Design Guide › level 4
Cyclotron design rules, level 4: second-order refinement and specific configurations
278 of the guide’s 1878 rules sit at level 4: second-order refinement and specific configurations.
The level ranks how early and how universally a rule binds a cyclotron design — breadth,
never weight. It is not permission to skip a rule whose trigger a machine has, and safety
rules are never skippable on level alone; how the levels were assigned and audited is on
the methodology page. Each rule keeps its
formula where the source gives one, a verbatim quote, a page-level citation, and a stable
identifier (dg-NNNN) that resolves here, on its
subsystem page, and on the
all-in-one guide. Where an editorial note says “the
reference machine”, its parameters are on the
guide’s front page.
This level’s rules by subsystem — each link opens just that subset, in the all-in-one guide’s filters: Fabrication (87) · Targets (82) · RF (68) · Materials (51) · Beam measurement (36) · Beam dynamics (33) · Detectors (31) · Safety (28) · Ion source (27) · Vacuum (24) · Dee (21) · Extraction (21) · Magnet (19) · Modeling (15) · Shielding (9) · Vacuum chamber (7) · Coils (7) · Seals (7) · Cyclotron general (6) · Pedagogy (4) · Physics theory (3) · Controls & instrumentation (2) · RF matching (2) · Project management (2). A rule carrying several tags is counted under each; a subsystem’s complete rule set, across all levels, is on its own page in the subsystem directory. To add a search term or a second subsystem, open this level in the all-in-one guide with filters, which carries every rule and filters in the browser.
Verify before use. Every rule here is a source extract in the vocabulary of the editorial methodology — faithful to its cited page, not an independently validated engineering requirement. Re-read any rule that drives a real design decision at the cited page before committing metal, money, or high voltage to it. The editorial note under each quote is this site’s extrapolation to a tabletop machine, not something the source said: an editor’s judgement, audited for overreach, never a citation.
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Put a 45-degree chamfer on the pole edges to prevent local magnetic saturation at the corners and to soften the fringing field.
45 deg edge taperSource quote & editorial note
the edges of the pole have a 45 degree taper. This is to prevent magnetic saturation at the edges of the pole. The field due to the taper also fringes less sharply.
Heuer & Baumgartner, Design of a 2 MeV Cyclotron (2009) — p. 31
Editorial note, tabletop extrapolation: Trivial machining step for a next machine's pole tips that buys margin against edge saturation at higher fields.
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Clad the leakage surfaces of a permanent-magnet circuit with oppositely-polarized magnet material: in Leupold's horseshoe example cladding raised the gap field from 0.8 T to 2 T, and a 7 kg clad assembly outperformed a 55 kg unclad one (1.6 T) - but cladding pays only when leakage permeance dominates.
clad: 0.8 T -> 2.0 T, 7 kg vs 55 kg; gain small (0.5->0.8 T) when gap dominates permeanceSource quote & editorial note
The latter has a gap field of 2 T, as compared with only 0.8 T for the unclad structure... 7 kg mass of such an assembly compared to the 55 kg required to produce only 1.6 T ... When the horseshoe-like structure has no tapered pole pieces as in Fig. 7, most of the external permeance is in the gap, and cladding raises the gap field from 0.5 T to only 0.8 T.
Leupold & Potenziani, A Permanent Magnet Circuit Design Primer — ARL-TR-946 (1996) — p. 15-16
Editorial note, tabletop extrapolation: Mostly a curiosity at cyclotron-gap geometry - the source's own no-taper horseshoe shows the gain collapsing (0.5 to 0.8 T) when the gap dominates the permeance - but valuable for compact PM ion-source or steering assemblies. The field and mass comparisons are between the source's specific example assemblies, not like-for-like scaling laws.
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A Halbach 'magic cylinder' delivers a transverse bore field Bw = Br*ln(R2/R1) with, in the ideal infinitely-long continuous model, zero exterior field; fields up to about twice the remanence (~2.0-2.5 T with NdFeB) are practicable, e.g. Br=1.2 T with 2.5 cm bore in a 15 cm OD gives 2.1 T with no power supply. Real finite, segmented assemblies leak: fringe and stray fields must be mapped, not assumed absent.
Bw = Br*ln(R2/R1) (ideal long continuous cylinder); practical max ~2*BrSource quote & editorial note
fields of twice the material remanence should be practicable, namely 2.0 to 2.5 T... Bw = 1.2 ln(15/2.5) = 2.1 T
Leupold & Potenziani, A Permanent Magnet Circuit Design Primer — ARL-TR-946 (1996) — p. 24-25
Editorial note, tabletop extrapolation: Shows what PM technology can do at small bore: not a cyclotron gap replacement, but a zero-power option for beamline analysis/steering dipoles on a next machine's extracted beam.
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Terminate high-field pole edges/ends with the Rogowski roll-off profile y = g/2 + (g/pi)*exp(pi*x/g - 1): it is the fastest gap increase that keeps surface flux density monotonically decreasing, i.e. no local saturation anywhere on the edge.
y = g/2 + (g/pi)*exp((pi*x/g) - 1); y = 0 is the gap centre line, and the surface asymptotes to the flat pole (y -> g/2) toward the magnet interior - the -1 inside the exponential is an x-origin shift (exp((pi*x/g)-1) = exp(pi*(x - g/pi)/g)), not an errorSource quote & editorial note
The 'Rogowski' roll-off: Equation: y = g/2 +(g/π) exp ((πx/g)-1); g/2 is dipole half gap; y = 0 is centre line of gap. This profile provides the maximum rate of increase in gap with a monotonic decrease in flux density at the surface ie no saturation
Marks, Conventional Magnets for Accelerators — CAS lecture (2004) — p. 48-49
Editorial note, tabletop extrapolation: The mathematically graded version of the Cyclotron Kids' 45-degree chamfer; worth machining on a next machine's pole edges when field analysis predicts pole-edge flux density approaching the steel's saturation. (The 1.4 T in the source is the Diamond dipole's field, not a switch-on threshold.)
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The 3-D fringe field of an unchamfered dipole is longest at the pole center and shorter at the edges (roughly quadratic across the pole), so its integrated error looks like a sextupole; SPEAR3 reduced it with a chamfer whose depth profile was determined empirically and was approximately parabolic, prototyped on a removable machined insert.
fringe length ~ h at pole end, varying ~quadratically across widthSource quote & editorial note
the fringe field is longer at the center of the magnet and drops off near the edges. This distribution is approximately quadratic and the integrated multipole field looks like a sextupole field. ... a removable insert with a machined chamfer installed on the SPEAR3 prototype gradient magnet. ... The shape of the chamfer depth was determined empirically and was approximately parabolic. It was designed to reduce the integrated sextupole field.
Editorial note, tabletop extrapolation: Mostly relevant if the builder adds edge shaping for extraction: expect the field falloff at the pole rim to vary azimuthally with any non-axisymmetric pole feature, and fix it empirically with removable machined inserts.
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When end-chamfering poles to fix the integrated field, machine the depth distribution computed from the measured field integral; the cut angle itself is unimportant - 45 degrees is convenient because it splits the corner into two equal half-angles and minimizes local saturation. SPEAR3 did this on bolted-on steel end pieces, remachining after measurement, and reached the final shape in two iterations.
chamfer depth Delta-z(x) from measured Leff(x); cut angle 45 degSource quote & editorial note
The angle of the cut is unimportant. However, a 45 degree angle cut is convenient and distributes the same angle at two points and minimizes saturation effects due to the sharp corners. ... solid steel pieces, machined with the two dimensional pole contour, were bolted onto the pole ends. These pieces were removed, machined with the required distribution of the chamfer depth determined by the described iterative process and replaced. After replacement, the distribution of the field integral was measured. The final chamfer shape was achieved after two iterations.
Tanabe, Iron Dominated Electromagnets: Design, Fabrication, Assembly and Measurements — SLAC-R-754 (2005) — p. 253-254
Editorial note, tabletop extrapolation: If the next machine's pole edge is chamfered or radiused to soften the field falloff for extraction - a different geometry and objective than a dipole end chamfer, so model or map it for the cyclotron case - use bolt-on machinable end pieces so the shape can be iterated the way SPEAR3 did.
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Size the Dee tank circuit from the Dee capacitance: on the cited machine ~76 pF of Dee against a 0.87 uH secondary resonates up to 19.5 MHz (411 keV protons at its 1.28 T maximum field), with both inductors wound from 1/4 inch copper tubing coaxially - 6 cm diameter primary outside a 4 cm secondary - and coupling set by swapping primaries of different turn counts.
cited machine: C_dee ~ 76 pF, L >= 0.87 uH -> f up to 19.5 MHz; 1/4 in copper tubing; 6 cm dia primary over 4 cm dia secondary; interchangeable primaries set couplingSource quote & editorial note
the Dee may be oscillated with voltage amplitudes of up to approximately 3000V relative to the grounded Dummy Dee. The Dee capacitance is approximately 76 pF. The secondary coil inductance of 0.87 uH or more in parallel with the Dee capacitance yields a resonance as high at 19.5 MHz, which is the maximum cyclotron frequency corresponding to 411 keV protons in the maximum magnetic field of 1.28 T. ... These inductors are 1/4 inch copper tubing, wound coaxially, with the 6 cm diameter primary coil outside the 4 cm diameter secondary coil. The inductance of the primary coil can be changed by replacing the coil with one having a different number of turns, several of which have been constructed
Editorial note, tabletop extrapolation: Concrete worked values at the same scale, but measure your own machine's total capacitance (dee + stray + coil) and size the coil from L = 1/((2*pi*f)^2 * C_total); the swappable-primary approach lets you retune coupling without rebuilding the tank. The 411 keV is that machine's figure at its own field and extraction radius.
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Specify electrical-grade copper for RF parts: common phosphorus-deoxidized copper tube (0.015-0.08% P) runs only 60-90% IACS conductivity, versus ~100-101% minimum for certified electrical grades (C11000/C10100).
P-deox Cu tube: 60-90% IACS; electrical grade: ~100-101% IACS min (certify, don't assume); Rs ~ 1/sqrt(sigma), so the conductivity gap is worth ~6-23% in RF surface resistanceSource quote & editorial note
Most commercially available copper tube contains 0.015% to 0.08% phosphorus as a de-oxidising agent, so that its conductivity may range from 60% to 90% I.A.C.S.
Fowler, Radio Frequency Performance of Electroplated Finishes — Proc. IREE Australia (1970) — p. 6
Editorial note, tabletop extrapolation: Buy the tank-coil tubing as electrolytic/electrical-grade (C10100/C11000) copper with certified conductivity, not generic plumbing tube - worth roughly 6-23% lower RF surface resistance depending on where the plumbing tube fell in its range.
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Expect a Q meter to read below true coil Q: the instrument measures circuit Q, and the coil's distributed capacitance loads the reading down.
Q_measured < Q_true (distributed-capacitance error); circuit Q != coil QSource quote & editorial note
the presence of the coil's distributed capacity causes the Q observed by the Q meter to be lower than the true Q of the coil
Murphy, The Elusive Q of Single-Layer Air-Core Coils — CQ Magazine, May 1999 (1999) — p. 1
Editorial note, tabletop extrapolation: For the cited Q-meter method, treat the reading as a lower bound and keep leads and fixture capacitance minimal. A VNA measurement is a different animal: state whether loaded or unloaded Q is being extracted, calibrate and de-embed the fixture, and include the distributed capacitance in the fit - VNA errors can bias either direction.
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Do not trust simple coil design equations outside their validity range: L/d below 0.35, fewer than about 4 turns, or wire-to-spacing ratios outside 0.45-0.70.
Callender/Medhurst Q equations valid only for L/d >= 0.35, n >= ~4, 0.45 <= dia/S <= 0.70Source quote & editorial note
The equations do not hold for coils with a length-to-diameter ratio of less than 0.35:1, coils with less than about 4 turns, or coils with conductor diameter-to-turn spacing ratios of less than 0.45:1 or greater than 0.70:1.
Murphy, The Elusive Q of Single-Layer Air-Core Coils — CQ Magazine, May 1999 (1999) — p. 3
Editorial note, tabletop extrapolation: A 2-3 turn link or coupling loop at 9 MHz is outside the formulas; measure it rather than calculate it.
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A high-voltage probe loads the tank measurably - the Tektronix P6015 added 3.0 pF and shifted the resonant frequency accordingly - so retune or correct for probe capacitance whenever a probe touches the dee stem.
delta-C_probe = 3.0 pF (P6015)Source quote & editorial note
the P6015 probe introduced 3.0pF of capacitance; the tank circuit was indeed reduced in frequency corresponding to 3 pF
Editorial note, tabletop extrapolation: With the reference machine's ~78 pF-class dee, 3 pF is a ~2% frequency pull - enough to detune a high-Q tank, so calibrate with the probe on, then remove it and retune.
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On the cited 12-inch machine's resonator (L = 1.1 uH, C = 78.1 pF, estimated AC resistance 50 mOhm), ~1000 W forward power produced ~15 kV p-p dee voltage; the chamber withstood 2000 W but the tank, housing, chamber and dee stem became very warm.
1000 W -> ~15 kVp-p measured; 2000 W withstood with significant heatingSource quote & editorial note
inductance of 1.1uHy, capacitance of 78.1pF, and the estimated AC resistance of 50mOhm ... Preliminary tests with the new generator show that the cyclotron chamber is capable of withstanding 2000 watts of input power. The tank, tank housing, cyclotron chamber and DEE stem become very warm. It is not necessary to operate at 2000 watts, as shown above 1000 watts produces a peak-to-peak DEE voltage of approximately 15kV.
Editorial note, tabletop extrapolation: Scales the reference machine's plan only under ideal sqrt-power scaling at unchanged loaded shunt impedance: 500 W -> ~10.6 kVp-p, comfortably in the 5-13 kV target - but measure the actual dee voltage with a calibrated pickup; thermal management of stem and coil becomes the real issue.
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Choose dee-to-lid clearance for the working dee voltage: MIT's 1.25-in clearance (5-in lid gap) capped dee voltage at ~70 kV by breakdown, and the source's remedies are greater clearance plus round, smooth contours and clean, polished surfaces.
MIT: 5-in gap between lids, 2.5-in dee height, 1.25-in clearance -> ~70 kV limit (~56 kV/in working gradient)Source quote & editorial note
The gap between chamber lids was chosen to be 5 in., leaving 1 1/4-in. clearance between D's and lids ... resulting in a D-voltage limit of about 70 kv due to breakdown. ... The limit can be raised by designing for greater clearance between D's and chamber lids and by providing round, smooth contours and clean, polished surfaces.
Livingston & Blewett, Particle Accelerators (1962) — p. 175, 189
Editorial note, tabletop extrapolation: At 1.3 kV the reference machine has large margin against this failure mode. For a next machine at several kV, treat MIT's ~56 kV/in at breakdown as one calibration point, not an allowable: analyze peak surface fields, round and polish, assemble clean, and expect to condition (see dg-253) - no universal safe kV/in exists for vacuum gaps.
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For automated matching prefer an L-network over T or Pi: only one L-C combination per load simplifies the tuning algorithm; one L-network cannot match all impedances, so the cited system switches between two complementary L configurations with an RF switch, giving a wider matching range.
2 complementary L-network topologies + RF switch = wider matching range (coverage set by component ranges - verify against the actual load domain)Source quote & editorial note
Compared to T or Pi networks, the L network uses only one combination of inductance and capacitance. This simplifies the microcontroller tuning algorithm. The disadvantage is that one L network cannot match all possible load impedances. Figure 3 shows two L network types with complimentary matching ranges on the Smith Chart. The IMS uses an RF switch to select one of the two L networks, allowing a wider matching range.
Blodgett, 3.5 to 30 MHz Automatic Antenna Impedance Matching System (2012) — p. 11
Editorial note, tabletop extrapolation: If the builder automates their dee match at 9 MHz, a stepper-driven L-network is the simplest topology for the search algorithm; verify the two configurations' combined range covers the tank's actual impedance excursions (a Smith-chart sweep or simulation) before committing.
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Sample line power through a directional coupler sized so the detector never exceeds its rating: the source pairs a ~30 dB coupler with an AD8307 log detector for 200 W measurements, but 200 W is 53 dBm and 30 dB of coupling still delivers 23 dBm - above the AD8307's +17 dBm rated maximum - so budget additional attenuation between coupler and detector: at least 36 dB total for 200 W, 40 dB for 500 W, plus margin.
P_detector = P_line - coupling - pad; 200 W = 53 dBm -> 23 dBm after 30 dB; pad so P_detector <= +17 dBm at maximum power with margin for mismatch peaksSource quote & editorial note
The coupling factor is high, ~1000 or 30 dB, to minimize main line power loss ... enables 200 W power measurements using the AD8307 logarithmic detector IC
Blodgett, 3.5 to 30 MHz Automatic Antenna Impedance Matching System (2012) — p. 18
Editorial note, tabletop extrapolation: For the reference machine's 100-500 W upgrade: a homebrew 30 dB coupler plus AD8307 board works with a calibrated pad (10 dB or more) between them; include coupler tolerance and mismatch peaks in the level budget, and calibrate the chain end to end.
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Build the HF coupler the Kaune way: ferrite toroids wound with AWG 26 wire surrounding two 2-inch sections of RG-8 coax form the coupling transformers (the core type, directivity figures, and the exact shield/ground arrangement are the thesis's details - scan re-read queued).
FT-82-67 toroids, AWG 26 windings, 2-in RG-8 through-line sections; directivity 35 dB at 3.5 MHz, 28 dB at 30 MHzSource quote & editorial note
Ferrite toroids wound with AWG 26 wire and surrounding two 2 inch sections of RG-8 50 Ohm coaxial cable form the coupling transformers.
Blodgett, 3.5 to 30 MHz Automatic Antenna Impedance Matching System (2012) — p. 18-19
Editorial note, tabletop extrapolation: A cheap coupler build bracketing the reference machine's 9 MHz band - built from the source's full schematic, not the one-line summary: the shield treatment and grounding are what make the directivity, so replicate them exactly, then bench-test directivity, insertion loss and core heating at 9 MHz through the intended power and mismatch range before trusting it.
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A workable auto-tune algorithm: alternately step the inductor and capacitor toward the SWR minimum, stopping at SWR < 1.5:1 (4% reflected power); the source system matched loads from initial VSWRs up to 26:1 across 3.5-30 MHz.
SWR 1.5:1 <=> |Gamma| = 0.2 <=> 4% reflected; source matching range: up to 26:1 initial VSWR, 3.5-30 MHzSource quote & editorial note
actuates stepper motors to alternately adjust a variable capacitor and a variable inductor to reduce VSWR to less than 1.5:1 ... The antenna tuner system can match loads of up to 26:1 initial VSWR within a frequency range of 3.5 MHz to 30 MHz.
Blodgett, 3.5 to 30 MHz Automatic Antenna Impedance Matching System (2012) — p. 6-8, 40
Editorial note, tabletop extrapolation: Coordinate-descent on C then L is not guaranteed to converge on an interacting high-Q load - test it against the dee resonator before trusting it - and set the LDMOS amplifier's reflected-power shutdown from that device's own specification, not from the 1.5:1 convention.
