the same length (compute from actual bores - DN designations don't fix the ID). For short stubs (L/D < 10) the long-tube limit OVER-predicts - it diverges as L -> 0 - so cap it with the aperture term via the series combination.

Dabei ist noch zu berücksichtigen, dass jetzt nicht mehr Luft, sondern im wesentlichen nur noch Wasserstoff H2 abgepumpt wird [tr.: it is now essentially only hydrogen that is pumped]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 52, 83

Editorial note, tabletop extrapolation: Take the H2 column from the pump datasheet and compute conductances with hydrogen's v_bar (1.75 km/s at 293 K vs 0.469 for N2). Terminology discipline: BASE pressure is the no-feed number; during source operation the relevant quantities are OPERATING pressure and residual composition - hydrogen-dominated when the feed throughput exceeds the measured background load.

Nun lässt sich mit der Vorpumpe der Druck nicht weiter erniedrigen. Die weitere Druckreduzierung erfolgt jetzt durch die Turbomolekularpumpe [tr.: the backing pump can go no lower; the turbo takes over]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 55-56

Editorial note, tabletop extrapolation: The two-stage division of labor is standard but its numbers are technology-specific: take the crossover pressure and backing requirement from the high-vacuum pump's own specification (turbo, diffusion, cryo all differ - a diffusion stage wants a rotary-vane backer and a trap or baffle). An oil-free diaphragm backer keeps hydrocarbons out and is classroom-quiet - this machine's genuine transferables.

Ein Nachteil ist die relativ hohe Permeation von Wasserstoff durch Schläuche und Kanülen; dies betrifft insbesondere die Ionenquelle [tr.: a drawback is hydrogen permeation through hoses and cannulas]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 30

Editorial note, tabletop extrapolation: Use metal lines with a mass-flow controller rather than elastomer tubing (PEEK is lower-permeation than elastomers, not zero). A small cartridge is still HYDROGEN: even ~10 standard litres forms a flammable mixture in air, so ventilate, leak-check, control ignition sources and handle the pressurized cartridge properly. Runtime: compute from the cartridge's usable standard volume at the actual MFC setting rather than quoting a lifetime.

Dieser Druck wird durch einen Druckminderer auf pH2 = 300 mbar reduziert [tr.: the pressure is reduced by a regulator to 300 mbar]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 61

Editorial note, tabletop extrapolation: Fix the reducer pressure and log it - it is a term in the balance. Whatever meters the flow, state its reference conditions and take accuracy and repeatability from its specification rather than assuming a resolution.

Die Anzahl der gebildeten Ionen hängt aber auch von der Elektronenenergie ab. Sie erreicht bei 100–150 eV ein Maximum [tr.: ion yield depends on electron energy, peaking at 100-150 eV]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 62, 70

Editorial note, tabletop extrapolation: Sweep anode voltage against extracted ion current on the actual source - the optimum is broad and machine-specific, anode volts are not electron collision energy volt-for-volt (sheaths and where ionisation happens intervene), and a current-limited 0-200 V supply covers the whole plausible band.

Der differentielle Ionisierungswirkungsquerschnitt σ liegt in der Größenordnung von 1–3 1/(cm·mbar) [tr.: the differential ionisation coefficient is of order 1-3 per cm mbar]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 63-64

Editorial note, tabletop extrapolation: Compare with measurement honestly: at 2-5 mA emission the sigma=1 estimate gives ~0.3-0.7 uA against measured 1-3 uA - a factor of a few, not an order of magnitude, and the gap closes further once the CHIMNEY pressure (well above chamber pressure) and the sigma range are used. The formula omits extraction efficiency and losses in both directions - calibrate it per source rather than reading it as floor or ceiling.