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At an insulator-cathode junction, terminate the insulator at ~31.5 degrees to the cathode - the measured zero-surface-charge angle, voltage-independent, with positive charging below it and negative above; screening the cathode end or covering it with a semiconducting layer raised breakdown voltage ~2.5x, and roughening the insulator surface near the cathode added ~40% (near the anode: little effect).
junction angle ~ 31.5 deg (zero surface charge, voltage-independent); cathode-end screening/semiconducting layer: x2.5; roughen near cathode: +40%; ensure intimate metal-insulator contact (conductive coating on insulator end)Source quote & editorial note
They found that at a critical angle of 31.5 deg, the surface charge was zero; this angle was independent of the applied voltage. The surface charges were positive at smaller angles, but negative at larger ones. ... Fryszman and colleagues found that by screening the section of the insulation surface near the cathode or covering this section with a semiconducting layer, the breakdown voltage was raised by a factor of approximately 2.5. ... Roughening the surface of the insulator in a region adjacent to the cathode increased the breakdown voltage by about 40 %. Roughening the surface adjacent to the anode had little effect.
Miley & Murali, Inertial Electrostatic Confinement (IEC) Fusion: Fundamentals and Applications (2014) — p. 113-114
Editorial note, tabletop extrapolation: For the next machine's source stalk - a DC cathode-junction context like the studies' - cone the insulator toward the negative electrode and consider recessing the triple junction behind a screen. The factors come from separate experiments and are not multiplicative, and a dee-stem RF feedthrough alternates polarity every half cycle: there, treat all of this as qualitative guidance to be tested, not booked margin.
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Houghton's ion-source filament circuit: a standard AEI hairpin electron-microscope filament floating at about -90 V, heated by 2 A, with RF pickup on each filament lead shorted to ground through a 0.001 uF capacitor.
filament bias -90 V, heater 2 A, 0.001 uF RF bypass on each leadSource quote & editorial note
A standard AEI hairpin electron microscope filament floating at approximately -90 V is heated by 2 A of current ... RF pickup on each filament lead is shorted through a 0.001 uF capacitor to ground.
Editorial note, tabletop extrapolation: A replaceable-filament pattern worth copying next to a live dee: bias the filament, and RF-bypass every lead at the feedthrough - but size the bypass for the actual RF impedance and current, and use capacitors rated for the DC bias plus transients rather than copying 1 nF.
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The ORNL 86-inch supply architecture: multiple supplies each with a fused disconnect switch in its output, so the operator could remove a faulty unit from service without disturbing the remainder.
Source quote & editorial note
a fused disconnect switch in the output of each supply permits the operator to remove a faulty unit from service without disturbing the remainder
Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 61
Editorial note, tabletop extrapolation: Modular paralleled supplies (or PA pallets) with individual protection can give a home machine graceful degradation - but that takes design, not just fuses: current sharing or ORing, backfeed isolation, DC-rated load-break disconnects, fault coordination, and a written de-energization procedure before anyone touches a unit. Never hot-swap hardware that wasn't designed and tested for it.
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One machine's design point for dee-to-liner spacing: its selected 100 kV peak required about 1.5 in of vacuum clearance (~26 kV/cm), taken at the minimum because magnetic gap is precious.
cited design point: ~1.5 in clearance at 100 kV peak (~26 kV/cm); not a linear scaling lawSource quote & editorial note
The selected value of 100 kv peak voltage requires about 1.5-in. clearance from dee-to-liner ... Since the magnetic gap is so precious ... this minimum value is taken for design.
Editorial note, tabletop extrapolation: The reference machine's 1.3 kV is electrically trivial by this calibration - its clearances are set by beam aperture and mechanical tolerance. For a 20-50 kV dee on a next machine, set clearance from electrostatic analysis of the actual geometry (edges, finish, conditioning, pressure regime), not by scaling kV/cm linearly.
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The notebook's LDMOS build mounts the RF power board to its copper spreader with screws only - no solder - with heat-sink compound between the copper spreader and the aluminium heat sink.
Source quote & editorial note
No solder to hold the board to the spreader, the screws are enough. Heat sink compound between copper spreader and aluminum heat sink.
Buckler, Solid-State, 2-Decade, 1.25 kW Linear Amplifier — Development Notebook (2015) — p. 10
Editorial note, tabletop extrapolation: A workable pattern for a kW-class dee driver assembled from LDMOS boards - but the transistor/module manufacturer's mounting spec wins: check flange flatness, clamping force, and which interfaces want grease, pads, solder, or dry metal contact for the specific device.
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The cited LDMOS deck stabilized its low-frequency end with degenerative drain-to-gate feedback whose series inductances were literally 1.5 cm of #20 wire per side (~15 nH in that layout) - not wound coils.
L = 15 nH = 1.5 cm of #20 AWG wire, drain-to-gate, in series with feedback resistorSource quote & editorial note
the part description says '15 nH, connecting wires to R14 and R15, 1.5 cm each #20 AWG,' implying that they are just wires, not even coiled.
Buckler, Solid-State, 2-Decade, 1.25 kW Linear Amplifier — Development Notebook (2015) — p. 15
Editorial note, tabletop extrapolation: Relevant if building a broadband solid-state dee driver: these devices carry enormous low-frequency gain, so low-end stability needs deliberate design - feedback networks of this kind are one tool, verified by stability analysis or measurement on the actual amplifier; neither the 15 nH value nor certain oscillation without it transfers between layouts.
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Add a series current-limiting resistor (20 ohm, 50 W) in the 50 V feed to the controller pass transistor and use 1000 V mica capacitors rather than 500 V in high-power filter positions; both failures happened in service.
20 ohm / 50 W series resistor; 1000 V micas replacing 500 VSource quote & editorial note
I also added a limiting power resistor (20 ohms at 50w) in series with 50v to the TIP102 as a precaution...with this resistor in place, a short on the 12v line will limit the current and prevent a catastrophic failure. ... I used 500v micas but slowly but surely I am changing them to 1000v specs because they are more robust.
Buckler, Solid-State, 2-Decade, 1.25 kW Linear Amplifier — Development Notebook (2015) — p. 31-32
Editorial note, tabletop extrapolation: Cheap fault-tolerance for a homebuilt RF deck, as the source built it. Check the fault arithmetic before copying: 50 V across 20 ohm is 2.5 A and 125 W, above the resistor's continuous rating, so the part rides through brief faults only - pair it with a fuse or fast shutdown rather than treating it as continuous-duty protection. Voltage-derating the filter caps matters more with the reactive load a dee presents.
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A lower-conductivity plating hurts most at about 1.5 skin depths of the plated metal (the composite's resistance maximum); the mirror-image minimum for higher-conductivity plating is the companion result in the same analysis.
R_max at t ~ 1.5*delta_plating for sigma_plate < sigma_base; R_min at t ~ 1.5*delta for sigma_plate > sigma_baseSource quote & editorial note
The resistance of the composite conductor reaches a maximum value when the thickness of the plating is approximately one and one half times the skin depth for the plated metal.
Fowler, Radio Frequency Performance of Electroplated Finishes — Proc. IREE Australia (1970) — p. 3
Editorial note, tabletop extrapolation: Assess a proposed coating by computing the multilayer surface impedance with the coating's own conductivity AND permeability against its own skin depth - the trap case is a mid-thickness medium-conductivity layer, and magnetic coatings (nickel!) cannot be cleared by nonmagnetic skin-depth arithmetic; very thin protective flashes are usually small in effect at 9 MHz, verified by that same calculation rather than assumed harmless.
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A thin gold flash (10 microinches) over silver is porous; the cited work found at least 200 microinches of gold necessary for adequate protection of the silver beneath.
t_Au >= 200 uin (~5 um) for adequate protection in the cited deposits; not established as pore-freeSource quote & editorial note
A gold flash (10 micro-inches) is often used although many workers have shown that the deposits are not pore-free and that at least 200 micro-inches of gold are necessary to provide adequate protection.
Fowler, Radio Frequency Performance of Electroplated Finishes — Proc. IREE Australia (1970) — p. 7
Editorial note, tabletop extrapolation: For RF contact fingers and connectors on the resonator, distrust thin gold flash: specify a qualified contact-plating system at proven thickness. Lacquer belongs only on non-contact surfaces, and only after RF-loss and vacuum-outgassing checks - never on a current-carrying contact interface.
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Tarnished silver is a real contact-resistance hazard: silver-plated wire contacts rose from 6 milliohms to 200 milliohms after two hours in a hydrogen-sulfide atmosphere.
R_contact: 6 mOhm -> 200 mOhm after 2 h H2S exposureSource quote & editorial note
the contact resistance of two silver-plated wires rose from 6 milliohms to 200 milliohms after two hours' exposure to hydrogen sulphide.
Fowler, Radio Frequency Performance of Electroplated Finishes — Proc. IREE Australia (1970) — p. 7
Editorial note, tabletop extrapolation: Where sulfur contamination is credible (some shop atmospheres, rubber outgassing, industrial air), protect silver-plated RF joints or periodically inspect and measure their resistance - raised contact resistance heats under the resonator's high circulating RF current.
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Use regulated, temperature-compensated gate bias to stabilize quiescent current, and feed VDD to each drain separately so high DC currents stay out of the RF output transformers (no DC core bias).
Source quote & editorial note
regulated and temperature compensated bias, separate VDD feeds to the output transistor drains to keep high dc currents out of the RF transformers
Buckler, A Solid State 1.25 kW Linear Amplifier — QST, January 2015 (2015) — p. 2
Editorial note, tabletop extrapolation: Directly applicable to a homebrew 9 MHz LDMOS deck: thermal-tracking bias holds the operating point against drift, and DC-free transformers remove one saturation mechanism - still verify RF flux density and transformer temperature at full drive.
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Follow the LDMOS package's mounting specification and compute the whole junction-to-coolant thermal path: the source's construction flow-solders the output transistors to a thick copper heat spreader, which then mounts to the heat sink - use a spreader where flange heat flux demands it, and solder the package only when its assembly spec permits.
Source quote & editorial note
Rather than mounting the output transistors directly to a heat sink, they are first flow soldered to a thick copper heat spreader, which is then mounted to the heat sink.
Buckler, A Solid State 1.25 kW Linear Amplifier — QST, January 2015 (2015) — p. 3
Editorial note, tabletop extrapolation: At 100-500 W a copper spreader under the LDMOS pallet is cheap thermal margin; the reference machine's earlier MOSFET amplifiers died in service without a firm post-mortem, and die-temperature margin is the inexpensive insurance either way.
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Treat the drain-trace tap point of the output transformer as a tuning element: its physical position along the trace sets the output match.
Source quote & editorial note
The position of the connection point at the drain trace is critical as it affects the match.
Buckler, A Solid State 1.25 kW Linear Amplifier — QST, January 2015 (2015) — p. 4
Editorial note, tabletop extrapolation: When copying an LDMOS pallet layout, preserve the cited design's output-transformer tap geometry, and if anything about it changes, remeasure the output match - the source says position is critical; how sensitive, at what power, is a measurement on the actual build.
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Practical vacuum-gap breakdown fields span 5-200 MV/m, and smaller gaps withstand higher fields: in the source's data, fields above 100 MV/m were reached only with gaps under 150 microns - so do not credit millimeter-scale gaps with those numbers.
breakdown range 5-200 MV/m; >100 MV/m observed only at gaps < 150 umSource quote & editorial note
breakdown occurs between 5 and 200 MV/m ... In general, smaller gaps can withstand higher fields. ... Note that cathodes can reach fields higher than 100 MV/m, but, observing the maximum voltage, only with a gap smaller than 150 microns
Werner, Probing and Modeling Voltage Breakdown in Vacuum — Cornell dissertation (2004) — p. 78, 95
Editorial note, tabletop extrapolation: At 13 kV across the reference machine's ~6 mm gap the mean field is ~2 MV/m, comfortably low - but mean field is only the first check. Local enhancement at edges and asperities, particles, insulator surfaces and gas pressure can still start an arc, so treat sparking there as a diagnostic checklist, not an impossibility.
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Build the Dee/dummy-Dee pair from one 1.27 cm thick, 0.6 cm wide aluminium ring of 15.6 cm OD, cut into a 7.8 cm Dee and a 3.2 cm dummy Dee separated by 0.635 cm ceramic spacers, skinned with 0.13 cm sheet and supported on three KF-16 feedthroughs at 120 degrees.
ring 15.6 cm OD, 1.27 cm thick; Dee 7.8 cm wide, dummy 3.2 cm; accelerating gap 0.635 cm; skins 0.13 cm; 3 supports at 120 degSource quote & editorial note
Ceramic spacers hold the Dee and Dummy Dee apart with a gap of 0.635 cm. The entire Dee electrode assembly is supported by three KF-16 electrical feedthroughs through ports at 120 degrees from each other. ... A circular ring of 6061 T6 aluminium, 1.27 cm thick, 0.6 cm wide, and 15.6 cm outside diameter, formed the walls for both the Dee and Dummy Dee. Two 5052 aluminium sheets, 0.13 cm thick, were fastened to the top and bottom of the ring with vented screws.
Editorial note, tabletop extrapolation: Direct fabrication prior art at exactly tabletop scale; the single-Dee-plus-dummy topology needs live RF on only one electrode - the design rationale for fewer HV feedthroughs - and the vented screws are the kind of vacuum detail worth copying wholesale.
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The historical design furnace-brazed five loops of flattened 7/8-in copper tubing to 1/8-in copper dee sides; both cooled designs proved satisfactory, and the brazed-tubing one was much easier and less expensive.
Source quote & editorial note
The sides of the second set of dees are 1/8 in. copper with five loops of 7/8 in. copper tubing flattened and furnace brazed ... Both designs have proved satisfactory but the latter is much easier and less expensive.
Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 50
Editorial note, tabletop extrapolation: At 1.3 kV and tens of RF watts the builder probably needs no water - but decide from computed or measured dissipation and temperature, not from voltage. If a next machine's dee runs kilowatt-class RF, brazed-on flattened tubing is the historically cheap construction; substituting soft solder needs its own validation (joint temperature, strength, vacuum compatibility).
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Space-charge-limited extraction current density follows Child-Langmuir in practical units: j[mA/cm^2] = 1.72*sqrt(q*/u)*U[kV]^1.5/d[cm]^2 -- for protons at 10 kV across a 5-mm (0.5 cm) gap that is ~220 mA/cm^2, far above a hobby cyclotron's needs. [Correction, Aug 2026: the source prints the denominator as d[mm], but the 1.72 coefficient requires d in centimeters; the originally extracted example (~2.2 mA/cm^2) was low by 100x. Verified against the SI form of Child-Langmuir. The verbatim quote below preserves the source's own text.]
j[mA/cm^2] = 1.72*sqrt(q*/u)*(phi[kV])^(3/2)/(d[cm])^2Source quote & editorial note
In more practical units, this equation can be rewritten: j[mA/cm2] = 1.72 * sqrt(q*/u) * phi[kV]^(3/2) / d[mm]^2.
Wolf (ed.), Handbook of Ion Sources (1995) — p. 376-377
Editorial note, tabletop extrapolation: Confirms the reference machine's nA beams are nowhere near space-charge limits; if extraction is weak the problem is geometry/plasma matching, not the Child-Langmuir ceiling.
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Kovalchick's IEC grid: inner-grid diameter chosen as one-fifth of the 21-cm chamber (4.2 cm), geometric transparency kept above the cited 92 percent threshold - three loops of 0.114-mm tungsten wire give 99.18 percent, calculated by comparing total wire cross-section to grid-sphere surface area.
d_grid ~ D_chamber/5; transparency = 1 - (pi*d_grid*N_loops*d_wire)/(4*pi*r^2) >= 0.92Source quote & editorial note
The grid was made of .0114 cm thick tungsten wire shaped into circles chosen to be one fifth of the chamber in size. The chamber diameter was 21 cm so the grid diameter was 4.2 cm. ... fusion efficiency is enhanced by transparency of at least 92 percent (Donovan). The inner grid is 99.18 percent transparent with three loops as calculated by comparing the cross section of the total grid wire used to the surface area of the grid sphere.
Kovalchick, Deuterium Fusion Using Inertial Electrostatic Confinement (2012) — p. 19-20
Editorial note, tabletop extrapolation: The transparency bookkeeping (wire cross-section vs aperture area) is the calculation method to transfer - but a circulating cyclotron beam hits a grid or slit repeatedly and directionally, so compute projected obstruction along the actual trajectory over many turns, not the spherical-area figure.
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W-25%Re is the cited work's grid sweet spot: spot-weldable (unlike pure W), low sputter yield, high melting point (the book prints 2,800 K), validated at 30-130 kV and 30-180 mA for over 1,000 h - and the grid survived over 2 years where stainless wires lasted under a week.
W-25%Re: book's melting figure 2,800 K (standard alloy data put the W-25Re solidus near ~3300 K - verify against a datasheet); validated 30-130 kV, 30-180 mA, >1000 h; pure-W spot welding needs a Ni foil interlayer (the Ni then limits temperature)Source quote & editorial note
The stainless steel wires previously used by Murali lasted for under a week depending on the power load. In contrast, with the W-25%Re alloy, the grid lasted for over 2 years. ... It is relatively cheap, has a high melting point (2,800 K), a low sputter yield, and is easy to manufacture by spot welding. To test this material, the 10-cm grid was run at various voltages in the range of 30-130 kV and with the current range of 30-180 mA for over 1,000 h
Miley & Murali, Inertial Electrostatic Confinement (IEC) Fusion: Fundamentals and Applications (2014) — p. 145-146
Editorial note, tabletop extrapolation: W-Re thermocouple wire is commercially available in small quantities - a strong candidate for any sputtered electrode in the reference machine's source, with W-class durability and far better workability than pure tungsten; fabrication, activation and sputter behavior remain application-specific, so qualify it in place.
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A transparent wire cathode breaks down at about three times lower pd than a solid cathode at the same striking voltage (the cited comparison, spherical and planar alike) - recirculation through the grid is the working explanation; the Star-mode microchannel regime and transparency limits are the book's further account (scan re-read queued).
pd(solid)/pd(grid) ~ 3 at fixed V_strike; Star mode below ~0.5 Torr-cm; rigid grids practical only to ~95% geometric transparencySource quote & editorial note
For fixed Vs, the value of (pd) is seen to be about three times higher for both the spherical and the planar solid-cathode discharges than for the transparent grid-type cathode discharges.
Editorial note, tabletop extrapolation: If building an IEC-style p-B11 test stand, grid-opening geometry is a real trade study - larger openings mean fewer grid hits and longer grid life, finer mesh means better field definition - informed by the cited 3x pd result, with the Star-mode operating claims taken from the re-read source rather than summary memory.
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Support and connect a floating PIG anode with two 0.5 mm stainless wires fed through alumina tubes sealed with ceramic epoxy (Ceramabond) into the cathode body; a third stainless tube serves as gas inlet.
Source quote & editorial note
Three holes are machined in the cathode body; two are used to support the anode and the third is used as a gas inlet. Alumina tubes are inserted into the two holes used for anode support, and a stainless steel tube is inserted into the gas inlet hole. Ceramic epoxy (Ceramabond) is used to mate the alumina and stainless tubes to the back of the cathode body. Stainless steel wire with 0.5 mm diameter was spot welded to the anode, and the wires were threaded through the alumina tubes in the cathode body. ... Essentially the anode floats inside the cathode body, being supported only by the two stainless steel wires that protrude through the alumina tubes and out the back of the cathode body.
Editorial note, tabletop extrapolation: An amateur-grade insulated support for a modest-voltage, low-current internal electrode - an ion-source anode and the like. Not unchanged for filament leads (0.5 mm stainless is a poor conductor for filament current) or for chamber-wall HV or current feedthroughs: use current-rated conductors and qualified vacuum/HV feedthroughs there, and test the ceramic-epoxy joint for bakeout, leakage and voltage standoff before trusting it. [Note revised 2026-08-23: earlier note extended the scheme to filament leads.]
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In Forringer's tested source, doubling the chimney slit from 0.25 mm to 0.51 mm (both 5.0 mm tall, 10 degree chamfer) raised beam current ~4.4x (52 to 230 uA at 50 mA arc) while radial emittance grew only ~1.7x (27 to 47 mm-mrad) - the larger slit gives more current at larger emittance.
0.010 in slit: 52 uA, 27 mm-mrad radial; 0.020 in slit: 230 uA, 47 mm-mrad (50 mA arc, 3.0 sccm, ~40 kV puller)Source quote & editorial note
The chimney with the larger slit produces a beam with a larger emittance. However, the beam is also of higher intensity.
Editorial note, tabletop extrapolation: Suggests slit width is a powerful knob worth sweeping on a next machine: expect more current and more emittance from a wider slit, and stop widening when the machine acceptance is filled - but the 4.4x/1.7x ratios are that source's numbers; do your own aperture sweep and acceptance analysis before extrapolating.
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Raising PIG arc current raised beam current sub-linearly in the cited scan: for the 0.25 mm slit, 50 to 450 mA of arc gave 52 to 227 uA of beam while beam/arc efficiency fell from 1.0e-3 to 0.5e-3; measured emittance stayed flat over the scan and luminosity climbed 1.7 to 7.1 A/(cm2-sr).
I_beam/I_arc drops 1.0e-3 -> 0.5e-3 over 50-450 mA arc; luminosity 1.7 -> 7.1 A/cm2-sr; emittance ~constantSource quote & editorial note
the general trend of increasing arc current producing increased beam current as expected... there was no noticeable change in the emittance of the beam for different currents
Forringer, Phase Space Characterization of an Internal Ion Source for Cyclotrons — MSU dissertation (2004) — p. 77-78, 81
Editorial note, tabletop extrapolation: Cranking arc power buys current with diminishing returns, and in this scan it did not spoil measured emittance. Do not read that as space charge being negligible in general: generalized perveance rises steeply at low velocity, so keep space charge in extraction and first-turn models until a sensitivity check shows it is negligible at your energy and current.
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Forringer's orbit simulations reproduced measured emittance for both slit and hole chimneys by starting ions on the plasma boundary with an effective plasma temperature of ~35,000 K (central starting energy ~4.5 eV, i.e. 3kT/2).
T_plasma ~ 35,000 K fitted; E_start ~ 4.5 eV = 3kT/2 at that temperature; flat boundary (slit) / concave boundary (hole)Source quote & editorial note
the plasma temperature that provides the best match for experimental beams is approximately 35,000 K (resulting in a central starting energy of 4.5 eV).
Forringer, Phase Space Characterization of an Internal Ion Source for Cyclotrons — MSU dissertation (2004) — p. 91-107
Editorial note, tabletop extrapolation: A starting calibration for any first-turn simulation of a next machine's central region: begin near 35,000 K / 4.5 eV, then sweep the initial temperature and meniscus shape and validate against measured emittance or beam profiles - the value is a fitted effective parameter, not a universal plasma property.
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Use a double-gasket seal with a pump-out connection between gaskets on large or troublesome flanges: the interspace lets you test the seal for tightness quickly and with certainty, and - when designed as a continuously pumped guard vacuum - intercepts outer-seal leakage before it reaches the chamber.
Source quote & editorial note
A double-gasket seal is frequently used with a pump-out connection to the space between gaskets. This arrangement makes it possible to test the seal for vacuum-tightness quickly and with certainty.
Livingston & Blewett, Particle Accelerators (1962) — p. 200
Editorial note, tabletop extrapolation: Worth adopting on a next machine's main lid: a guard-vacuum groove turns the worst leak hunt into a valve twist for TESTING; riding out a leak in service additionally needs the interspace continuously pumped with adequate speed, and only helps for leaks through the outer seal.
Cited in: Cyclotron Vacuum Chamber Design and Sealing · The Vacuum Budget of a Cyclotron
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Estimate O-ring permeation leak rate with the source's mixed-unit formula L = 0.7*F*D*P*Q*(1-S)^2 - L in std cc/s, F the elastomer's permeability in std cc-cm/(cm^2 s bar), D ring ID in inches, P differential in psi, Q the squeeze/lubrication factor from the source's Figure II (~1.35 read off the dry-ring curve at 20 percent squeeze), S fractional squeeze - a rough order-of-magnitude approximation by the source's own statement.
L(std cc/s) = 0.7 F D P Q (1-S)^2; F in std cc-cm/(cm^2 s bar), D in inches, P in psiSource quote & editorial note
L = .7FDPQ(1-S)2 where: L = Approximate leak rate of the seal, std. cc/sec. F = Permeability rate of the gas through the elastomer at the anticipated operating temperature. Std cc cm/cm2 sec bar ... D = Inside diameter of the O-ring, inches. P = Pressure differential across the seal, lb/in2. Q = Factor depending on the percent squeeze and whether the O-ring is lubricated or dry. (From Figure II) S = Percent squeeze on the O-ring cross section expressed as a decimal. ... This formula provides only a rough order of magnitude approximation ... For convenience, the formula contains mixed units. ... The .7 factor provides dimensional homogeneity.
Parker Hannifin, O-Ring Vacuum Sealing, Catalog 5705B (1998) — p. 5
Editorial note, tabletop extrapolation: Computes the permeation floor of the 10-inch Viton lid seal - then convert to pressure via P = Q_gas/S_eff with the actual effective pumping speed, and remember outgassing and real leaks usually dominate above the permeation floor.
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When machining an extra-shallow gland to get heavy squeeze, widen the groove enough to accommodate the full O-ring volume, or the ring will be crushed instead of sealed.
Source quote & editorial note
when an extra-shallow gland is desired in order to increase the squeeze, it must be made wide enough to accomodate the full O-ring volume.
Parker Hannifin, O-Ring Vacuum Sealing, Catalog 5705B (1998) — p. 1-2
Editorial note, tabletop extrapolation: If a next machine's grooves are cut for 30% squeeze, groove cross-section area must still exceed ring cross-section area - check fill before cutting.
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Use dovetail grooves where the ring must be retained during assembly and maintenance (vertical faces, lids that open) - the guide's own purpose for them; take the dimensions from its Design Charts II & III, and hold the sharp-corner radius R closely: too small damages the ring on installation, too large invites extrusion.
Dovetail per the source's Design Charts II & III (66 deg walls; W=.139 -> L=.111-.113, G=.113-.117, ~20% squeeze, R=.010 - chart values, scan re-read queued); radius R is criticalSource quote & editorial note
Design Chart II For O-Ring Vacuum Dovetail Grooves ... 1/16 ... L Gland Depth .050 to .052 ... Squeeze % 27 ... G Gland Width .055 to .059 ... R .005 ... R1 1/64. Radius “R” is CRITICAL.
Parker Hannifin, O-Ring Vacuum Sealing, Catalog 5705B (1998) — p. PDF 10 (printed 7) carries Design Chart II; the retention sentence and the 'see pp 7-8' pointer are on PDF 5 (printed 2); Design Chart III (half-dovetail) is on PDF 11 (printed 8)
Editorial note, tabletop extrapolation: Worth it for a hinged or frequently-removed lid where the ring falls out during assembly; otherwise plain rectangular face grooves are cheaper and more tolerant.
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To run a standard round O-ring in a rectangular face-seal groove, keep every inside corner radius at least 3x the O-ring cross-section diameter, make the O-ring centerline length equal the groove centerline length, and size the ring with the source's equation: O-ring ID = (groove CL length / 3.14) - O-ring CS.
inside corner radius >= 3 * O-ring CS diameter; O-ring ID = (groove CL length / 3.14) - O-ring CSSource quote & editorial note
In order to use a standard round O-ring, the inside corner radius of the groove should not be less than three times (3X) the O-ring cross-section diameter. ... The length of the O-ring centerline should be equal to the length of the groove centerline. Following is an equation to assist in determining the O-ring inside diameter. O-ring ID = (Groove CL length / 3.14) - O-ring CS
Apple Rubber Products, Seal Design Guide — p. 84
Editorial note, tabletop extrapolation: Directly applicable to a racetrack or rectangular lid/port on a next machine: a 1/8 in. cord ring needs >=3/8 in. corner radii or it will bunch and leak at the corners. Note the source's rectangular sizing implies zero nominal stretch while its circular-groove guidance ideals 2% - follow the section matching your groove shape.
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Protect the septum from beam power with an open construction: MIT's septum is two 0.020-in tungsten strips, edges 1/8 in apart, each silver-soldered to a curved copper bar with cooling tubing soldered on - a geometry that lets most of the resonant beam pass into the deflector channel without striking metal; others distribute the heat with a long V-slot tungsten septum.
septum: 0.020-in W strips, edges 1/8 in apart, on a cooled copper bar (MIT); alternative: long V slot spreading heatSource quote & editorial note
allows most of the resonant beam to pass into the deflector channel without striking the channel walls. In the MIT cyclotron the septum is formed of two strips of tungsten, 0.020 in. thick and 12 in. long and with the edges spaced 1/8 in. apart. Each strip is silver-soldered to a copper bar bent to the correct curvature, with copper tubing also soldered to the bar for cooling. Other designers use a long V slot in a tungsten-strip septum, so the heat is distributed over an extended surface
Livingston & Blewett, Particle Accelerators (1962) — p. 184
Editorial note, tabletop extrapolation: At the reference machine's beam power the thermal load is small but not zero - intercepted power is loss current times energy per charge (1 uA of 500 keV beam is 0.5 W into a very small spot) - so compute it, and keep the slotted geometry: it maximizes transmitted current into the channel either way.
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Report p-B11 yields as alphas detected per luminosity (counts/(Nt*Np*dOmega)), not as a cross section: the number of alphas per reaction contributing to the main peak is energy-dependent - the paper's simulation puts ~2.1 in the peak at the 675 keV resonance.
X = Counts/(Nt*Np*dOmega) [cm2/sr]; simulated multiplicity in the dominant peak: ~2.1 at the 0.675 MeV resonance (energy- and window-specific)Source quote & editorial note
simulations show that out of the three emitted a-particles, on average 2.1 a-particles contribute to this peak at the 0.675 MeV resonance
Spraker et al., The 11B(p,α)8Be → α+α and the 11B(α,α)11B Reactions at Energies Below 5.4 MeV (2012) — p. 359-360
Editorial note, tabletop extrapolation: When the builder converts PIPS counts, publish counts-per-luminosity as this paper does. Extracting a cross section needs more than dividing by ~2: detector efficiency, angular acceptance, the alphas' angular/energy distributions and window effects all enter, and the multiplicity itself changes with beam energy and analysis window.
Cited in: Experiments by Energy Band
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Take multi-kW beams on grazing-incidence water-cooled targets so the power spreads over a long footprint: the 86-inch ran 500 uA of 23 MeV protons (11.5 kW) steadily on a 6 x 10 inch aluminum grazing target, and its highest calorimetrically stabilized point was 41.7 kW.
grazing incidence spreads P_beam over ~L/sin(theta) (theta to the target surface); steady 500 uA x 23 MeV = 11.5 kW; highest stabilized calorimetric point 41.7 kWSource quote & editorial note
operating steadily for some time with 500 ua of 23 Mev protons on a 6 by 10 inch water-cooled aluminum target of the grazing-incidence type ... The highest level at which operation was stabilized long enough to permit calorimetric measurement gave a beam power of 41.7 kw.
Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 24
Editorial note, tabletop extrapolation: Overkill at the reference machine's ~mW beam power, but the geometry trick transfers if a next machine ever puts tens of watts on a probe tip: tilt the target - and still do the cooling and stress arithmetic, since grazing only enlarges the footprint.
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Use a rotating multi-faced target (three faces at 45 degrees, each with a 1.2 cm x 1 mm recess for pressed powder) on a water-cooled stem so faces are shielded from each other's sputtering and targets can be compared without breaking vacuum or alignment.
3 faces at 45 deg; recess 1.2 cm dia x 1 mm deep; water-cooled rotating stemSource quote & editorial note
This is of steel and has three faces at 45 deg to the axis, which form a sort of truncated pyramid with a circular base. Each face bears a recess, 1.2 cm. in diameter and about 1 mm. deep. The metal or powder to be bombarded is pressed or hammered into these spaces and the beam strikes the surface which is uppermost. The target is carried on a water-cooled stem M which rotates in a ground joint and can be set so as to bring any one of the three faces into the beam. By having only three faces any one face is completely shielded from the material sputtered from that which is in the beam, and at the same time it is possible to make very rapid comparisons between various targets
Oliphant & Rutherford, Experiments on the Transmutation of Elements by Protons (1933) — p. 262
Editorial note, tabletop extrapolation: A boron target plus a blank plus a calibration face on one rotatable holder would let the builder switch targets and measure background without venting.
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Clean a PIPS face by first blowing dry air or N2 on the surface (to remove particles that could scratch), then swabbing with high-quality isopropyl alcohol - never methyl alcohol - and dry under vacuum 15 minutes or at 50 C for an hour before re-biasing. Cleaning may reduce contamination-related surface leakage but will not reverse bulk radiation damage.
Source quote & editorial note
PIPS detectors have an ion implanted entrance window of about 500 A thickness. ... To clean standard PIPS detectors first blow dry air or N2 gas on the surface to remove particles that might cause scratches ... use a cotton ball dampened with a good quality isopropyl alcohol; Do not use methyl alcohol ... put under vacuum for 15 minutes or heat to 50 C for an hour to remove residual moisture before applying bias.
Canberra, PIPS Detector Instruction Sheet (2012) — p. 1
Editorial note, tabletop extrapolation: The ~500-angstrom implanted window (the manual's figure) scratches easily; in a chamber with pump oil and target debris, stick to the manual's procedure.
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Operate the BKPD 50-11-500 PIPS at its recommended +130 V bias (full depletion +110 V) and never exceed the +150 V maximum bias.
V_rec = +130 V; V_full_depletion = +110 V; V_max = +150 V; depletion 500 um, chip 501 um, 8000 ohm-cmSource quote & editorial note
Recommended bias voltage +130 Volts ... Full depletion bias voltage +110 Volts ... Maximum bias voltage +150 Volts
Canberra, PIPS Detector Instruction Sheet (2012) — p. 2-3
Editorial note, tabletop extrapolation: The reference machine's two detectors (S/N 98343/98344) have only 20 V of headroom above recommended bias; a supply glitch to 150+ V risks breakdown, so use a current-limited, capped supply.
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Estimate front-end noise of a CR-RC shaper from Qn^2 = 12*tau*IB + 6e5*tau/RP + 3.6e4*vn^2*C^2/tau (rms electrons; tau in ns, IB in nA, RP in kOhm, vn in nV/rtHz, C in pF); the optimum tau balances the capacitance (series) term against BOTH parallel terms: tau_opt = sqrt(3.6e4*vn^2*C^2 / (12*IB + 6e5/RP)). Converting to energy: 3.6 eV mean energy per electron-hole pair in silicon.
Qn^2 = 12 tau IB + 6e5 tau/RP + 3.6e4 vn^2 C^2/tau [rms e-]; tau_opt = sqrt(3.6e4 vn^2 C^2/(12 IB + 6e5/RP)); sigma_E = 3.6 eV * Qn, FWHM_elec = 2.355 sigma_E (Si)Source quote & editorial note
en2 = 12 tau IB + 6e5 tau/RP + 3.6e4 vn2 C2/tau [rms electrons]
Spieler, Semiconductor Detectors Part 2 — SLUO Lectures on Detector Techniques, Lecture 7 (1998) — p. 42
Editorial note, tabletop extrapolation: Computes the expected electronic FWHM of the PIPS chain from datasheet numbers before buying a shaping amplifier, and says how tau should move if leakage rises - combine electronic, statistical and charge-collection terms in quadrature for the total resolution.
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Radiation-induced leakage current grows linearly with fluence, dI = alpha*Phi*(A*d), with alpha ~2e-17 A/cm for 1 MeV neutrons (3e-17 for 650 MeV protons) at room temperature.
dI = alpha * Phi * A * d; alpha(1 MeV n) = 2e-17 A/cm, alpha(650 MeV p) = 3e-17 A/cmSource quote & editorial note
For 650 MeV protons alpha = 3e-17 A/cm, 1 MeV neutrons alpha = 2e-17 A/cm.
Spieler, Semiconductor Detectors Part 2 — SLUO Lectures on Detector Techniques, Lecture 7 (1998) — p. 51-52
Editorial note, tabletop extrapolation: Track the PIPS bias current on the Keithley 617 as a damage INDICATOR: an unexplained, temperature-corrected secular rise warrants investigating beam or neutron exposure - after ruling out temperature (leakage roughly doubles per ~7 C), humidity/surface leakage and annealing history; raw current is not a calibrated dosimeter.
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Near the 675 keV resonance of 11B(p,alpha), the measured alpha angular distribution is nearly isotropic (|A1|,|A2| a few percent of A0 in the cited coefficients), while the 2.64 MeV resonance shows visible anisotropy.
at 0.65 MeV: A0=218.4, A1=-3.2, A2=6.3 mb/sr (isotropic to ~3%)Source quote & editorial note
While the resonance at 0.675 MeV exhibits isotropy, anisotropy can be seen for the resonance at 2.64 MeV
Spraker et al., The 11B(p,α)8Be → α+α and the 11B(α,α)11B Reactions at Energies Below 5.4 MeV (2012) — p. 358-360
Editorial note, tabletop extrapolation: For yield measurements NEAR the 675 keV resonance, detector angle costs only a few percent, so geometry and shielding can drive PIPS placement - at other beam energies get angular-distribution data or carry an anisotropy uncertainty, and remember angle still affects kinematic acceptance and scattered-particle background.
Cited in: Experiments by Energy Band
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Silicon detectors for p-B11 alphas, as fielded in the cited experiment: eight detectors at 30-160 degrees, 16.5 cm from the target, ~2.5e-4 sr each, thick enough to stop the alphas at all energies; their spectra show a large elastically-scattered-proton peak (just below 1 MeV at the cited beam energies) alongside the alpha peaks.
cited setup: 8 detectors at 30-160 deg, r = 16.5 cm, dOmega ~ 2.5e-4 sr each; elastic-proton peak position follows beam energy and angleSource quote & editorial note
The detectors were located 16.5 cm from the target ... 60, 75, 90, 115, 135, and 160 [degrees], with each detector subtending a solid angle of approximately 2.5 x 10-4 sr. ... The large peak just below 1 MeV is produced by elastically scattered protons
Spraker et al., The 11B(p,α)8Be → α+α and the 11B(α,α)11B Reactions at Energies Below 5.4 MeV (2012) — p. 358-360
Editorial note, tabletop extrapolation: Expect the PIPS spectra to carry a scattered-proton peak wherever two-body kinematics puts it for the actual beam energy and detector angle - compute that first, then set the alpha window or choose an absorber; a proton-stopping foil also costs the alphas energy and straggling, so evaluate it with stopping-power numbers before committing.