Zu diesem Zweck wurden an dem Dee zwei Extraktions- bzw. Pullerelektroden angebracht. Nun bleibt noch die eingangs gestellte Frage zu klären, warum kein zweiter Ionenstrahl während der positiven Halbwelle entsteht. Ein Grund dafür ist die Tatsache, dass die Ionen nur aus dem Schlitz extrahiert werden können, der dem Dee gegenüberliegt. Ein weiterer Grund ist das Potenzial des Kamins, das das gleiche ist wie das des Dummy-Dees, nämlich Masse. Somit könnten auch während der positiven Halbwelle der Beschleunigungsspannung keine Ionen in das Dummy-Dee extrahiert werden. [tr.: two extraction/puller electrodes were fitted to the dee; the question why no second ion beam forms during the positive half-wave is answered by two reasons - ions can only leave through the slit facing the dee, and the chimney sits at the same potential as the dummy dee, namely ground, so no ions can be extracted into the dummy dee during the positive half-wave]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 65-66

Editorial note, tabletop extrapolation: Grounding the chimney with a one-sided slit answers the reverse-beam question students raise - by construction on this machine. If the source is biased instead, the slit-to-puller spacing, the bias polarity and the counter-beam question all reopen: analyze, don't assume.

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

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

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

Die Herausforderung dieses Projekts bestand demnach darin, ein Zyklotron in diesem niedrigen Energiebereich zum Laufen zu bringen [tr.: the challenge was to get a cyclotron running in this low energy range]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 7-8

Editorial note, tabletop extrapolation: Define the teaching machine's safety envelope explicitly rather than declaring it hazard-free: maximum electrode potential (X-ray endpoint), ion species and energy (reaction thresholds - remembering exothermic channels like D-D have none, so deuterium is a different machine), beam current, target and contaminant composition, plus the ordinary electrical, RF, vacuum and stored-energy hazards that exist at ANY energy. Survey, don't assume; the low-energy regime shrinks the radiological terms, not the list.

Sicher hätte sich das Projekt nicht gelohnt, wenn es nach dem erfolgreichen Abschluss im Jahre 2014 beendet worden wäre [tr.: the project would not have been worth it had it ended in 2014]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 75-76

Editorial note, tabletop extrapolation: The listed follow-on improvements (magnet stand, acceleration simulation, probe translator, mechanical model) are the kind of second-year items a small-machine program should schedule rather than improvise - as this case study's pattern, adapted to local aims, not a universal checklist.

Trotzdem konnten wir nur bedingt auf bereits gemachte Erfahrungen zurückgreifen. Zu unterschiedlich waren die Voraussetzungen [tr.: prior experience was only partly usable; conditions were too different]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 8

Editorial note, tabletop extrapolation: The transferable layer across amateur machines is the METHOD - dependency diagram, rigidity sizing, vacuum chain, species-by-q/m - not the numbers: copy the method, recompute every quantity for your own boundary conditions. (Which differences blocked reuse here isn't itemized in the quote; the lesson survives without the itemization.)

Diese Gleichung gilt allerdings nur unter folgenden Voraussetzungen [tr.: this equation holds only under the following assumptions]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 84-85

Editorial note, tabletop extrapolation: Evaluate the sum numerically for your actual k (from injection energy, final energy and effective gain per crossing - higher voltage means FEWER crossings for the same energy); phase slip and gap curvature make the real path longer than the formula, so add margin before comparing with the mean free path.

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

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

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

The first attempted vacuum chamber was made of curved sheets of copper that clamped around the magnet's poles. Using gaskets to seal the chamber, the machine produced a beam current of 1.5 microamperes. However, the system could not maintain vacuum and a new design was sought. The modified chamber consisted of a section of 16.5 cm brass tubing used as the wall of the chamber, and two 0.3 cm thick circular steel plates as the top and bottom. The bottom plate was soldered to the brass, the top plate was screwed to the bottom plate with a rubber gasket between the brass and steel to form a seal.

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

Editorial note, tabletop extrapolation: A rigid soldered ring with one permanently sealed plate and one demountable gasketed plate is a simple chamber architecture with this documented precedent; the conformal clamp-around-sheet chamber has a documented vacuum-failure precedent. (The survey doesn't cost either build - 'low-cost' is our reading of brass tube and hand tools.)

Cited in: Cyclotron Vacuum Chamber Design and Sealing

The El Cerrito Cyclotron used only one dee, and did not employ a 'dummy dee,' but rather held the chamber itself at ground. ... The system was operated at 1,600 watts and could provide a maximum of 2,000 watts to the electrodes. ... with the new vacuum chamber a beam of 7 microamperes was produced.