Cited in: Experiments by Energy Band
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The cited experiment's p-B11 target: 56 +/- 2 ug/cm2 of isotopically pure 11B on a 9 ug/cm2 carbon backing, thickness measured two independent ways - via the known elastic/Rutherford cross-section ratio for alphas at 4.86 MeV and 165 deg, and via the energy-broadening of the elastic peak - agreeing to a 3.6 percent systematic uncertainty in yields.
target 56 +/- 2 ug/cm2 11B on 9 ug/cm2 C; thickness via elastic alpha scattering at 165 deg, 4.86 MeVSource quote & editorial note
the target, which was composed of 56 +/- 2 ug/cm2 of isotopically pure 11B deposited on a 9 ug/cm2 carbon backing. Target thickness was measured using elastically scattered a-particles at 4.86 MeV, where the ratio of the elastic scattering cross section to the purely electromagnetic Rutherford cross section is known at a scattering angle of 165 deg. This measurement provided two independent measures of the target thickness via the known cross section and via the energy loss as measured by the broadening of the elastic peak. Analyses of both results agree and provide a target thickness of 56 +/- 2 ug/cm2 leading to a 3.6% systematic uncertainty in our yields.
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: Defines 'thin' for the reference machine's boron target (tens of ug/cm2) and gives two thickness checks performable with their own detectors - reproducing the alpha-scattering one requires the stated alpha energy and angle where the ratio to Rutherford is known, plus calibrated fluence and solid angle.
Cited in: Experiments by Energy Band
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For thermal-neutron activation or moderated counting in the cited setup, a 3.89 cm (~1.5 inch) HDPE layer gave the peak capture rate with the moderator as close to the source as possible; their activation chamber backed the silver target with a second HDPE layer.
HDPE moderator thickness ~3.89 cm for peak capture; Ag-108 t1/2 2.37 min activation targetSource quote & editorial note
a peak capture rate is obtained with a 3.89 cm layer of HDPE. This detection method involves positioning the HDPE as close to the neutron source as possible ... A piece of silver ... and its subsequent radioactive decay can be measured. An activation chamber was made HDPE with another layer behind the silver
Kovalchick, Deuterium Fusion Using Inertial Electrostatic Confinement (2012) — p. 23-24
Editorial note, tabletop extrapolation: If the builder cross-checks PIPS counting with activation or a moderated tube (e.g., for D-D work), start from the cited thickness but optimize for the actual geometry - a thickness scan or transport estimate - since the optimum moves with source spectrum and arrangement. Ag-108 (t1/2 2.37 min) remains the classic activation target.
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The cited design traces its central-region accelerating-gap voltage boundary at 1.3-1.4 times the Kilpatrick criterion f(MHz) = 1.64*E^2*exp(-8.5/E) (E in MV/m) - an empirical benchmark for RF vacuum gaps, not a guarantee.
Kilpatrick: f[MHz] = 1.64*E^2*exp(-8.5/E), E in MV/m; cited machine's adopted boundary: <= 1.3-1.4 x KilpatrickSource quote & editorial note
the common boundary of the maximum voltage in the accelerating gaps in the central region of the accelerator is traced, which is 1.3-1.4 times higher than the Kilpatrick criterion
Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 57-58
Editorial note, tabletop extrapolation: The right sizing framework if a next machine pushes dee voltage to tens of kV across small central-region gaps: compute the LOCAL peak surface field from the electrode geometry (not the average gap field), compare against Kilpatrick as a benchmark, and plan on conditioning and breakdown testing - margin is demonstrated, not assumed.
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Optimize the internal-source slit with chamfer angles of 40-60 degrees, and make the slit's axial size several times its radial size; slit shape strongly changes extracted current (calculated spread 90-850 nA between variants).
chamfer angle 40-60 deg; axial/radial slit size ratio ~ several; the source's Fig. 56 slit variants span max I = 90-850 nASource quote & editorial note
The shape of the source slit, when its axial size is several times larger than the radial one, is most frequently used... They are optimized according to the chamfer angle, which is usually 40-60 degrees. ... the angle of the chamfers directly affect the magnitude of the beam current extracted from the source, which is confirmed by numerous calculations [132] and measurement results (Fig. 56).
Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 52-53
Editorial note, tabletop extrapolation: Cheap, high-leverage geometry rule for the reference machine's PIG-style source: start from a tall-and-narrow slit with ~45-degree chamfers - the source's most-used geometry - then optimize against measured beam, since the chamfer angle demonstrably moves extracted current by an order of magnitude across variants.
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With external axial injection, choose an injection energy (in eV per charge) below the dee voltage amplitude: the first gap crossings then rapidly enlarge the orbit, minimizing central-structure size and radial losses.
E_inj/q < U_dee (injection energy less than accelerating-voltage amplitude)Source quote & editorial note
the optimal case from the viewpoint of minimizing the radial beam losses is a mode of operation in which the value of the injection energy is less than the amplitude of the accelerating voltage across the dees
Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 55-56
Editorial note, tabletop extrapolation: If a next machine ever moves to an external source and axial injection: the cited criterion (injection energy per charge below the dee amplitude) minimizes radial losses by letting the first gap crossings enlarge the orbit fast - set the actual injection energy jointly with inflector acceptance, transport and RF capture, not from the radial-loss criterion alone.
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In the cited design context, the transition to high-intensity (space-charge-dominated) operation is most often placed at a few hundred microamperes of beam current.
cited rule of thumb: high-intensity boundary ~ few 100 uA; check by comparing the space-charge term against emittance and focusing terms (generalized perveance / tune depression), using PEAK currentSource quote & editorial note
Most often, the boundary of the transition to high intensities is determined at the level of a few hundred microamperes.
Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 40
Editorial note, tabletop extrapolation: The reference machine's nA-uA beams sit far below the cited boundary, so omitting space-charge solvers is a reasonable default for the builder tool - but earn it with one calculation: peak (bunched) current through the low-energy first turns is where space charge bites first, so run the perveance estimate there before declaring it negligible.
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Lorentz (magnetic) stripping of H- has rest-frame lifetime tau = (A1/E)*exp(A2/E) with A1=2.714e-6 s*V/m, A2=4.474e9 V/m, E=gamma*beta*c*B - negligible below a few MeV even at 4 T.
tau = (A1/E)*exp(A2/E), E = gamma*beta*c*BSource quote & editorial note
a 4 T magnetic field for the maximum achievable energy of 8.5 MeV in the AMIT cyclotron corresponds to a beam-rest-frame electric field of E = 160 MV/m. This entails a marginal beam fraction loss per unit length of 1.42e-6 m-1
Calvo et al., Beam Stripping Interactions in Compact Cyclotrons — PRAB 24, 090101 (2021) — p. 7-8, 14
Editorial note, tabletop extrapolation: At 0.889 T and 500 keV the rest-frame field is ~9 MV/m, where the exponential makes the lifetime effectively infinite - Lorentz stripping can be ignored entirely for a next machine.
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Cold-cathode arc power is limited to about 1 kW per cathode in the source's account, because thermal electron emission sets in beyond that; higher power means pulsing or accepting transition to the hot regime.
P_arc,max(cold, dc) ~ 1 kW per cathodeSource quote & editorial note
The arc power for cold cathode operation is limited to about 1 kW per cathode, because of the start of thermal electron emission
Wolf (ed.), Handbook of Ion Sources (1995) — p. 84
Editorial note, tabletop extrapolation: The reference machine's 50-150 W arc sits well below the cited onset, which makes cold (secondary-emission) operation the expectation - but confirm it: per-cathode heat loading, geometry and cooling set the actual cathode temperature, so check the buttons for signs of running hot rather than assuming the regime from arc power alone.
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In a heated-cathode PIG the anticathode is kept cold and collects a net electron current; more than -20 V of bias is needed to suppress it. Anticathode is usually strapped to cathode potential, sometimes left floating for space reasons.
V_suppress(anticathode) < -20 V; usual connection anticathode = cathodeSource quote & editorial note
More than -20 V is necessary to suppress this electron current ... The anticathode is usually connected to the cathode, but sometimes just floating because of space problems in some cyclotrons.
Wolf (ed.), Handbook of Ion Sources (1995) — p. 86
Editorial note, tabletop extrapolation: For the symmetric cold-cathode chimney, strap both cathodes together on one HV feed - that is the intended symmetric topology, not the anticathode case the quote describes. A floating anticathode is a documented space-saving variant in some cyclotrons; if used, verify its self-bias, stability and thermal loading, since floating changes the electron interception the strapped connection sets.
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PIG beam energy spread is tabulated at 10-50 V (read as eV per unit charge), with typical currents in the 5-500 mA class.
dE(PIG) = 10-50 eV per charge state; typical currents 5-500 mA class (source table)Source quote & editorial note
PIG ion source 10-50 [energy spread, V] 5-500 [typical ion current, mA] (Table 2.1)
Wolf (ed.), Handbook of Ion Sources (1995) — p. 51
Editorial note, tabletop extrapolation: Against a few-keV effective first-gap gain a 10-50 eV spread is a ~1 percent perturbation, so source simplicity is worth keeping - confirm with the machine's own capture/acceptance estimate, since capture depends on RF phase and central-region geometry, not the gap voltage alone; the filament-arc comparison needs its own source.
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Forringer chimney/slit trade (measured, 40 kV dc puller, 3 sccm H2): the 0.25 x 5.0 mm slit gives 52-227 uA at 50-450 mA arc (I_beam/I_arc ~ 1.0e-3 falling to 0.5e-3) with radial emittance ~25 mm-mrad independent of current; the 0.51 mm slit gives 230-590 uA at only 50-150 mA (~4.6e-3 x I_arc) but emittance grows with current (47 -> 65 mm-mrad). Wider slit = more current per arc-watt; brighter is narrower.
I_beam ~ (0.5-4.6)e-3 x I_arc for 0.25-0.51 mm slits at 40 kV dc extractionSource quote & editorial note
Table 3.4: Slit 0.010" 40 kV, 450 mA, 3.0 cc/min -> 227 uA; Slit 0.020" 40 kV, 150 mA, 3.0 cc/min -> 590 uA
Editorial note, tabletop extrapolation: Start a next machine with the 0.5 x 5 mm slit - at 50-150 mA arc it made 230-590 uA at 40 kV. A fixed-gap Child-Langmuir scaling to a 4 kV dee (V^1.5) would read ~7-19 uA, but treat that as a blackboard exercise, not available beam: RF extraction changes gap, meniscus and phase acceptance, so model the actual central region before booking any of it against the present 3 nA best.
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Chimney machining details from Forringer: slits chamfered 10 deg, relieved 0.010 in deep in a 0.020 in wall leaving a 0.010 in 'tunnel'; the hole chimney is 0.047 in (1.19 mm) diameter with a 60 deg chamfer. The hole chimney's radial normalized emittance (0.66 mm-mrad) ran about 50 percent larger than the slit's (0.44 mm-mrad); a flat plasma boundary best matched the slit beams, a highly concave one the hole beam. The thesis's Conclusion adds a beam datum: after the puller, slit-chimney beams averaged about 70 percent of the chimney opening's height - a beam-height-to-aperture ratio, not a chimney geometry ratio.
slit land/tunnel 0.25 mm, chamfer 10 deg (slit) / 60 deg (hole); emittance 0.44 (slit) vs 0.66 mm-mrad (hole)Source quote & editorial note
The slit chimneys produced a beam that was nearly horizontal (in z) and was, on average 70% as tall as the chimney opening after passing through the puller. The hole chimney produced a beam that (in the absence of strong focusing) diverged in z.
Forringer, Phase Space Characterization of an Internal Ion Source for Cyclotrons — MSU dissertation (2004) — p. PDF p. 121 (printed p. 111) for the 70% claim; PDF p. 84 (printed p. 74) for the Fig. 3.12 caption
Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: the actual machining callouts for a chimney a home shop can cut. The thin-land/outward-chamfer rationale (don't collimate the beam away; the thesis suggests deeper chamfers may raise current) is engineering reading of the source's optimization remarks.
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Siemens PET-source upgrades, as measured: grooved molybdenum anodes lowered arc power 7% and raised target beam 20% (material and groove tested together, not separated); a cesium getter pill in the cathode gave +26% beam at -25% arc power; thoriated-tungsten cathodes were a net loss; widening the plasma-to-wall 'cool ring' also gained beam - with the printed dimensions carrying an arithmetic slip: a 5.0 mm bore with the column collimated 4.0 -> 3.8 mm gives 0.50 -> 0.60 mm of ring, not the 0.70 previously stated (re-read queued for the true bore).
plasma-to-wall gap 0.5-0.7 mm (H- volume production); Mo grooved anode +20%; Cs pill +26%Source quote & editorial note
Ø5.0 mm Anode I.D. ... 0.5 mm Plasma Column to Anode Wall ... Ø4.0 mm Collimator I.D. ... Plasma column diameter is defined by the collimators, which have inside diameter of 4.0 mm.
Potkins et al., Improvements to Siemens Eclipse PET Cyclotron Penning Ion Source (2017) — p. bore and ring dimensions in Fig. 1b and its caption, PDF p. 2; the 'cool' region experiments on PDF p. 3
Editorial note, tabletop extrapolation: The cool-ring and Cs tricks are H(-)-specific; the transferable lessons for a positive-ion source are that geometry near the slit dominates output, molybdenum is a sound anode material, and exotic cathode materials earned nothing - with the grooved-anode gain belonging to the whole tested configuration, not to Mo as such.
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PIG thermal budget (IRANCYC-10, ~500 W total at 1.1 A discharge): cathode heads reach 1992 K from ion bombardment, anode peaks at 472 K adjacent to the exit slit, cathode thermal distortion 0.2 mm; 0.007-0.04 kg/s of 18 C water holds everything. Thermionic contribution at 1992 K is only 0.6% of the discharge current.
hot spots = cathode heads and slit region; ~0.5 kW needs ~0.01-0.04 kg/s waterSource quote & editorial note
the maximum temperature of the cathodes are 1992 K, which is far away from the cathode melting point ... an electron current of 0.00706 A at 500 V which is negligible in comparison to the discharge current of 1.10352 A
Zakerhosseini et al., Heat Transfer Study of PIG Ion Source for 10 MeV Cyclotron — IPAC 2016 (2016) — p. 1-3
Editorial note, tabletop extrapolation: At the reference machine's ~100 W arc the cathode heads may or may not run incandescent - temperature scales with T^4 radiation, bombardment distribution and contact conductance, none linearly with arc power. Mount the heads on refractory stems either way, and size the chimney's heat path (copper stalk to a cooled or finned flange) from a small thermal model or a calorimetric test, including what happens on loss of cooling.
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Verify dimensional stability before committing to high-saturation alloy shims: CIT repeated its Hiperco edge-shim tests and dropped the material after finding it dimensionally unstable.
Source quote & editorial note
The Hiperco tests were repeated but dropped when this material was found to be dimensionally unstable.
Creutz, Design and Construction of Synchro-Cyclotron — NYO-780 (1950) — p. 9
Editorial note, tabletop extrapolation: Any exotic Co-Fe edge ring for the next machine's pole edge needs dimensional and magnetic checks after machining, heat treatment, assembly and excitation cycling - modern grades and treatments may behave differently from CIT's stock. Low-carbon steel is the conventional baseline, not a guaranteed adequate answer.
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Before freezing the design, CIT machined a final pair of model poles from the same steel forgings used for the full-scale poles and re-verified the shim performance - repeat the model validation with production-representative pole steel.
Source quote & editorial note
A final pair of model poles was machined out of the steel forgings actually used for the full-scale magnet poles. The results were satisfactory, and the design was frozen.
Creutz, Design and Construction of Synchro-Cyclotron — NYO-780 (1950) — p. 10
Editorial note, tabletop extrapolation: Transferable principle: validate on material representative of the production poles - measure coupons from the actual pole stock or the finished poles themselves; same-lot shim stock is a reasonable extra precaution but is beyond what the source demonstrates.
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When welding cases or fittings around finished coil windings, mask every metal seam (CIT: glass tape) so weld flash cannot reach the insulation.
Source quote & editorial note
Glass tape is inserted along all metal seams to prevent weld-flash from entering the can.
Creutz, Design and Construction of Synchro-Cyclotron — NYO-780 (1950) — p. 14
Editorial note, tabletop extrapolation: Directly applicable craft rule for welding on or near a next machine's coil case: glass tape or an equivalent temporary barrier keeps weld flash and spatter out of the can. It does nothing against brazing flux, molten filler or conducted heat - hot work near a wound coil also needs thermal protection and temperature monitoring, or should be finished before winding. [Note revised 2026-08-23: earlier note extended the barrier to 'any welding or brazing'.]
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Size dee-to-ground vacuum clearance from RF voltage the way the 184-inch did: a 3-inch minimum at the hot open dee end for 50 kV RF, relaxing to 2 inches at the supported (low-voltage) end - informed by their bench result that a polished 0.080-inch copper gap held 50 kV at 13 Mc and ~5e-6 mm.
184-inch design points: 3 in at 50 kV (open end), 2 in (supported end); bench: 0.080 in polished Cu gap held 50 kV at 13 Mc, ~5e-6 mm - NOT a linear kV/inch lawSource quote & editorial note
the vacuum gap be sufficient to withstand 50 kilovolts rf at the accelerating gap. Consequently, a minimum of 3" spacing was employed in the vicinity of the open front end of the dee; near the rear end (i.e. supported end) a minimum of 2" was allowed. ... [a] 0.080" 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. 10
Editorial note, tabletop extrapolation: Do not scale these linearly: vacuum holdoff is nonlinear in gap and dominated by geometry, finish and conditioning (their own bench gap held the same 50 kV across 0.080 inch). Set a next machine's clearance by electrostatic analysis of the actual geometry with conservative peak-field limits, then prove it by conditioning at full voltage.
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Check for a re-entrant cavity resonator mode between the two magnet pole pieces with the vacuum tank walls as the return circuit; the 184-inch found one near its lower frequency limit and suppressed it easily by strapping the pole pieces together.
Source quote & editorial note
disclosed a re-entrant cavity resonator mode between the two pole pieces of the magnet with the vacuum tank walls as the return circuit resonant near the lower frequency limit. This was easily suppressed by strapping the pole pieces together.
MacKenzie et al., Design of the Radio-Frequency System for the 184-inch Cyclotron — UCRL-64 (1948) — p. 22
Editorial note, tabletop extrapolation: The pole-chamber geometry of an 8-inch machine forms the same class of parasitic cavity - sweep or model the assembled structure, and add a verified pole-to-pole RF bond if a mode lands near the operating band; don't strap preemptively, since added straps can perturb the intended RF structure or form current loops.
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The 37-inch built low-inductance grid/bypass capacitors as flat metal rings with radiused (1/8 inch) edges over 0.010-inch polystyrene - good in their service for >15 kV DC and ~1500 V RF, but only while the metal parts stayed cool.
0.010 in polystyrene sandwich -> >15 kV DC, ~1500 V RF when coolSource quote & editorial note
Polystyrene of this thickness used in this manner will stand over 15,000 volts DC and approximately 1500 volts r.f. provided the metal parts remain cool.
MacKenzie & Waithman, R.F. System for Frequency Modulated Cyclotron — MDDC-1045 (1946) — p. 8
Editorial note, tabletop extrapolation: A historical construction worth knowing, not a transferable rating: the implied DC stress is ~59 kV/mm, so the numbers belong to that geometry, cooling and test practice. For a next machine's RF chain, prefer certified RF/HV capacitors; if building, take the dielectric's own data (Kapton is often lossier than polystyrene or PTFE at RF), derate heavily, design creepage and corona control, and test thermally and at withstand voltage.