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

Editorial note, tabletop extrapolation: Deleting the dummy dee simplifies the in-chamber assembly at the cost of a less-defined gap field; the precedent documents that the geometry can work at the microampere scale - it does not promise that current class, which came from the whole machine, not the electrode choice alone.

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

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

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

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

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

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

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

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

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

The RF was provided by a ham radio transceiver, using an oven controlled crystal.

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

Editorial note, tabletop extrapolation: Oven-controlled crystal stability addresses the drift side of resonance keeping, and ham gear is well-documented and repairable - as the frequency-stable SOURCE/exciter; what amplification, matching and electrode voltage sat downstream isn't in this sentence, so size the rest of the chain from its own requirements before crediting amateur gear with the whole job.

A dee and dummy dee system was used with the electrodes separated by approximately 1 mm.

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

Editorial note, tabletop extrapolation: A millimetre-class gap maximizes gap FIELD per volt and can improve the transit-time factor - the ideal energy gain per crossing stays q*deltaV regardless - while tightening alignment, flatness and holdoff tolerances (field enhancement rises as the gap closes). One documented small end of the range, not an established bound; choose the gap from the transit-time and holdoff calculation (dg-1396).

A system of two brass dees with differing radii allowed for ion extraction. ... For a collector, a small copper sheet was set into the path of ions leaving the larger dee, which drew electrons to itself when the ion beam was incident.

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

Editorial note, tabletop extrapolation: An asymmetric dee pair is a construction-level extraction trick published almost nowhere else - the radius step letting outward-spiraling ions escape the smaller electrode's envelope is the natural geometric reading (our reconstruction; the survey states the arrangement and the collector, not the mechanism), and no deflector is mentioned for this machine.

either a filament was created from that metal, or a nichrome wire was coated with the metal, and raised to a negative potential

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

Editorial note, tabletop extrapolation: A coated-filament thermal source avoids the PROCESS-GAS feed for suitable metals - suitability turning on the metal's vapor pressure, filament compatibility and ionization efficiency - trading species flexibility and current for vacuum simplicity. A candidate for minimal first-beam configurations, evaluated per metal rather than assumed.

A mechanical roughing pump with a cold trap were used to evacuate the chamber

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

Editorial note, tabletop extrapolation: Read as recorded history, not a pumping recipe: a cold trap captures condensables, not hydrogen or air, so rough-pump-plus-trap has no general sufficiency - what made this credible is the solid coated-filament source (no continuous gas load). For any repeat: measure base and operating pressure under load and check mean free path against the spiral; the same survey's gas-fed machines carry diffusion pumps.

one a 22.9 cm diameter prototype and the other was the final 30.5 cm diameter machine, finished in 2001. The prototype operated at 0.889 T, using a dee and dummy dee design. The prototype chamber was constructed for use in the 30.5 cm cyclotron that was the ultimate goal of this project, and so was much larger than required. It was stainless steel, as were the ports and flanges. ... The larger machine used a 30.5 cm pole face electromagnet that operated in excess of 1.0 T, with the same chamber as the 22.9 cm cyclotron but with a different ion source.

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 17

Editorial note, tabletop extrapolation: Oversizing the first chamber lets the highest-labor component survive the upgrade - a trade, not a law: a larger chamber costs pumping speed, gap (if it sits in the magnet) and money now against rework later; the same survey documents the opposite staging too, so decide from where the rework hurts most on YOUR roadmap.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

The filament was kept isolated from ground so it could be negatively biased to increase the energy of the emitted electrons.

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 17

Editorial note, tabletop extrapolation: Filament bias is the cheapest ionization-rate knob, but it forces the heater supply off any grounded control bus: the supply must be galvanically isolated and float AT the filament's NEGATIVE bias relative to the chamber (the Houghton machine floats its filament near -90 V, dg-310), with insulation rated for the full bias plus coupled RF and transients. And bias raises electron energy, not necessarily ion yield monotonically - scan it (dg-402).

The negatively biased filament was mounted in a block of ceramic material to which hydrogen gas was supplied through a small hole. The ion source was then covered with a ceramic plate with an aperture ... [allowing] a cone of protons to stream out in the center of the evacuated cyclotron chamber, while maintaining a higher pressure of hydrogen around the filament

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 17

Editorial note, tabletop extrapolation: A drilled ceramic block with an aperture is a buildable chimney-style source. The pressure decoupling it delivers is set by the aperture conductance against the gas throughput and chamber pumping - match those (the dg-409/dg-1400 balances) rather than expecting the geometry alone to do it.

[The RF] signal was produced using a HP8656B signal source, which had greater frequency resolution than the HP8165, and an ENI NMR-300L solid state amplifier. Its maximum output was 2,500 W, but was usually operated at 50 W with satisfactory results.

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 17

Editorial note, tabletop extrapolation: Tens of watts sufficed for a 30.5 cm, above-1-T machine with a resonant matching network - at ITS reported operating conditions; the 50x headroom was available, and whether more drive would have bought more beam is not in the record. A useful anchor for amplifier shopping: buy the headroom, expect to run far below it.

The copper tube also shielded the collector from the RF signal.

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 17

Editorial note, tabletop extrapolation: A grounded slotted shield around the pickup is a sound and documented defense for beam readings taken inside a dee-drive RF field - one layer of several: pair it with shielded signal cable, verify the grounding actually sinks the induced current, and do a beam-off RF-only background run (dg-689's discipline) before crediting the residual as beam.

As the ion source was considered experimental and a weak design aspect, it was made to be completely removable.

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 18

Editorial note, tabletop extrapolation: Design for swap-out on the least-trusted subsystem - mount whatever you expect to iterate for convenient replacement. Ion sources are a common iteration target in this literature (COLUMBUS's Penning investigation, Rutgers' source change between machines), though no count across the survey backs a strongest-claim ranking.

The capacitance of the dee's was not measured before building the resonating circuit, rather trial and error was used to tune the circuit. ... [Houghton:] The capacitance of the dee and chamber of the Houghton College cyclotron has been determined to be 79 pf.

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 18

Editorial note, tabletop extrapolation: A capacitance measurement on the assembled stack converts resonator design from blind cut-and-try into calculation-plus-trim: include estimated lead/feedthrough parasitics (tens of pF scale means they matter), choose the initial inductance from the formula, and still provide adjustment range - installed resonance always lands off the paper value.

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

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

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

For a deuteron in an accelerating potential of 1,000 volts, the energy limit is 1.94 MeV, for an accelerating potential of 10,000 volts, the limit is 6.13 MeV, and for an accelerating potential of 20,000 volts, the limit is 8.67 MeV. ... the effects of relativity can be countered by more than just increasing the electrode voltage, it can also be mitigated by adjusting the shape and strength of the magnetic field. The actual relativistic limit for magnetic resonators accelerating protons is closer to 25 MeV.

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 28

Editorial note, tabletop extrapolation: For sub-MeV machines relativity is far from limiting even at 1 kV dees on any convention - both the thesis's numbers and the halved re-derivation agree on that. If energies ever approach the MeV scale, dee voltage and field shaping are BOTH levers, per the thesis's own remark.

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

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

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

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

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

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

two QF16-075-VP Kurt J. Lesker glass viewports, one Kurt J. Lesker EFT1213258 power feed-through for the dee

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 39

Editorial note, tabletop extrapolation: The cited machine's eight-port budget with named catalog parts is a concrete STARTING template - port count and ratings are functions of your source biasing, RF monitoring, cooling and diagnostics, so derive your own list and check current catalog substitutes' voltage/current/vacuum ratings. One specific: a dummy dee wanting RF ground usually needs a short low-inductance chamber bond, not a shared multi-pin conductor - verify which this machine's sharing actually implies before copying it.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

The capacitance of the dee and chamber of the Houghton College cyclotron has been determined to be 79 pf. If the maximum magnetic field of 1.127 T is used then the frequency of orbit for singly ionized helium is 4.32 MHz, and thus the inductance, using (23), must be 17.2 uH. In this system the maximum energy for singly ionized helium is 77.2 keV. For doubly ionized helium, the frequency in the same magnetic field is 8.63 MHz, so the inductance is 4.29 uH, and the maximum energy is 309 keV.