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An in-tank DC electrostatic deflector electrode held about 60 kV in the operating 184-inch cyclotron - amid magnetic field, RF, and beam - a demonstrated 1947 operating value (fed, per the report, through a current-limiting series resistor; scan re-read queued for its value).
Source quote & editorial note
Approximately 60 kv could be held on the high voltage electrode of this deflector.
Sewell, 184″ Cyclotron: Vertical D.C. Electrostatic Deflector — MDDC-1051 (1947) — p. 2
Editorial note, tabletop extrapolation: Compute the next machine's required deflector field from beam rigidity, channel length and allowed interception - then design insulation, clearances and stored-energy limiting for that voltage in its own right. The series spark-limiting resistor is worth copying; the assumption that deflector HV is low-risk is not.
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Let the current-limit reference track the RF plate (output) voltage so that plate dissipation, not plate current, is what is held constant: the amplifier is then protected when the dee circuit is tuned off resonance, while full power remains available when properly tuned. [Corrected 2026-08-23: the earlier formula implied I_limit proportional to V_rf is itself the protection; it is one input to a dissipation estimate, and the note below says what else an LDMOS stage needs.]
Limit on estimated device dissipation, e.g. P_dc_in - P_rf_out, or Vds*Id averaged over the RF cycle - not a fixed current clamp, and not simply I_limit ~ V_rfSource quote & editorial note
to let the reference voltage vary with the rf plate voltage so that plate dissipation would be limited to a constant value
Editorial note, tabletop extrapolation: The LDMOS analogue (editorial transfer, informed by modern device practice rather than this source): foldback on a calibrated dissipation estimate - DC input minus delivered RF between defined measurement planes (which lumps matching-network loss into the estimate), or cycle-averaged <vds(t)*id(t)> - tightened under mistuning. Dissipation limiting is one protection layer, not sufficient: add drain-voltage clamping, a reflected-power/VSWR trip, device-temperature sensing and fast fault shutdown, since LDMOS also dies of RF-cycle overvoltage, mismatch and fast thermal transients.
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Be wary of vacuum capacitors in the high-power PA plate circuit - in this system every vacuum-capacitor arrangement tried in the final plate circuit failed, and the design settled on fixed capacitive coupling plus a movable-short coaxial resonator.
Source quote & editorial note
vacuum capacitors have been used in various ways in its plate circuit. None has been found to stand up satisfactorily.
Editorial note, tabletop extrapolation: Dated in absolute terms - but 'modern vacuum caps are fine at kW-class' is a ratings question, not a vintage question: they are suitable where the manufacturer's peak-voltage, RF-current, frequency and thermal ratings are met with margin, and fault energy is considered. The placement lesson stands either way: put lumped variable capacitors where RF current is low and do coarse tuning with distributed elements.
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Squaring the dee waveform by adding a 1/3-amplitude third harmonic attacks what the source calls ordinarily a major beam-loss mechanism: it minimizes the axial electric defocusing force and even provides some focusing during the usually defocusing part of the phase excursion, where magnetic focusing is weakest.
V(t) ~ sin(wt) + (1/3)sin(3wt) (first two Fourier terms of a square wave)Source quote & editorial note
It minimizes electric defocusing, which is ordinarily a major cause of beam loss, and actually provides some focusing during the usually defocusing part of the phase excursion.
Goodman, A Square-Wave Cyclotron Oscillator — ORNL-2403 (1958) — p. 10-11
Editorial note, tabletop extrapolation: Electric defocusing on the first turns is a plausible and testable contributor to the reference machine's losses - not an established attribution; a flat-topped dee is likely too much RF plumbing for a next machine, but the mechanism explains why phase excursion and gap-crossing timing deserve modeling attention in any small machine.
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The source's analysis found the same central-region bunching occurs even with a third harmonic added to square the RF waveform - ions still group to cross the gap near the fundamental's peak - so flat-topping and automatic phase grouping coexisted in that analysis.
dominant term -w*t*sin(wt+theta) unchanged by third harmonic (Appendix I)Source quote & editorial note
the same bunching occurs even if a third harmonic is added to the r-f wave form to square the wave
Goodman, A Square-Wave Cyclotron Oscillator — ORNL-2403 (1958) — p. 10
Editorial note, tabletop extrapolation: Reassurance that waveform shaping and center-region bunching are separable problems in the source's treatment; any claimed voltage benefit depends on harmonic amplitude/phase and what is held fixed (peak voltage vs RF power), so quantify longitudinal acceptance by calculation before banking on it. The bunching mechanism itself (Cohen) is what sets which ions survive the center region. OCR note - theta prints as (c) in these appendix equations.
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To make one dee resonate simultaneously at the fundamental and third harmonic, terminate the dee capacitance in two shorted transmission-line stubs whose electrical lengths satisfy cot(a1 w) + b cot(a2 w) - ac w = 0 with w=1 and w=3 as roots; a coax bench model matched calculated lengths within about 2%.
cot(a1*w) + b*cot(a2*w) - ac*w = 0 with roots at w=1 and w=3; solving both conditions gives b13 = (cot(3*a1) - 3*cot(a1))/(3*cot(a2) - cot(3*a2)); a1 < pi/3 < a2Source quote & editorial note
The extra current element can, however, be a second transmission line
Goodman, A Square-Wave Cyclotron Oscillator — ORNL-2403 (1958) — p. 18
Editorial note, tabletop extrapolation: A lumped-plus-stub version is buildable at tabletop scale and the design tables (PDF 33-60) are precomputed; even unused, the method shows how to place a resonator's higher modes deliberately instead of discovering them by accident.
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Tune a dual-resonance system iteratively, one frequency at a time (the source's five-step procedure): null the input admittance at the fundamental with one line length; measure the admittance sign at the third harmonic; trade length between the two lines while keeping the fundamental nulled, using the sign and interpolated tables (its Appendix III) to know which way to tune; repeat until both frequencies null.
Source quote & editorial note
The following tuning procedure was found to be easy to follow: 1) Set the oscillator frequency at w0 and set the admittance meter to the correct reading for zero admittance at the junction to the system. 2) Tune the length of one of the lines for a null on the admittance meter. 3) Set the oscillator frequency to 3w and measure the admittance; note whether it is positive or negative. 4) Return to w0 and change a1, compensating with a change in a2 to keep the system tuned to w0. One can determine which way to tune by comparing the position of the resonances with numbers interpolated from Appendix III. 5) Remeasure admittance at 3w, and repeat the procedure until the admittance measures zero at 3w.
Goodman, A Square-Wave Cyclotron Oscillator — ORNL-2403 (1958) — p. 21
Editorial note, tabletop extrapolation: The written five-step procedure is a model for documenting any coupled-adjustment RF tune-up - a next machine's coupling loop and trimmer interact the same general way; precomputed knowing-which-way-to-tune tables are the transferable trick, though the dual-line tables themselves don't map onto a different topology.
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A single quarter-wave coupling line can feed both the fundamental and third harmonic to the resonator: an (ideally lossless, nondispersive TEM) line that is lambda/4 at the fundamental is 3*lambda/4 at the third harmonic and inverts impedances at both frequencies - if the resonator is tuned resistive at both, the driver sees resistive loads at both.
l = lambda1/4 = 3*lambda3/4; Z_in = Z0^2/Z_load at both frequenciesSource quote & editorial note
if the coupling line is one-quarter of the fundamental wave length it is three-quarters of the third harmonic wave length, and the impedances are simply inverted by the line at both frequencies
Goodman, A Square-Wave Cyclotron Oscillator — ORNL-2403 (1958) — p. 22
Editorial note, tabletop extrapolation: A handy odd-harmonic identity - and a warning that a quarter-wave feeder presents TRANSFORMED impedances to your amplifier's harmonics even in a plain sine-wave system: evaluate the actual harmonic load with Z0(f) and measured S-parameters (connectors and loading shift the third-harmonic electrical length) before assuming either benefit or instability.
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Ion bunching by the RF displaces orbit centers by Delta-r = 2D sin(theta) with D = eV/(2*m*omega^2*d); in the ORNL Analogue I example this was equivalent to ~20 turns, ~2 kV, or ~1% energy spread at the exit radius.
Delta-r = 2*D*sin(theta), D = eV/(2*m*omega^2*d) characteristic bunching displacementSource quote & editorial note
the radial displacement amplitude is equivalent to about twenty turns, or to about two kilovolts, or about 1% spread in energy at the exit radius
Goodman, A Square-Wave Cyclotron Oscillator — ORNL-2403 (1958) — p. 12
Editorial note, tabletop extrapolation: Budget this effect for any future extraction work by evaluating D and Delta-r with the machine's own V, omega, gap and phase distribution and tracking the offsets to extraction - the ORNL equivalences are that machine's numbers, not a floor. Flat-topping reduces the phase-dependent part; neither AVF nor flat-topping removes the displacement wholesale.
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Build the tuning-loop phase detector to null exactly at the desired phase with high, KNOWN sensitivity: the cited detector produced 0.76 V per degree of phase error (its null-point phase and sign convention are the report's circuit details - re-read queued).
K_d = 0.76 V/deg at the nullSource quote & editorial note
The phase detector is quite sensitive and produces an output signal of 0.76 volt for a phase error of 1
Smith, A Three-Phase Radiofrequency System for Cloverleaf Cyclotrons — UCRL-3153 (1955) — p. 13
Editorial note, tabletop extrapolation: Characterize K_d on the actual detector near the chosen null so loop gain is a number, not a knob - then size downstream amplification from the full loop model (actuator, mechanics, delays). Modern detector options span analog slopes to charge pumps to digital outputs; their gain is a datasheet-plus-measurement fact, not a folklore mV/deg figure.
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A 45-degree (lambda/8) transmission line makes a constant-amplitude phase shifter: for an ideal lossless line with resistive termination, |Z_in| = Z0 independent of the load resistance, so driving from a constant-current source and servo-varying a load pot (250-ohm, ~7 ft of RG-58 at 11.2 Mc in the cited system) shifts phase without changing amplitude.
45-deg (lambda/8) line; |Z_in| = Z0 independent of R_L; phase of V_in depends on R_LSource quote & editorial note
if the line is excited from a constant current source the magnitude of the voltage appearing across the input of the line is constant but the phase of the voltage depends upon the load resistance
Smith, A Three-Phase Radiofrequency System for Cloverleaf Cyclotrons — UCRL-3153 (1955) — p. 11
Editorial note, tabletop extrapolation: A DDS sets phase digitally today, but the lambda/8 trick remains a zero-active-parts phase adjuster and a nice classroom transmission-line demonstration - measure the residual amplitude variation of the real cable, pot parasitics and finite source impedance before using it where amplitude flatness matters.
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With spark-current control at the supply and tungsten anodes, the report could compensate for deflector capacitance: at lower capacitance they could crowbar at higher spark currents, and vice versa (their tests spanned tens to hundreds of pF - figures queued for scan re-read).
compensation relationship: lower C_deflector <-> higher tolerable crowbar current; re-optimize the crowbar per configurationSource quote & editorial note
we could compensate for deflector capacitance; at lower capacitance we could crowbar at higher spark currents, and vice versa.
Editorial note, tabletop extrapolation: Cable and feedthrough capacitance in a tabletop deflector still stores 0.5*C*V^2 right at the gap, where a supply-side crowbar cannot intercept it - so it is a design input, not a non-issue: compute the local stored energy at maximum voltage and add local series impedance or other discharge-energy limiting, then set the crowbar point for the configuration as the source did.
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In the cited 100-kc stack, diode storage time did not spoil rectification into the capacitive load - the load still charged to peak. (The report also irradiated diodes to improve rectification above 100 kc; the direction and size of the back-resistance change need the scan re-read before quoting.)
cited circuit: ~2 us storage acceptable at 100 kc into a capacitive loadSource quote & editorial note
the diode charges a capacitive load to the peak value, and the stored charge does not subtract (appreciably, at any rate) from the output voltage.
Smith, Deflector Power Supply for Sector-Focused Cyclotrons — UCRL-10655 (1963) — p. 10
Editorial note, tabletop extrapolation: Historical for parts choice - modern fast-recovery diodes moot the issue - and do NOT generalize the tolerance: reverse-recovery charge at 100 kHz can mean reverse current, heating, and poor sharing in other topologies. Select diodes on reverse voltage, recovery charge, leakage and sharing arithmetic; spend the savings on voltage rating and grading.
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Regulation is limited by the precision divider: for 0.01% deflector-voltage stability the cited system's divider resistors had to track within about 3 C of each other (the carrier-frequency, loop-bandwidth and divider-construction details are the report's - re-read queued).
f_carrier 100 kc -> f_unity 2500 c/s; 0.01% regulation; divider spec 36 ppm/C, dT < 3 CSource quote & editorial note
for a stability of 0.01% the temperature difference between resistors must be within about 3 C.
Smith, Deflector Power Supply for Sector-Focused Cyclotrons — UCRL-10655 (1963) — p. 21
Editorial note, tabletop extrapolation: Deflector voltage stability maps directly (first-order) to extracted-beam steering stability, so buy or build the divider first - and set the actual tolerance from a beam-clearance budget at the septum (beam size, orbit spacing, drift) rather than assuming either 0.01% is needed or 1% is fine.
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Derate pulsed switches for what operation does to them, not the data sheet: 5C22 thyratrons rated 16 kV could not run above 11 kV because the plate voltage reverses in 0.3 us each shot, arcing plate to grid; and where duty exceeds one tube's peak-current rating the report parallels tubes with ballast inductances (their ~5000 A service).
operate 5C22 at <=11 kV (rated 16 kV) under 0.3-us voltage reversal; parallel N tubes with ballast inductance to share 5000 A each bank (verified on page image)Source quote & editorial note
the switch must pass a peak current of 5000 amperes per transformer ... 8 in parallel on each transformer or 16 in all and introducing a very small inductance in each plate lead to make the tubes share the load
Kerns et al., High Voltage Pulser for 184-inch Cyclotron Electric Deflector — UCRL-95 (1948) — p. PDF p.13 (printed p.-10-)
Editorial note, tabletop extrapolation: The derating discipline - waveform-specific stress, not catalog rating - transfers to every switching element an amateur uses: MOSFET/IGBT avalanche and dV/dt limits in a Marx or inverter play exactly the role the 5C22's reversal limit played here.
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To fire many parallel switches simultaneously, the cited system fed the grids from artificial transmission lines: a 1000-V, 20-ohm trigger of ~0.20 us produced positive ionization of all the tubes in 0.10 +/- 0.01 us (the tube count and per-tube line topology are the report's construction - re-read queued).
per-tube pulse-forming line, 1 kV / 20 ohm / 0.2 us; jitter < 0.01 us across 16 tubesSource quote & editorial note
These lines provide a 1000 volt trigger of 20 ohms impedance for approximately 0.20 microseconds. Applying this trigger to the grids results in positive ionization of all the tubes in 0.1 +/- 0.01 us.
Kerns et al., High Voltage Pulser for 184-inch Cyclotron Electric Deflector — UCRL-95 (1948) — p. 13
Editorial note, tabletop extrapolation: Relevant only if a next machine adds a pulsed element (fast chopper, time-of-flight kicker): pulse-forming-line triggering is the classic paralleling technique, one option beside modern isolated solid-state drivers - and note the quoted 0.1 +/- 0.01 us is turn-on delay with spread, from which inter-channel jitter is bounded, not measured.
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Specify pulse-discharge capacitors for the real waveform: they had to survive complete charge reversal in 0.3 us, 100 times per second - the best commercial units (GE 0.03 uF / 16 kV, four paralleled per transformer) still failed every 10-20 hours at 11 kV, and their ~0.13 uH internal inductance ate the rise-time budget (total allowance ~0.1 uH referred to the primary). A one-ohm line of 50 paralleled RG-8U cables worked electrically but was abandoned as bulky (6000 ft of cable).
reversal stress 0.3 us full reversal at 100 pps; L_internal 0.13 uH vs 0.1 uH total budget; MTBF 10-20 h (verified on page image)Source quote & editorial note
the capacitor must withstand a complete reversal of charge in 0.3 us 100 times a second without failure.
Kerns et al., High Voltage Pulser for 184-inch Cyclotron Electric Deflector — UCRL-95 (1948) — p. 14
Editorial note, tabletop extrapolation: Two lessons that outlive the hardware: (1) reversal fraction and reversal time belong in a pulse capacitor's complete duty spec - alongside peak/RMS current, dV/dt, temperature and derating, all of which shorten life too; (2) ESL budgets, not just C and V, set rise time. The paralleled-coax alternative is a distributed pulse-forming line, not a lumped capacitor - engineer it as one (impedance, delay, termination, voltage rating, stored energy).
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RF resonant extraction, as the source frames the choice: among the allowed drive harmonics l, choose the smallest - it needs the least precise match between perturbing frequency and particle motion, which matters where the edge field (and radial tune) changes rapidly (the force model, sector geometry and resonance equation are the report's analysis - re-read queued).
omega = omega0*2*sqrt(1-n)/l, l = 1,2,3...; perturbation F = A*rho*cos(omega*t) for rho>0 in a 60-deg sectorSource quote & editorial note
It is an advantage to choose the smallest value of l, since the choice allows the least sensitivity in matching the perturbing frequency to the particle motion.
Stubbins, Radiofrequency System for Extracting Particles from a Cyclotron — UCRL-8578 (1958) — p. 7
Editorial note, tabletop extrapolation: A candidate extraction assist worth a TRACKER experiment before hardware: note that for l = 1 with nu_r near 1 the drive lands near TWICE the revolution frequency, and the required gradient, electrode voltage, bandwidth against tune spread, and isolation from the main RF are exactly what the tracking study must produce before 'an electrode pair and a small oscillator' can be promised.
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The rf gradient needed is modest: the study's IBM 650 median-plane orbit calculations used E = 4.3 kV/cm (design ceiling 'less than 5 kV/cm') applied over a 100-160 degree azimuth region beyond the synchronous radius, for 50-MeV deuterons at 17 kG (n = 0.1) - a field the authors believed easily obtainable from an oscillator independent of the main dee rf, tunable in frequency and amplitude.
E_rf = 4.3 kV/cm, 60-deg sector, two parabolic + one flat electrode; 50-MeV deuterons, B = 17 kG, r0 = 33.68 in, n = 0.1Source quote & editorial note
where we use E = 4.3 kv/cm as the electrical gradient. ... This rf electrical-field gradient, less than 5 kv/cm, is believed to be easily obtainable by an oscillator which is independent of the cyclotron oscillator and which can be tuned to the optimum frequency and amplitude. ... Calculations on the IBM 650 have been done in the median plane only. The perturbation is introduced when the particle is beyond the synchronous radius in a region from 100 to 160 [deg].
Stubbins, Radiofrequency System for Extracting Particles from a Cyclotron — UCRL-8578 (1958) — p. 8
Editorial note, tabletop extrapolation: At a next machine's scale the voltages are small - 4.3 kV/cm across a 2 mm gap is ~860 V peak - but feasibility still means vacuum-RF behavior, feedthroughs, tuning and breakdown checks, and the scheme was never demonstrated on hardware in this report: a promising computed option, not proven practice.