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 46

Editorial note, tabletop extrapolation: A rare published electrode-system capacitance anchor for microhenry-scale resonator sizing at this machine class - noting the energy quadrupling with charge state at fixed field (the implied orbit radius is ~7.1 cm), that 79 pF is build-specific, and that the installed resonance still needs the parasitics-and-trim treatment (dg-1462).

In order to avoid sparking in the gaps in the cyclotron chamber, the voltage supplied by the amplifier must be carefully chosen.

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 45

Editorial note, tabletop extrapolation: With a high-Q resonator the dee voltage is set indirectly, so the spark limit must be designed in rather than discovered: use the measured or modeled loaded transfer function from amplifier to dee, verify with a calibrated pickup (dg-307/dg-1356), and back it with arc detection - the branch-current subtlety is exactly where a naive I*X_C sizing goes wrong.

The immediate objective is to accelerate Helium nuclei to test the machine, and the ultimate is to accelerate deuterons to produce neutrons ... The expected energy for deuterons is 0.15 MeV, and 0.08 MeV for Helium nuclei. ... the maximum energy for singly ionized helium is 77.2 keV. For doubly ionized helium, the frequency in the same magnetic field is 8.63 MHz ... and the maximum energy is 309 [keV]

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 2

Editorial note, tabletop extrapolation: Debugging resonance, focusing and diagnostics on helium defers the deuteron-specific neutron/activation source term - NOT all radiological consequences: RF/HV dark current makes bremsstrahlung with any gas, and He2+ is an alpha that can drive exothermic reactions on light contaminants (Be-9, C-13). Survey from first powered operation; the staging defers the big term, not the survey.

A copper target will be placed in the chamber, which will as a result of the beam be impregnated with deuterons. More ions from the beam will collide with the trapped deuterons, undergoing one of two reactions, d(d,n)3He or d(d,p)3H. Since neutrons are the desirable result of the reaction, no extraction system will be required. ... the outgoing neutrons will be produced with 2.8 MeV. The electrically neutral neutrons will pass through the chamber walls and can then be used for inelastic scattering measurements.

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 48

Editorial note, tabletop extrapolation: A beam-loaded (drive-in) copper target avoids separately fabricating a deuterated target and removes extraction from the critical path. Physics notes on the thesis's numbers: D(d,n)3He neutrons at ~150 keV bombarding energy are angle-dependent, roughly 2.1-3.0 MeV in the lab - 2.8 MeV is one point on that curve, not the spectrum - and the thesis does not analyze dose or shielding beyond its concrete room, so the radiological planning is entirely on the builder.

in a concrete brick room with an interlock control system to prevent the accelerator from being turned on when a person is in the room

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 29

Editorial note, tabletop extrapolation: The documented access-control arrangement of the source machine - occupancy interlock plus (per its electronics chapter) remote operation - is a COMPONENT of protection, not a certified minimum: shielding calculations, surveys, monitors, fail-safe interlock design and applicable regulatory requirements decide sufficiency for any neutron-capable machine, and the thesis presents no dose analysis.

Longer range plans include building a larger vacuum chamber and electrodes

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 48

Editorial note, tabletop extrapolation: Starting with an undersized chamber inside a full-size magnet is the documented counter-strategy to Rutgers' build-the-final-chamber-first (dg-1451) - the stated plan here being a larger chamber and electrodes later. Faster first beam and deferred precision work are the plausible payoffs to EVALUATE, not documented outcomes; either staging is defensible depending on where rework hurts.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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

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

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

The vacuum was produced by a vacuum reservoir with a cryopump system.

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

Editorial note, tabletop extrapolation: Read carefully: a cryopump IS a pump (it keeps pumping while cold), so this is oil-free, low-vibration pumping plus buffer capacity - not a pumpless machine. The architecture suits a source with little gas load (Cyclotrino's cesium-sputter source); the reservoir buys hold time against transients, not indefinite operation. Get the actual cryogenic arrangement before copying claims about power or vibration at the machine.

The maximum energy of the current cyclotron, using (6), is 150 keV for deuterons, which puts the cross section near the maximum. ... [the d(d,n)3He reaction is] exothermic with 2.227 MeV released for each deuteron pair.