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Do not expect an rf perturbation to kick particles out in one pass: in the analyzed arrangement, orbit precession caused repeated phase-dependent encounters with the perturbation, and ultimately all particles were perturbed to larger radial oscillation amplitudes.
amplitude growth is episodic over many turns; ultimately all phases perturbed to large amplitudeSource quote & editorial note
because of the precession of orbits all particles are ultimately perturbed to larger radial oscillation amplitudes.
Stubbins, Radiofrequency System for Extracting Particles from a Cyclotron — UCRL-8578 (1958) — p. 9
Editorial note, tabletop extrapolation: Sets expectations for any resonant/precessional scheme on a next machine: the growth is episodic over many turns, so judge schemes in the tracker by turns-to-extraction and septum-hit fraction rather than single-pass kick size - the detailed evolution is deterministic and scheme-dependent, so track your own.
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Negative dee bias can substitute weakly for an accelerating slit: on the 22-inch, increased (negative) dee bias raised full-radius beam by up to 30%, but only with no accelerating slit mounted - ORNL reports the effect 'is not observable when an accelerating slit is used'. [Corrected 2026-08-23: the earlier rule also said the slit 'outperforms the optimum bias'; the source shows the two are not additive, not that one beats the other. The sign of the bias and the with-slit null are on the cited page, just outside the quote - ORNL-1339 p. 16: 'This effect is not observable when an accelerating slit is used' and 'the increased negative bias potential gives non-optimum-phased ions ... a deeper penetration into the rf electric field'.]
Source quote & editorial note
an increase in bias potential on the dees increases the beam accelerated to maximum radius by a factor of as much as 30% when the cyclotron is operated without an accelerating slit (rf) mounted on the dee.
Editorial note, tabletop extrapolation: Worth a cheap experiment on the reference machine - with a proper RF-rated bias-injection network (choke/filter, insulation, supply protection), never a bare DC supply on a live dee. ORNL's stated reading is that bias pulls badly-phased ions deeper into the gap field; with a slit installed they saw no bias effect. The source does not rank the two approaches - test both on the actual machine.
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Shape central-region iron with a plug and deliberately saturating caps so one geometry serves multiple field levels: the final Davis design put the 8-in axial plug 5.5 in from the valley floor with 3.5-in caps that saturate at high field - their incremental contribution shrinking - while filling in the central field hole at low field.
Source quote & editorial note
moving the 8 inch plug to 5.5 inches from the valley floor and to extend the caps to a length of 3 1/2 inches. These caps saturate at high levels, but fill in the central "hole" at low fields.
Editorial note, tabletop extrapolation: Deliberately-saturating iron as a field-programming element is a trick FEMM (with the real BH curve) models well: a piece sized to saturate at the main operating point contributes mostly at low field - but saturated iron keeps its magnetization, so verify the high-field map still meets spec rather than treating the cap as magnetically gone.
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Estimate the field contribution of fully saturated cylindrical shim features by treating them as uniformly magnetized: cylindrical spikes act approximately as point charges m = M*A at their tips (plus images in the adjacent poles), with M = (B-H)/4pi (Gaussian units - in SI, M = B/mu0 - H).
Gaussian cgs: m = M*A, M = (B-H)/4pi at saturation; midplane field from point charges at spike tips + images (source Eqs. 7-8); SI: M = B/mu0 - HSource quote & editorial note
If the spikes are cylindrical, the field due to them may be treated approximately as that of point charges placed at their tips with strength m = MA.
Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 8
Editorial note, tabletop extrapolation: Handy closed-form sanity check for slender, demonstrably saturated cylindrical features (a spike or thin button) before FEMM; treat the excitation independence as approximate - the saturated region and residual susceptibility still move a little with drive - and don't stretch the point-charge picture to fat cones.
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The A^2/OL duct formula underestimates rectangular-duct conductance: the corrected value is C = K * C_approx, with the report's Table 4.3 giving K = 1.108 to 1.444 as a/b runs 1 to 10 - equivalently, the uncorrected estimate sits 10-31% below the true conductance. The cited design deliberately omitted K to keep pump sizing conservative.
C_corr = K*C_approx; K(a/b): 1.108/1, 1.126/1.5, 1.151/2, 1.198/3, 1.297/5, 1.400/8, 1.444/10; percentages referenced to the corrected value: estimate low by (1 - 1/K) = 10-31%Source quote & editorial note
when applied to ducts of other than circular cross section, sizable errors may be introduced ... the correction factor K, by which the right side of Eq. 41 must be multiplied to give a more accurate value.
Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 145
Editorial note, tabletop extrapolation: The correction handbooks skip - and a margin policy worth copying with its limits understood: omitting K is a duct-conductance allowance, not a system margin. Effective speed obeys 1/S_eff = 1/S_pump + 1/C, so when the pump dominates, the extra conductance buys little; run the series combination before crediting headroom.
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The report's crystal oscillators held frequency within one part in 10,000, ovened at the crystals' turnover temperature; its frequency-critical discriminator elements shared controlled-temperature enclosure (oven contents and the 140 F setting report-attributed - scan re-read queued).
crystal at its own turnover temperature in an oven -> df/f ~ 1e-4 for the cited oscillators (turnover is device-specific)Source quote & editorial note
The crystal oscillators, Nos. 3 and 5, will maintain a constant frequency within one part in 10,000.
Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 169-170
Editorial note, tabletop extrapolation: The stabilization pattern transfers even where the parts are now silicon: put the reference AND the analog discrimination components in one controlled thermal box, because the filter drifting is as fatal as the oscillator drifting - then budget the whole chain (oscillator, filter, mixer, threshold) instead of assuming the oven number covers it.
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Gain-stabilize a sparse narrow-pulse chain with a PEAK-reading automatic level control - the cited circuit 'had to work on a peak-reading principle' because the tiny duty cycle starves an average-reading loop - and put its detector at the final trigger point so the loop spans every gain stage before it.
Source quote & editorial note
the automatic pulse-height circuit had to work on a peak-reading principle.
Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 171
Editorial note, tabletop extrapolation: Directly applicable to pulse chains fed by beam pickups or PMTs at low rep rate: stabilize on detected peak height at the discriminator input. This compensates multiplicative gain drift in the stages inside the loop and reduces amplitude-induced time walk - pulse-shape changes, baseline shifts and discriminator drift are outside it, so keep a timing calibration (or constant-fraction discrimination) as well.
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Benchmark for a home-built trigger discriminator, vacuum-tube era: the report's instrument fired with probable error under 1 microsecond over a 19-21.5 Mc range (its input/output/pulse specifications are the report's data tables - scan re-read queued for the exact values).
reported: probable firing-time error < 1 us; range 19-21.5 Mc, with provision for changing itSource quote & editorial note
Probable error in firing time, <1 microsecond. Range of firing frequency, 19 to 21-1/2 megacycles, with provision for changing this.
Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 174
Editorial note, tabletop extrapolation: Calibrates ambition - microsecond-class event timing off a small RF sample needed no exotic parts in 1952. A modern comparator-plus-MCU implementation should do well against that; measure its jitter rather than assuming orders of magnitude, and copy the architecture, not the hardware.
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For a uniform field from a split coil pair at high field, the source's criticism is that thin-winding Helmholtz sections (cross section small next to radius squared) require excessive power; its doctrine is to set uniformity by a power-series expansion of the mid-plane field, choosing coil boundaries to null low-order terms rather than simply making the coils huge.
expand H(u) in powers of u in the mid-plane (Eqs. 1-3) and null low-order derivative terms by choice of coil boundary; thick sections (cross section ~ a^2) for power economySource quote & editorial note
Helmholtz coils have cross sections small in comparison with their radii squared, and thus require excessive power where a high field is required.
Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 108
Editorial note, tabletop extrapolation: The right doctrine for any air-core uniform-field fixture - probe-calibration coils, a beamline corrector, a small synchrotron's reference field: choose the winding section from the ampere-turns, resistance, I^2R and temperature-rise arithmetic, and reach for thick optimized sections when that arithmetic shows a power problem - a classic thin Helmholtz pair is fine where it doesn't.
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Wrap one of a matched foil pair in cadmium to split induced activity into a slow-neutron capture part and a fast-particle part; at the 184-inch the Cd-wrapped (fast-only) copper foil showed ~1/1.6 of the bare foil's Cu64.
Cu64(Cd-wrapped)/Cu64(bare) ~ 1/1.6, i.e. ~40% of activation was thermal-neutron captureSource quote & editorial note
the ratio of Cu64 activity in the cadmium-wrapped sample (due only to fast particles) to that in the uncovered foil was ~1/1.6.
Boom, Toth & Zucker, Residual Radiation of the LRL 184-inch Cyclotron — ORNL-3158 (1961) — p. 15
Editorial note, tabletop extrapolation: ENERGY SCOPE: relevant only when neutrons exist to be moderated. The Cd-difference technique splits capture activation into below- and above-cutoff parts APPROXIMATELY - epithermal response and the wrapper's spectrum perturbation blur the split, which is why practice reports cadmium ratios rather than clean fractions. Keep it in the toolkit for any future neutron-producing experiment; meaningless for pure sub-MeV proton running.
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In target-handling work the hands take roughly ten times the whole-body dose, so extremity monitoring (finger films/rings) and tools that add inches of distance matter more than badge numbers suggest.
extremity dose ~ 10x whole-body dose for target setup/dismantlingSource quote & editorial note
Finger films show that the hands receive about ten times as much exposure as the body for target operations; i.e., setting up and dismantling.
McWalters et al., Radiation Exposures of Personnel at the 60-inch Cyclotron — UCRL-8276 (1958) — p. 16
Editorial note, tabletop extrapolation: ENERGY SCOPE: measured on multi-MeV activated targets. The geometry lesson transfers: the hands work closest to the source, where rates are highest (inverse-square for a compact source, and higher still in contact geometry, where the simple 1/r^2 picture breaks down) - so tongs that add inches and a ring dosimeter are the response if the machine ever handles activated or tritiated items. For energized circuits the analogue is distance by design - insulated tools and clearances - not speed (dg-871).
Cited in: Shielding a Small Cyclotron
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Evaporate boron from a COVERED slotted boat machined from spectroscopic-grade carbon rod; the cover both cuts radiative heat loss (boron needs white heat) and stops the charge scattering out of the boat during heating.
boat from 5/16-in dia spectroscopic carbon rod, covered cavity (No. 1 drill, 0.228 in), charge ~250 mg amorphous boron powderSource quote & editorial note
It was found necessary, however, to use a covered carbon boat both to reduce the radiation cooling of the boron and to prevent scattering of the material during the heating.
Hoke & Newman, Self-Supported Cyclotron Targets of Boron and Magnesium — ORNL-3021 (1961) — p. 6
Editorial note, tabletop extrapolation: Boron is among the worst common elements to evaporate - it runs at white heat and attacks refractory-metal boats - and carbon-rod stock is cheap and machinable with ordinary tooling, so this is the boat design to copy for B-11 films. The recipe handles the isotope like any boron; the TARGET still needs its own qualification: verify enrichment survives the process, check carbon/carbide pickup, and measure uniformity and areal density before calling it experiment-ready.
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Working boron-evaporation parameters: pressure below 1e-5 mm Hg, ~280 A at 8 V (~2.2 kW) through the carbon boat to white heat, deposition onto 3.25 x 4-in glass plates; endpoint is visual — the charge stays darker than the boat until just before vaporizing, then brightens and disappears in seconds.
P < 1e-5 mm Hg; I ~ 280 A @ 8 V; T = white heat; substrate = cleaned glassSource quote & editorial note
Pressure was maintained below 1 x 10-5 mm of Hg while the boat was being brought to temperature. Then, by passing a current of about 280 amp at 8 volts through the boat, a sufficiently high temperature was reached (white heat) to vaporize the boron. The progress of the evaporation was followed by observing the material as it heated in the boat. The boron remained darker than the boat until just before vaporization, then it became bright and quickly disappeared. The boron was evaporated onto 3 1/4 x 4-in. glass plates.
Hoke & Newman, Self-Supported Cyclotron Targets of Boron and Magnesium — ORNL-3021 (1961) — p. 6
Editorial note, tabletop extrapolation: Scope honestly: this is EVAPORATION producing ug/cm2-class self-supported films - potentially suitable for a p+B11 cross-section or resonance-yield measurement once areal density, uniformity and purity are characterized - and NOT the route to a thick target for a maximum-alpha-yield demo. The hardware (2.2 kW low-voltage supply, 1e-5 torr bell jar) is within amateur reach ONLY with the engineering done: rated water-cooled feedthroughs for 280 A, fault protection, implosion screening, and hot-material handling.
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Budget boron-evaporation boats as consumables in the cited (carbon-boat, slotted) apparatus: hot boron converts the carbon boat to boron carbide, the slot clogs, and a boat survives at most two evaporations - so machine boats in batches before a target campaign.
cited apparatus: boat life <= 2 evaporations (B4C slot clogging; carbon boats)Source quote & editorial note
The boats are useful for only two evaporations at most since the slot rapidly becomes clogged with boron carbide.
Hoke & Newman, Self-Supported Cyclotron Targets of Boron and Magnesium — ORNL-3021 (1961) — p. 6
Editorial note, tabletop extrapolation: Plan an enriched-B11 evaporation campaign around several pre-machined spare boats rather than debugging mid-run. The failure mode is the carbon: refractory-metal boats, compatible crucibles or non-contact heating change or avoid it - candidate fixes to compatibility-test, not guarantees.
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Recover self-supported films by float-off: pre-clean the glass in Calgonite (detergent) solution, tilt ~20 deg, run warm tap water in slowly, cut the floating film to size, and lift it on 0.030-in aluminum frames; add a pinch of detergent to cut surface tension and pause before lifting clear so trapped water drains.
Source quote & editorial note
the method found successful here was to float the boron off the plate with warm tap water. Prior to evaporation the plate was cleaned by washing in a Calgonite solution and rinsed with water. The plates were placed at an angle of about 20 deg to the horizontal and water was allowed to run in slowly. The floating film was then cut into appropriate sizes, and the pieces were picked up on square target frames of aluminum 0.030 in. thick. ... breakage of films can be greatly reduced by adding a pinch of detergent, such as Calgonite, to the water to reduce surface tension just before the film is picked up, and also by stopping just before removing the frame from the water to allow trapped water to drain off.
Hoke & Newman, Self-Supported Cyclotron Targets of Boron and Magnesium — ORNL-3021 (1961) — p. 6
Editorial note, tabletop extrapolation: The film-recovery toolchain is modest (named detergent, tap water, glass plates) and the skill is in the sequence - which the card now quotes in full. Use the source's Calgonite or a validated low-residue lab surfactant rather than assuming any modern dishwasher detergent is equivalent. Practice on natural boron before spending enriched B-11.
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When a single-thickness film is too fragile, bring the frame up under the middle of the floating film so it folds double over the frame and the two layers adhere — Hoke and Newman's double 50-100 ug/cm2 enriched-B10 targets were far easier to make than single 25-50 films.
double-fold pickup; B10 double films 50-100 ug/cm2; carbon precedent 25-100 ug/cm2Source quote & editorial note
Stronger double films, which proved to be much easier to make, were made by bringing the frame up in the middle of the film. The film then folded over the frame
Hoke & Newman, Self-Supported Cyclotron Targets of Boron and Magnesium — ORNL-3021 (1961) — p. 8
Editorial note, tabletop extrapolation: For a next machine's B11(p,alpha) internal-target work, the double-fold film is the mechanically survivable construction - but qualify its thickness against the experiment's energy budget with current stopping data: compute the proton energy loss and straggling through the actual post-fold areal density with PSTAR/SRIM at the actual beam energy before calling it thin enough for resonance-tail work (at ~170 keV the loss through these films is substantial, not negligible).
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For water-sensitive evaporated films (e.g. magnesium), first arc-coat the soap-primed glass with 5-10 ug/cm2 of carbon as a parting and backing layer, and ramp evaporator current slowly (10-20 min) so the charge outgasses quietly instead of spattering; conserve enriched isotope with a glass recovery hood over the source.
Mg: 3-mil Ta boat, ~3/4-in wide, P < 2e-5 mm Hg, I -> ~100 A over 10-20 min; C parting layer 5-10 ug/cm2; films 30-80 ug/cm2Source quote & editorial note
For the evaporation of magnesium, boats of 3-mil tantalum about 3/4-in. wide were used. The pressure was maintained below 2 x 10-5 mm of Hg, and the current was increased to about 100 amperes. The scattering of the MgO by violent outgassing can be minimized by increasing the current slowly over a period of 10 to 20 minutes so that the outgassing can occur quietly. ... the glass was coated with a weak soap solution (Calgonite) and allowed to dry before it was coated with about 5 to 10 ug/cm2 of carbon from an arc ... One function of the carbon layer is to help keep the magnesium from making contact with the water; magnesium is slightly soluble in water and decomposes to form Mg(OH)2. The carbon also helps hold the magnesium film together both while it is being removed from the glass and afterwards. ... a glass hood was constructed from lantern slide covers so that all of the collected material could be recovered.
Hoke & Newman, Self-Supported Cyclotron Targets of Boron and Magnesium — ORNL-3021 (1961) — p. 9
Editorial note, tabletop extrapolation: Three tricks generalizable WITH per-material validation: sacrificial arc-carbon parting layers under fragile or water-reactive films (validate compatibility - carbon can add reaction background or stick badly to another material), slow-ramp outgassing before full evaporation power, and a cheap glass recovery hood (lantern-slide covers) so enriched material can be recovered - recovered stock needs a purity check before reuse.
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Turn a known activation excitation function into a beam spectrometer: bombard a stack of thin foils whose reaction is well measured, count each foil, and unfold activity-vs-depth into the energy spectrum - the steeply falling cross section makes the discretized system near-triangular, solvable foil by foil (stack details report-attributed; scan re-read queued).
A(r) ~ integral over R of sigma(R-r)*I(R) dR, discretized as block/line spectrum -> near-triangular linear system; choose Rn spacing to avoid oscillating/negative weightsSource quote & editorial note
the energy distribution of protons in the cyclotron beam is readily determined by measuring this excitation function and comparing it with the published data.
Editorial note, tabletop extrapolation: ENERGY SCOPE: Cu63(p,n)Zn63 needs ~4.2 MeV (verify against evaluated data at use time) - closed at reference-machine energies. What transfers is narrower than the note once claimed: the unfolding needs multiple independent response kernels, so a single B11(p,alpha) yield number constrains but cannot recover a spectrum; measurements at several calibrated degrader settings can build a response matrix, and a PIPS behind degraders is range spectrometry - a different, complementary method.
Cited in: Shielding a Small Cyclotron
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In weak-guide-field machines or field regions, measure and where necessary compensate the ambient (geomagnetic) field: in the cited 42-gauss electron Analogue, canceling the horizontal geomagnetic component eliminated an observed beam attenuation.
Source quote & editorial note
When the horizontal component of the geomagnetic field was canceled, this attenuation was eliminated.
Oak Ridge National Laboratory, A Proposal for the Mc² Isochronous Cyclotron — ORNL-3540 (1963) — p. 276
Editorial note, tabletop extrapolation: Earth's field (~0.5 G total; the horizontal component is what mattered there) is normally a negligible perturbation inside the reference machine's 0.59-T gap, but real for any low-field electron-analogue experiment, long injection path, or fringe-field beamline - measure the local vector rather than assuming.