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 49

Editorial note, tabletop extrapolation: Working back from the excitation curve converts machine energy from a bragging number into a requirement - the transferable design move. D-D is the standout low-energy neutron reaction because its cross-section is already usable near 100 keV; take Q-values and cross-sections from live evaluated data (per site policy), not from the thesis's figures.

After the FZ Juelich provided a magnet, VACOM, a company for vacuum components, sponsored a suitable vacuum chamber ... the cyclotron COLUMBUS began in 2012. ... The first beam was registered in April 2014 (see Fig. 2), which was followed by the first workshop with students in autumn of the same year. ... The COLUMBUS project, started in 2012, has developed very positively in the last 10 years.

Wolf & Prechtl, COLUMBUS — A Small Cyclotron for School and Teaching Purposes — THPO001, Proceedings of Cyclotrons2022 (2022) — p. 1

Editorial note, tabletop extrapolation: A realistic schedule anchor for the plan's teaching-machine ambitions: two years start-to-beam WITH a donated magnet and sponsored chamber - the in-kind support is part of the datum. And the methodological point stands: a conference paper's year dates the claim; prefer the builders' own retrospective dates when reconstructing a machine's history.

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

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

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

Vaccum in the chamber 10-6 mbar dto with H2 10-5 mbar

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

Editorial note, tabletop extrapolation: Plan pumping capacity for the gas-on state, not the base pressure; a decade of pressure rise under source gas load is the demonstrated working regime for a keV-class internal-source machine at this scale. (Quote reproduces the table verbatim including its spelling; exponents are superscripts in the original.)

or investigate a Penning ion source with the aim of using it for the installation in the accelerator.

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

Editorial note, tabletop extrapolation: A filament source reached first beam here and a candidate Penning source is being investigated as a student project - the sensible pattern being to characterize any replacement source off-machine, then verify its mechanical, vacuum, electrical, gas-feed and central-region interfaces before installation; a source swap touches more of the machine than the source (recommendation, not the paper's documented method).

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

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

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

Cited in: Cyclotron Vacuum Chamber Design and Sealing

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

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

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

The RF-power-source is a short-wave transceiver for marine radio. It provides an AC voltage of 50-70 Veff at frequencies from 500 kHz to 35 MHz. The available power is 120 W. … As well as an impedance converter the matchbox is also an RF-transformer transforming the 50 - 70 V output voltage of the power-source up to 2000-3000 V voltage, which is needed for the acceleration of the protons.

Wolf, Frank & Held, COLUMBUS — A Small Cyclotron for School and Teaching Purposes — WE1PB03, Proceedings of Cyclotrons2013 (2013) — p. 2

Editorial note, tabletop extrapolation: The transmitter's rated power is a design-era catalog figure; the usable continuous carrier in the modulation mode actually chosen should be verified on the bench before the RF power budget is frozen.

For the setup of the ion source, it is considered that the ion source remains adjustable in direction of the gap, so that the ideal position can be found by experiments. Normally the ion source is centred in the cyclotron. However, in our case – with our small cyclotron and such a small amount of revolutions (≤ 10) - it is better to optimize the starting position of the first path. Due to this fact the ion source will not be fixed mounted but it will be stuck under the dummy-dee instead

Frank, Wolf & Held, COLUMBUS — A Simple Ion Source — WEPPT021, Proceedings of Cyclotrons2013 (2013) — p. 1

Editorial note, tabletop extrapolation: With only a handful of turns there is no adiabatic settling; an adjustable source mount converts a machining guess about the first half-turn into a tunable parameter, and the optimum need not be the centred position.

the angle of emission shall be adjustable for a better acceleration and to prevent that the protons remain in the gap between the dees

Frank, Wolf & Held, COLUMBUS — A Simple Ion Source — WEPPT021, Proceedings of Cyclotrons2013 (2013) — p. 1

Editorial note, tabletop extrapolation: A rotatable head is a cheap second degree of freedom on top of source position; both exist because low-energy ions do not forgive alignment errors in the first gap.