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Assign contingency per item, not as one number: the cited estimate averaged ~20% contingency but varied it from 15% to 40% per item according to the accuracy with which each estimate could be made (the engineering and escalation adders are the report's companion structure - re-read queued).
total = basic * (1 + ~0.15 eng) + per-item contingency (15-40% by precision) + escalation (their 4%/yr)Source quote & editorial note
the average contingency for the project is approximately 20%, but it varies on specific items from 15% to 40%, depending on the accuracy with which the estimate could be made.
Oak Ridge National Laboratory, A Proposal for the Mc² Isochronous Cyclotron — ORNL-3540 (1963) — p. 234
Editorial note, tabletop extrapolation: 1963 AEC percentages, but the structure transfers to any bill-of-materials estimate: catalog items get little contingency, anything not yet fully designed gets a lot - and write down which base each adder applies to (basic cost vs basic-plus-engineering) so the arithmetic is reproducible.
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For the 86-inch Be-on-aluminum neutron targets, flux brazing was rejected: the extreme probability of large flux inclusions between the beryllium and the aluminum base would seriously impair heat transfer. The reported alternative - vacuum-furnace brazing with a thin Al-Si interlayer - is report-attributed (scan re-read queued for the interlayer spec and bond result).
0.006-in. Al-Si (11.5% Si) interlayer, vacuum furnace -> 100% bondSource quote & editorial note
The method of brazing is considered unsatisfactory because of the extreme probability of leaving large flux inclusions between the beryllium metal and the aluminum base, which would seriously impair heat transfer.
Editorial note, tabletop extrapolation: The corpus's targetry shelf is thin, and the transferable core is real: flux is a void-former at exactly the interface a beam target cannot afford. For a next machine's boron or beryllium targets on copper or aluminum, treat flux-free vacuum or controlled-atmosphere brazing as the candidate route - and qualify it with coupon brazes, sectioning and thermal cycling, because wetting and expansion behavior change with each material pair.
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Thick-target neutron yield planning number: bombarding beryllium with ~20-MeV-class protons on the 86-inch gave approximately 1 neutron per 50 protons — the machine served as a controlled fast-neutron source for a biology program on this basis.
Y(n) ~ 1 neutron / 50 protons, thick Be target, ~20 MeV protonsSource quote & editorial note
a beryllium target is bombarded with protons, approximately 1 neutron for 50 protons is obtained.
Editorial note, tabletop extrapolation: SCALE-SCOPED - this 2% yield is a ~20-MeV number; at the reference machine's and a next machine's energies (0.15-5 MeV) p-Be yields are orders of magnitude lower. Useful as the upper anchor when building the shielding/licensing dose model for any future MeV-class educational machine.
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One machine, two energies by mechanical reconfiguration: on the ORNL 44-inch, shifting the position of the dees and target selects a working radius of 11 in. or 20 in., while the ion source position remains unchanged and the beam orbits remain centered; the spacer dimension (14.5 in.) and the 1.5/4.9-MeV proton energies are reported in the companion specifications (ORNL-1670 and the ORNL-1663 spec table, dg-947).
fixed B and f; target radius 11 or 20 in. -> 1.5 or 4.9 MeV (E ~ r^2)Source quote & editorial note
a choice of radius, 11 in. or 20 in., is thus obtained by shifting the position of the dees and target. In either case the ion source position remains unchanged and the beam orbits remain centered
Editorial note, tabletop extrapolation: Variable energy WITHOUT retuning B or rf - E ~ r^2 at fixed field and frequency - by repositioning the dee assembly AND target together as ORNL did; a target-only intercept at reduced radius is a simpler tabletop variant (an extrapolation, not ORNL's method), and either way the delivered energy is verified from the mapped field and measured target radius, not assumed calibrated.
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Coupled-secondary (transmission-line) tuning works but watch the Q: a series coil-and-variable-capacitor secondary magnetically coupled to the dee stems reflected a variable impedance into them, sweeping resonance from 6 to 12 Mc - but the secondary's comparatively low Q made the dee-stem resonant impedance vary markedly across the band.
reflected impedance of coupled secondary shifts f0; low secondary Q -> impedance swings with fSource quote & editorial note
This circuit consists of a coil and variable capacitor connected in series, plus the inherent resistance of both elements. The magnetic coupling between the dee stems and secondary circuit results in an impedance being reflected into the dee stems from the secondary. ... A resonant frequency varying from 6 megacycles to 12 megacycles was achieved with the particular circuit tested. ... the resonant impedance of the dee stems varies markedly with the frequency due to the comparatively low 'Q' of the secondary circuit.
Editorial note, tabletop extrapolation: Relevant if a next machine ever adds a variable-frequency or remote trim element: any lossy tuning appendage coupled to the dee resonator drags its shunt impedance (hence dee voltage per watt) across the tuning range - minimize tuner loss and measure loaded Q and shunt impedance over the whole range, whatever the tuner's construction.
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Automatic resonance tracking by sweep-and-store: a control that sweeps the oscillator across its band, stores the peak voltage seen across the coupled secondary, then re-sweeps and stops when the live voltage equals the stored peak, tuned to the SECONDARY'S resonance within ~0.1% (114-inch study, tested with a small oscillator).
two-pass sweep; stop when V_live = V_stored(peak); tuning error ~0.1%Source quote & editorial note
The error of the control in tuning the oscillator to the frequency of the secondary is of the order of 0.1%.
Editorial note, tabletop extrapolation: A 1954 peak-hold autotune implementable today in a microcontroller: sweep the exciter, record the dee pickup peak, re-sweep and lock. Two scope-of-validity notes: it locks to the CAVITY resonance, not to the beam-synchronous f = qB/(2*pi*gamma*m) - the field still sets that independently; and 0.1% was demonstrated unloaded, so validate peak detection and drift on the beam-loaded resonator before trusting it.
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Weigh pole-profile precision against need: the authors had custom milling cutters made to generate true hyperbolic quadrupole profiles and later concluded plain circular arcs would have been satisfactory for their quadrupoles.
Source quote & editorial note
Morley Machine Company, Rochester, N.Y., produced milling cutters conforming to this equation ... Subsequent work has shown that circular arcs would have been satisfactory.
Editorial note, tabletop extrapolation: A candidate money-saver for a next machine's quads: circular-arc (or round-stock) tips - validated by checking the integrated multipoles and end effects in FEMM against the beam's actual field-quality requirement, which is where the modeling time belongs; adequacy depends on aperture fraction used and multipole tolerance, so it is not automatic.
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Design the focal-plane detector for exposure multiplexing: a cassette holding three 80x200 mm emulsions allowed six different exposures without breaking spectrograph vacuum; alongside it the system used a solid-state counter array covering the focal region where only a few groups mattered (array details reported elsewhere in the source).
Source quote & editorial note
Three emulsions each 80 x 200 mm can be mounted in a special camera ... which allows six different exposures to be made without breaking the spectrograph vacuum.
Editorial note, tabletop extrapolation: The principle is vacuum cycles are the tax on focal-plane work - amortize them: a movable frame of film/CR-39 chips (integrating, etched after removal - a survey detector, not prompt readout) or a silicon strip/PIN-diode array (direct charged-particle detection; a bare SiPM is a photon detector and needs a scintillator) behind the next machine's analyzer. Their split - survey in emulsion, precision groups in counters - still maps cleanly.
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Opening a spectrograph's in-plane angular acceptance costs kinematic broadening of peaks when scattering off light nuclei; the cited instrument accepted that trade for large-angle reach.
Source quote & editorial note
In scattering from light nuclei, this introduces appreciable kinematic broadening of peaks as the entrance aperture is opened.
Editorial note, tabletop extrapolation: For a next machine's Rutherford-scattering station the same knob exists: closing the entrance aperture trades count rate for resolution. State the broadening honestly - dE ~ |dE/dtheta|*dtheta depends on beam energy, angle and kinematics in general; only the FRACTIONAL elastic broadening at fixed masses and angle drops out energy-independent - so compute it for the actual geometry rather than quoting a mass-ratio shortcut.
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A simple single-scattering model predicts organic-scintillator neutron efficiency usefully: eff = (1 - E0/En)*(1 - exp(-nH*sigma_np*l)). The source calls the first factor exact and response-shape-independent - which holds given its implicit assumptions: isotropic center-of-mass n-p scattering (uniform recoil spectrum), a single hydrogen scatter, and a sharp threshold; find E0 per threshold setting from a calibration reaction.
eff = (1 - E0/En)(1 - exp(-n_H*sigma_np(En)*l)); valid as a first-order model for thin hydrogenous scintillators; degrades with n-p anisotropy at higher energy, carbon interactions, proton escape, multiple scatteringSource quote & editorial note
The first factor in (1) is exact. It does not depend on the exact shape of the response curve (pulse-height vs proton recoil energy) of the scintillator.
Fulbright et al., A Fast Neutron Time of Flight System for Use with Cyclotrons — NYO-9360 (1962) — p. 15
Editorial note, tabletop extrapolation: A lovely teaching derivation - a two-factor closed form students can test against a calibration reaction - and the transferable habit is identifying which factor rests on which assumption. Validate against calibration or Monte Carlo for the actual detector and energy range before leaning on it.
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When slow neutrons from one burst can be overtaken by fast neutrons from the next (frame overlap), cut the beam-pulse rate by electrostatically deflecting bunches at a subharmonic of the machine RF - ~3 Mc effective rate virtually eliminated the source's problem. Prefer odd division ratios: at even ratios bunches pass at both zero crossings of the deflection voltage, changing the effective scaling (1:6 passes every third bunch, not every sixth).
f_scaled = f_cyc/3 typical (3.3-5 Mc from 10-15 Mc); even subharmonic 1:2k passes bunches at both voltage zerosSource quote & editorial note
In our case reducing the frequency of beam pulses to about 3 mc can virtually eliminate the problem.
Fulbright et al., A Fast Neutron Time of Flight System for Use with Cyclotrons — NYO-9360 (1962) — p. 16
Editorial note, tabletop extrapolation: Check overlap arithmetically for the actual spectrum and flight path - t[ns] ~ 72.3*L[m]/sqrt(E[MeV]), so even an all-sub-MeV spectrum overlaps at a 10 MHz rate over a 1 m path, and D-D work adds multi-MeV neutrons on a sub-MeV machine. The subharmonic plate pair is a genuinely cheap cyclotron chopper for periodic bunch rejection and duty-cycle control - single-bunch selection needs a gating scheme beyond a sinusoidal drive - and the odd/even zero-crossing subtlety is real circuit physics worth teaching.
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To map the phase-space topology at an energy, locate the unstable fixed points first, then launch orbits displaced slightly from them - along the transfer-matrix eigenvector directions - and integrate both forward AND backward in time: the trajectories trace the stable and unstable manifolds (separatrices where the map is near-integrable), far cheaper than blanketing the plane with orbits.
Source quote & editorial note
the general orbit code is employed to trace forward and backward in time orbits with initial conditions displaced slightly from the unstable fixed points.
Editorial note, tabletop extrapolation: Directly reusable in a Python tracker (a symplectic or invertible integrator makes the backward branch trustworthy); the efficient way to draw the r-pr stability picture near resonances - cross-check with a scatter of ordinary orbits where the manifolds tangle, since in a nonintegrable map they can intersect and form stochastic layers rather than clean boundaries.
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Distortion bookkeeping: motion of the beam spot driven by flow-rate gradients on a fixed static plot (the "static effect") stretches, bends, shears, and filaments the beam; motion driven by the plot itself shifting with energy (the "acceleration effect") moves the beam without deforming it. Design rule: program the turns to avoid flow-gradient regions — especially near unstable fixed points.
Source quote & editorial note
The essential design requirement of such a system is a turn program which avoids regions of large flow rate gradient in the static phase space.
Editorial note, tabletop extrapolation: The doctrine transfers to schemes where a static phase-plot analysis applies: superimpose the accelerated beam path on static phase plots (cheap tracker post-processing), identify the large-flow-gradient regions - especially near unstable fixed points - and compare candidate turn programs by accelerated tracking. Crossing faster reduces exposure to a bad region but can excite other resonances non-adiabatically, so test, don't assume.
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A closed-form, size-independent solution exists for the cyclotron dee-gap field (Schwarz-Christoffel, per Murray & Ratner 1953 with corrections): for zero-thickness semi-infinite plate pairs at y = +/-h, tips at x = +/-k, potentials -/+V0, the median-plane field and potential are two-line formulas once one transcendental equation is solved. Geometry caution: k is the HALF-gap and h the HALF-aperture (plate tips map exactly to x = +/-k; re-derived from eq. 1 during extraction — the Fig. 1 scan invites misreading the full gap as k).
median plane (eqs. 6-8): E_x(x,0) = (V0/h)*sech(X1)/(1 + alpha*sech^2(X1)); V(x,0) = sign(x)*(2*V0/pi)*arccos(sech(X1)); with X = pi*x/(2h) = X1 + alpha*tanh(X1); alpha = (1-a^2)/a^2; a from (pi/2)*(k/h) = arccosh(1/a) + sqrt(1-a^2)/a^2. E_y = 0 on the median plane; E_x even, V odd in x. (Report writes E = +dV/dx — fix sign on implementation.)Source quote & editorial note
This paper presents in summary formulas for the computation of electric fields and potentials of an idealized cyclotron dee geometry.
Beal, Computation of Electric Field and Potential of an Idealized Dee Geometry — MSUCP-12 (1961) — p. 6
Editorial note, tabletop extrapolation: TRACKER SEED (flagged): this is directly implementable as the gap-field model in the tiny and the next machine's Python trackers — roughly ten lines plus a Newton solve — replacing or validating FEMM electrostatic maps. Identify 2h with the dee aperture, 2k with the dee-to-dummy-dee gap, 2V0 with the full dee-to-dummy-dee voltage (a grounded dummy dee is the same solution shifted by a constant, V0 = V_dee/2).
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The same solution gives the full off-median-plane E field — the ingredient needed for electric (gap) focusing models: E_x and E_y anywhere in the aperture follow from two coupled transcendental equations in (X1, Y1). Beal tabulated only the median plane, but eqs. 1-5 contain the whole 2-D field.
physical convention (E = -grad V): E_x = -(V0/h)*Xv/(Xv^2+Xu^2); E_y = -(V0/h)*Xu/(Xv^2+Xu^2) with the report's Xv, Xu, F as tabulated (the report prints the positive-gradient convention - flip the sign before tracking); potential v = arccos(cos(Y1)/F) needs the antisymmetric branch for x < 0 (plain arccos returns the same value both sides); verify an implementation against finite differences of VSource quote & editorial note
Therefore, equations 2 and 4 coupled with equations 3 and 5 can be used to determine the electric field and potential at a point X, Y of the dee region.
Beal, Computation of Electric Field and Potential of an Idealized Dee Geometry — MSUCP-12 (1961) — p. 5
Editorial note, tabletop extrapolation: E_y(x,y) is what a tracker needs for the Rose/Wilson electric gap-focusing term - available analytically at any point, no field map required. Whether that term dominates first-turn axial stability on a sub-kV machine is for the axial-stability calculation to say; implement, verify against finite differences, and let the tracking decide.
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Solve the gap-field transcendental equation with Gordon's iteration: Murray-Ratner's original converges slowly for small alpha and not at all for large alpha, while Gordon's Newton linearization of tanh(X1) 'was found to work well for all cases', with local quadratic convergence and the source's two-branch initial guess (X1 ~ X/(1+alpha) for small X1; X1 ~ X - alpha for large X1).
eq. 9: X1_new = [X - alpha*tanh(X1c) + alpha*X1c*sech^2(X1c)] / [1 + alpha*sech^2(X1c)], X1c the current iterate; initial guess X/(1+alpha) or X-alpha by branchSource quote & editorial note
The iteration process suggested by Murray and Ratner for calculation of X1 converges slowly for small values of a, and does not converge at all for large a. An iteration process, described below, suggested by M.M. Gordon was used and was found to work well for all cases. ... This iteration is Newtonian in character such that if a given X1 has an error of order e, then X1 given by equation 9 will have an error at order e squared. ... X1 ~ X/(1+a) for X1 small ... X1 ~ X - a for X1 large.
Beal, Computation of Electric Field and Potential of an Idealized Dee Geometry — MSUCP-12 (1961) — p. 7
Editorial note, tabletop extrapolation: Copy the iteration and its initial-guess branch into the tracker's field routine; iterate to a set tolerance - quadratic convergence is local, so the branch guess is what makes it robust - cheap enough to call per integration step, or use once to build a spline.
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Table 1 is a ready-made verification dataset: E/(V0/h) and V/V0 at x/h = 0 to 5.0 in steps of 0.2, five significant figures, for nine gap ratios k/h = 0.1, 0.3, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5 — computed on MISTIC (D. A. Johnson's fixed-point program), the same machine as the MSUCP-9 orbit codes. [Erratum 2026-08-30, from an upstream implementation + scan/math verification: the transcribed equations are EXACT (E(0)/(V0/h) = a^2 identically), but Table 1's printed values are reliable only to ~3 decimals — the 1960 computation carried its a-roots to 4 decimals, giving up to 3.2e-3 relative error at k/h = 2.0, each block internally consistent with its own imprecise root. Verify implementations against the equations, not the printed table; matching the table to only ~1e-3 is the signature of a CORRECT implementation.]
benchmark anchors: E(0)/(V0/h) = 0.99388 (k/h=0.1), 0.87049 (0.5), 0.65448 (1.0), 0.48916 (1.5), 0.37823 (2.0), 0.21623 (3.5); V/V0 at x/h=1.0: 0.73760, 0.70319, 0.60615, 0.48545, 0.38270, 0.21862 respectively [printed values, reliable to ~3 decimals — see the rule's dated erratum]Source quote & editorial note
Table 1 gives values of electric field and potential for a wide range of dee gap arrangements. [tables span PDF pages 11-19]
Beal, Computation of Electric Field and Potential of an Idealized Dee Geometry — MSUCP-12 (1961) — p. 11
Editorial note, tabletop extrapolation: Unit-test targets for the tracker's gap-field routine AND an independent check on FEMM electrostatic runs: model the same idealized geometry once and agree within a DOCUMENTED convergence tolerance - set by a mesh/domain convergence study against the table's demonstrated accuracy - before trusting FEMM on the real electrode shapes; the table's five printed digits are formatting, not a five-digit acceptance criterion — a five-figure match to the printed table would mean an implementation reproducing the paper's rounding errors (see the rule's dated erratum).
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Know the idealization's edges before leaning on it: the solution is 2-D (infinitely long straight edge — no dee-tip curvature, corners, or azimuthal variation), zero plate thickness, semi-infinite plates, electrostatic (quasi-static per RF cycle), no space charge, and symmetric +/-V0 drive. Beal's MISTIC computations covered alpha < 4, i.e. k/h < ~3.77, though the formulas themselves have no such limit.