The protons for our cyclotron are produced in the ion source which was built after the pattern of Tim Koeth [1], which he used first in his cyclotron. … A specific design of the ion source was required due to the cyclotron's small size and the low number of revolutions … It was designed for adjusting the position of the ion source itself and the proton's angel of emission. … [1] Tim Koeth, "The Rutgers 12-Inch Cyclotron Ion Source Studies Part I"

Frank, Wolf & Held, COLUMBUS — A Simple Ion Source — WEPPT021, Proceedings of Cyclotrons2013 (2013) — p. 1, 2

Editorial note, tabletop extrapolation: A documented precedent for reusing a published hobby-machine source design: here the ionization geometry was adopted whole and the adaptation effort spent on mounting and adjustability.

This work is limited to the area of high vacuum. The limitation is due to the simple handling of the components and the existing pumping station, with which a minimum of 10-5 mbar is not undercut. … The present work shows that metal-based 3D printing can meet the requirements of vacuum technology in the area of high vacuum.

Wolf, Beck, Franz & Neumaier, 3D Printing for High Vacuum Applications — THC04, Proceedings of Cyclotrons2019 (2019) — p. 1, 4

Editorial note, tabletop extrapolation: Printed 316L-class components are demonstrated at high vacuum down to the study's achieved 1.5·10-5 mbar; the 10-6 decade was not reached by its pump station and UHV is explicitly untested, so claims below the tested pressure are extrapolation, not evidence.

Due to an elaborate post-processing, it is clear that the 3D printing of standard components will hardly be worthwhile. Consequently, in order to achieve an economic use of this technology, it is necessary to retrofit the printed components with standard parts from conventional manufacturing.

Wolf, Beck, Franz & Neumaier, 3D Printing for High Vacuum Applications — THC04, Proceedings of Cyclotrons2019 (2019) — p. 2

Editorial note, tabletop extrapolation: For a low-budget build the demonstrated pattern is catalog KF/CF hardware joined to a printed complex body; a plain straight connector is exactly the case the source found uneconomic to print. Compare current quotations - the economics move with the market.

Since no moldings and other tools are necessary for the production of 3D printed components, there are no further costs. … The basic body of the vacuum chamber was supplemented with a complex geometry and integrated flow channels and completed by welding standard components. In addition to a cost-effective production by avoiding unnecessary rework, this method also has the advantage of a flexible adaptation to different customer requirements.

Wolf, Beck, Franz & Neumaier, 3D Printing for High Vacuum Applications — THC04, Proceedings of Cyclotrons2019 (2019) — p. 1, 3

Editorial note, tabletop extrapolation: For a multi-port chamber whose port pattern is unique to one machine, a printed body with welded catalog flanges is a demonstrated alternative to welded-plate fabrication and machining from solid, and the port layout can be revised in CAD between builds without molds or dedicated tooling - the build itself still costs supports, fixtures, inspection and sealing-surface machining, so the comparison is build-specific.

Cited in: Cyclotron Vacuum Chamber Design and Sealing

Especially for single production and prototypes, 3D printing technology can be of considerable benefit. This is particularly due to the freedom in geometry and the possibility of function integration, such as the realization of a surface heating system.

Wolf, Beck, Franz & Neumaier, 3D Printing for High Vacuum Applications — THC04, Proceedings of Cyclotrons2019 (2019) — p. 4

Editorial note, tabletop extrapolation: A one-off machine is exactly the single-production case; a sound screening default is to consider printing where a part is unique and geometrically complex and to price catalog, machined, welded and printed options case by case.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

a mass resolution of about 1800 is needed to separate 14 C from 13 CH. The resolution of a CMS is approximately: R ≈ 3 x n x H, where n is the number of turns that in-phase particles make in a synchronous field before extraction and H is the rf harmonic number

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

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: an estimating relation, not a law — the coefficient depends on the phase-slip criterion that defines an in-phase turn. Useful for order-of-magnitude estimates of how sharply a small machine discriminates species or off-resonance drive; derive the real number from a phase-history calculation for the actual field and RF program.

The overall size of the machine is dictated by the mass resolution needed, the turn separation needed to clear the center region, and the injection energy. Better center region clearance requires a larger magnet, which is more expensive, or it requires a smaller injection radius, making the transit time worse for high harmonics. So a compromise has to be made giving good transmission in the center region and a large enough injection radius to give a good transit time factor