Beal's MISTIC computations covered alpha < 4; the alpha-to-geometry conversion needs the source's definition re-read before quoting a k/h bound (the previously printed formula evaluated to ~2.06, not its own claimed 3.77 - scan re-read queued; the likely intended form is k/h = (2/pi)*(arccosh(sqrt(1+alpha)) + sqrt(alpha*(1+alpha))), which gives 3.77 at alpha = 4)Source quote & editorial note
A fixed point computer program written by D.A. Johnson for use on MISTIC was used to calculate the above equations for Ex and Vx at the point (X,0) with alpha<4. [defs: alpha = 1/A ; A = a^2/(1-a^2) ; (pi/2)(k/h) = cosh^-1(1/a) + (1-a^2)^1/2 / a^2]
Beal, Computation of Electric Field and Potential of an Idealized Dee Geometry — MSUCP-12 (1961) — p. PDF 8 (printed p. 5), Sec. IV Results, for the alpha<4 statement; alpha's definition on PDF 7 (printed p. 4), and the k/h relation on PDF 5 (printed p. 2)
Editorial note, tabletop extrapolation: For use on a next machine, the real deviations to check against FEMM are finite dee thickness, the rounded tip, and the curved gap line near the source at small radius - run the comparison over the actual geometry rather than assuming the analytic solution's quality at any radius; near center the ion-source chimney dominates the field regardless.
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Photoneutron thresholds run 6-19 MeV for nearly all nuclei with ONE trap: deuterium at 2.23 MeV — hydrogenous (water-containing) materials with natural deuterium are the exception to "low-Z is safe around photon flux," so audit D-bearing materials wherever multi-MeV photons exist.
E_thr(gamma,n): H-2 2.23 MeV; C-12 18.7; O-16 16.3; Cu-63 10.9; Pb-208 7.44 (Table III-2)Source quote & editorial note
H2(gamma,n)H1 ... 2.23 ... C12(gamma,n)C11 ... 18.7 ... O16(gamma,n)O15 ... 16.3
Editorial note, tabletop extrapolation: At the reference machine's photon energies (keV-class bremsstrahlung) every channel in the table is closed. Two honesty caveats for reuse in hazard analyses: 9Be sits below the deuterium trap (S_n = 1.665 MeV, IAEA NDS/AME, retrieved 2026-08-25), so beryllium joins heavy water on the audit list wherever multi-MeV photons exist; and reaction gammas can exceed the projectile energy - 11B(p,gamma) capture emits ~16 MeV photons at small cross-section, so a p-B11 machine's analysis must bound that two-step channel rather than declare photonuclear reactions impossible.
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D(d,n)He3 and T(d,n)He4 are EXOENERGETIC - they run at very low bombarding energy (Cockcroft-Walton scale) - so any deuterium in source gas or beam-loaded surfaces makes neutrons with no threshold protection. Other deuteron channels are exoenergetic too (9Be(d,n) Q ~ +4.4 MeV, 7Li(d,n) Q ~ +15 MeV): thresholdlessness is a property of deuteron beams on several light targets, while the common PROTON channels, (p,n), are threshold-protected.
D(d,n)He3 Q = +3.27 MeV; T(d,n)He4 Q = +17.6 MeV; also exoenergetic: 9Be(d,n), 7Li(d,n); common (p,n) and (gamma,n) channels are threshold-protectedSource quote & editorial note
Two of these reactions, the D(d,n)He3 reaction and the T(d,n)He4 reaction are exoenergetic and can be initiated at very low energies. Thus these two reactions can be produced in small Cockcroft-Walton accelerators.
Editorial note, tabletop extrapolation: THE loophole in the 'sub-MeV machines make no neutrons' argument: natural hydrogen is ~150 ppm deuterium and D accumulates in beam-loaded surfaces, so a D-on-D source term exists in principle on any hydrogen machine - at yields the Coulomb barrier suppresses steeply at low energy, which is why the honest posture is a survey requirement, not alarm.
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In the report's assessment of ordinary concrete, only Na-24 (15 h) and perhaps K-42 (12.4 h) presented any hazard - a shutdown of three to five days lets them decay to very low levels; barytes concrete adds Ba-139 (83 m), which builds up during a day's running but decays away overnight.
concrete activation governed by Na-24 (15 h) / K-42 (12.4 h); 3-5 day cooldown -> negligibleSource quote & editorial note
Only Na24 and perhaps K42 could present any kind of hazard. Because of the half-lives of these two isotopes, a shut down of three to five days will allow decay to very low levels.
Editorial note, tabletop extrapolation: Cooldown-scheduling logic for any future neutron-producing work, as the report's era assessed its concrete: modern assessments add impurity-driven products (Mn-56, Co-60, Eu-152/154, tritium and others) whose relevance depends on the actual aggregate and spectrum, so a real facility characterizes its own concrete rather than inheriting this list. For the current machines the practical point stands: with no neutron source term there is nothing to activate the basement structure - deuteron operation being the standing exception.
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Because thermal neutrons attenuate to ~1/3 of initial flux in the first 10 cm of ordinary concrete, about 2/3 of neutron activation lives in the shield's inner skin — so design shields with a removable row of concrete blocks on the inside that can be disposed of and replaced if they grow too active.
thermal flux ~1/3 per 10 cm concrete -> ~2/3 of activation in first 10 cm -> sacrificial inner block rowSource quote & editorial note
Thermal neutrons are attenuated to about one-third of their initial flux by the first 10 cm of ordinary concrete. Therefore 2/3 of the activity produced by the neutrons would occur in this region. This makes it possible to design shielding with a row of concrete blocks on the inside.
Editorial note, tabletop extrapolation: The modular-block enclosure pattern already favored for product machines gets a second justification: the inner course doubles as the sacrificial activation layer, replaceable without demolishing the shield. Two conditions travel with it: the 2/3-in-10-cm figure is for thermal neutrons in ordinary concrete, not every spectrum; and replaced blocks are surveyed and characterized before anything is 'disposed of' - activated material is a regulated waste stream (see /legal/).
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The 1972 ICRP-era quality factor was approximated in tissue as QF = 0.8 + 0.16 * LET (LET in keV/um of water) - the era's one-line conversion from stopping power to protection weighting.
QF ~ 0.8 + 0.16*LET(keV/um H2O)Source quote & editorial note
QF = 0.8 + 0.16 LET where LET is in keV/u.
Editorial note, tabletop extrapolation: A window into how weighting works, not a generator of modern factors: current practice assigns wR by radiation type (alphas: 20) and the Q(L) relation differs from this 1972 line. The 11B(p,alpha) reaction shares ~8.7 MeV across a broad three-alpha spectrum - not fixed 1.7 MeV lines - and alpha weighting today is simply wR = 20. Flag anywhere it appears as the 1972 formulation of what is now wR.
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For neutron streaming through mazes the manual uses the albedo chain phi_p = (phi_s/(4pi r_n^2)) * prod[beta*Omega_i]: its albedo values run from 0.66 for thermal neutrons down to ~0.05 for fast, with 0.4 offered as a conservative fast-neutron choice, and boron loading on the shield-wall surface absorbs thermal neutrons instead of reflecting them.
albedo beta = 0.66 (thermal) -> ~0.05 (fast); 0.4 conservative; boron loading cuts thermal reflection. [2026-09-06 re-read: the printed eq. VII-2 divides by a bare 2*r_n^2, but the manual's own worked example uses 4*pi*r_n^2 and only that reproduces its printed 3.2e-3 answer - the 2*r_n^2 is an original typo; the card's 4*pi form follows the manual's practice.]Source quote & editorial note
albedo for neutrons (from 0.66 for thermal neutrons to approx. 0.05 for fast neutrons) ... using an albedo of 0.4 which is relatively conservative for fast neutron ... Boron loaded concrete on the surface of the shield wall will increase the probability of absorption, decreasing the probability of scatter in reflection
Martin (ed.), Accelerator Radiation Protection — AD-755510 / USA-NLABS-TR-73-7, US Army Natick Laboratories (1972) — p. PDF 148 (printed 139) for the albedo range and the 0.4 choice; PDF 147 (printed 138) for eq. VII-2 and the boron sentence
Editorial note, tabletop extrapolation: Contingency reference only at current energies. If a future neutron source term streams through an enclosure penetration, the boron-surface idea (borated HDPE lining a duct) reduces the thermal reflection specifically - it does nothing for the fast component - so it is one element of a duct fix, sized with the chain using energy-appropriate albedos and checked by survey, not a standalone cheap cure.
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Rate materials in the radiation zone: semiconductor circuits must stay out of high-radiation positions, and insulation ranges over eight decades of tolerance — Teflon is the WORST common insulator (5e4 rad gamma) while phenolic-glass laminate, polyurethane, diallyl phthalate exceed 1e10 rad and ceramics 1e11-1e12 — choose in-cell wiring accordingly.
radiation tolerance (gamma): Teflon 5e4 rad; PVC 1e8; epoxy/polystyrene 5e9; phenolic-glass >1e10; Al2O3 1e12Source quote & editorial note
Teflon 5 x 104 ... Phenolic, Glass laminate >1 x 1010 ... Aluminum Oxide 1 x 1012
Editorial note, tabletop extrapolation: Counterintuitive and worth flagging in the next machine's design notes: PTFE, the amateur's default HV insulator, is the most radiation-fragile common insulator on the table - by four decades against phenolic-glass. At the reference machine's current operation insulators see no significant dose in the first place; the flag matters wherever a future neutron- or target-adjacent position exists - specify ceramic or glass-laminate there, per the table.
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Massive shielding doors carry their own hazards in the manual's treatment: slow travel with great momentum (engineer the stopping so the door cannot trap personnel or crack walls), shielding at least equal to the adjoining wall, and - the quoted requirement - every door manually openable from BOTH inside and outside after a loss of power.
door shielding >= wall; manual egress inside+outside under power loss; engineered decelerationSource quote & editorial note
Doors should be designed to provide shielding at least equivalent to the adjoining walls ... Travel of these large doors is necessarily slow but the momentum is great ... one must be able to open these doors even after a loss of power. Some manual method of opening the door from inside and outside must be included in the design.
Martin (ed.), Accelerator Radiation Protection — AD-755510 / USA-NLABS-TR-73-7, US Army Natick Laboratories (1972) — p. PDF 145 (printed 136)
Editorial note, tabletop extrapolation: Scale-invariant egress principle: even an interlocked benchtop lid or a walk-in enclosure door must never imprison anyone on power loss. The criterion is manual operability from both sides without power, verified by actually trying it - whatever the mechanism - and the door's own motion is a machinery hazard (pinch points, momentum) to engineer alongside its radiological job.
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In radiation service, LN2-cooled surfaces accumulate a hidden explosive: oxygen condensed from air into the liquid nitrogen is radiolyzed to ozone and left CONCENTRATED after the nitrogen evaporates - a significant explosion hazard, the quoted mechanism.
LN2 trap + radiation -> condensed O2 -> O3 concentrate on warm-up = explosion hazard; inspect irradiated insulation on shortened scheduleSource quote & editorial note
The oxygen from the air condensed in the liquid nitrogen, radiolyzed to ozone and left in concentrated form after the evaporation of the nitrogen presents a significant explosion hazard.
Editorial note, tabletop extrapolation: Directly applicable to any LN2 cold trap on the diff-pump line if machine energies ever rise - and worth a procedures line now: a trap that has sat in a radiation-plus-discharge environment gets attended warm-up and venting, because the quoted mechanism concentrates oxidizer exactly at boil-dry. (An editorial precaution drawn from the quoted physics.)
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Ozone is the dominant toxic gas from irradiating air in the manual's treatment (G = 13.8 +- 0.7 molecules O3 per 100 eV in oxygen radiolysis, X-ray value); predict cell concentration with its production model c0 = 600*G*i*d/V (i = beam current in A, d = beam path in air in m, V = cell volume in m3) balanced against exhaust rate and molecular lifetime.
c0 = 600*G(O3)*i*d/V; C = c0/(v/V+1/alpha)*(1-exp(-(v/V+1/alpha)t)); entry criterion ~0.1 ppmSource quote & editorial note
indicate a confident Xray value of 13.8 +- 0.7 molecules of O3/100 e.v. in the radiolysis of oxygen. This value is used here.
Editorial note, tabletop extrapolation: At the reference machine's beam powers the radiolytic term is negligible against the model's other terms - but the same production-vs-exhaust balance covers corona and discharge ozone from the HV and RF systems in a closed basement. Odor (threshold ~0.01-0.05 ppm) tells you ozone exists, not how much, and olfactory fatigue silences it during exposure - so the control is ventilation sized by the model or a measurement, with the era's 0.1 ppm occupational figure replaced by the jurisdiction's current limit.
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Monitor exhaust filtration by PRESSURE DIFFERENTIAL: serious changes in delta-P across the filter bank indicate either clogging or rupture; the manual pairs the delta-P watch with a detector (ion chamber or scintillator) at the filter face to track trapped-activity buildup.
filter health = delta-P trend (clog = rising, rupture = falling) + detector at filter faceSource quote & editorial note
Serious changes in the pressure differential on the up and down stream sides indicate that the filter has either clogged or ruptured.
Editorial note, tabletop extrapolation: The delta-P-as-health-monitor pattern transfers to every filtered exhaust in the lab (pump exhaust filters, fume paths for boron sputtering later): instrument the pressure drop, not the filter's appearance. Delta-P sees gross changes - clog rising, rupture falling - while pinholes and seal bypasses can pass it silently, so where a release would actually matter, periodic sampling still closes the loop.
-
Pass a rotating shaft into vacuum with a ferrofluidic seal: ferrite-loaded low-vapor-pressure liquid held in ~0.005 in. radial gaps by magnetic fields, sealing a full atmosphere with no sliding contact.
ferrofluidic rotary seal; ~0.005 in. radial gap; holds 1 atm differential; commercial item (Ferrofluidics Corp., 1971)Source quote & editorial note
a "Ferrofluidic" vacuum seal having ~ 0.005 in. radial gaps in which a ferrite loaded low vapor pressure liquid is held by magnetic fields
Editorial note, tabletop extrapolation: A candidate commercial component - available since 1971 - whenever an accelerator mechanism (chopper, rotating target, variable capacitor) needs rotary motion through the chamber wall; prices vary widely, so treat cost like any other spec. Verify the specific seal's pressure rating (one-atmosphere capability included), leak rate, vapour and backstreaming cleanliness, bakeout limit, speed and torque, and its behaviour in a nearby magnetic field before designing it in. [Note revised 2026-08-23: earlier note called it 'the clean answer any time'.]
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Couple RF to rotating elements without sliding contacts, as Nevis did: feed the stationary electrode and hold the rotor near RF ground through small high-capacitance face gaps (<0.010 in. there), keeping the shaft at RF ground so bearings and drive live in air at ground potential.
rotor-to-ground face gap < 0.010 in. (high C shunt); stator carries RF; shaft/drive at ground in airSource quote & editorial note
the rotors are at low RF due to their < 0.010 in. high capacitance face gaps to ground
Editorial note, tabletop extrapolation: The capacitive-shunting method transfers to rotating RF machinery (choppers, tuners) - by calculation, not copying: work out the gap capacitance (area and gap, not gap alone), the induced rotor voltage and displacement current at the actual frequency and power, and the field/breakdown margins in vacuum. The rotating-capacitor FM tuner itself is synchrocyclotron-specific and does NOT transfer to a fixed-frequency tabletop machine.
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When a resonator must tune over a band, vary the transmission-line characteristic impedance along its length - Nevis's profile (~6 -> ~2 -> 8 ohm) tends to minimize the required capacitor Cmax/Cmin ratio - and budget for structure inductance at the RF frequency considerably increasing the effective Cmax (their full-scale capacitors: 6.5/1.3 nF measured at 1000 Hz).
Nevis: Z0 ~6 ohm -> ~2 ohm -> 8 ohm profile gave Cmax/Cmin = 6.5 nF / 1.3 nF (measured at 1000 Hz)Source quote & editorial note
The basic variation of line Zo along the resonator tends to minimize the capacitor Cmax/Cmin ratio needed. Inductance effects in the structure at the RF frequency considerably increase the effective Cmax value. It is expected that the full scale capacitors will each have Cmax = 6.5 nF and Cmin = 1.3 nF (measured at 1000 Hz).
Editorial note, tabletop extrapolation: FM machinery itself does not transfer, but the impedance-profiling option applies to any tunable tank or swept/trimmed cavity: model the resonator as a transmission line and let the optimization pick the profile - Nevis's own is nonmonotonic, so 'taper' is the idea, not the shape.
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Line surfaces struck by lost beam to REDUCE activation of the structure behind them: Nevis expected marble pole liners 'to reduce sector iron, etc., activation' - stray beam deposits in the stone instead of iron and copper.
marble (CaCO3) liners over pole/sector iron in beam-loss regions - reduction, not elimination (the stone itself activates at Nevis energies)Source quote & editorial note
We expect to use marble pole liners where possible, as in the past, to reduce sector iron, etc., activation
Editorial note, tabletop extrapolation: A higher-energy note, with a scale-free idea inside: CHOOSE what lost beam hits. At any scale that choice already governs sputter contamination and outgassing; it becomes activation-relevant the moment a machine crosses into neutron or few-MeV territory - with thresholdless capture the standing exception to 'negligible below a few MeV'.
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Taper an extraction-channel septum from thin at the entrance to thick downstream, where measured orbit clearance has grown: Nevis's 0.125-in entrance thickening to 0.600 in by 16 in along the channel cut septum power to 40 kW, a factor of four below keeping the entrance thickness throughout, and made room for a larger cooling passage.
Nevis: 0.125 in. entrance -> 0.600 in. by 16 in. along channel; power 160 kW-equivalent -> 40 kW (4x)Source quote & editorial note
This septum will use only 40 kW of power, a factor of four smaller than if the original thickness were kept to the end
Editorial note, tabletop extrapolation: A current-septum channel is beyond tabletop needs, but the geometric principle - septum thickness need only be minimal on the first intercepting turn - applies to any conductive deflector septum on a next machine, subject to the beam-clearance check downstream. (Extraction FOILS are a different problem: stripping, scattering, heating and lifetime set foil thickness, not turn separation.)
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Formalize the safety function as the program grows - the 1974 survey's observed practice: 'there is often a safety officer appointed', many installations have review committees, and written guidance existed in the era's handbooks (NBS 107, TID-23992).
safety officer + independent review + written program (models in NBS 107, TID-23992)Source quote & editorial note
There is often a safety officer appointed. Many installations have safety review committees.
Editorial note, tabletop extrapolation: For a one-person program the transfer is external review - the archive's cross-review protocol is exactly this committee function. For the planned educational-accelerator business, whether a named safety officer and a written program are REQUIRED is the jurisdiction's call (/legal/); the survey records the practice, and the practice is worth adopting either way.
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Threshold-activation detectors sandwiched between absorber slabs gave attenuation half-values 'generally... with better precision than those with ionization chambers' - the quoted comparison for the carbon-disc experiments; their design virtues (threshold blindness to low-energy scatter, passive in-field operation) are the method's logic rather than the quote's claims.
activation of a threshold-reaction foil vs absorber depth -> half-value thickness; Moyer used C12(n,2n)C11, threshold ~20 MeVSource quote & editorial note
Experiments using carbon disc detectors sandwiched between slabs of absorber gave exponential attenuation with half-value determination which were generally made with better precision than those with ionization chambers.
Editorial note, tabletop extrapolation: The C12(n,2n) reaction itself is blind below ~20 MeV and useless at sub-MeV neutron energies; the transferable idea is the energy-thresholded activation foil as a passive, field-immune detector that answers one question cleanly.
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Pick the model scale so a real, available tube is a valid stand-in for the power tube: MacKenzie abandoned a 1/4-scale model because at 100 Mc electron transit-time effects falsified the oscillator's behavior on the fundamental, then chose 1/2 scale where an available tube could represent the big one faithfully.
model frequency must stay low enough that tube transit-time effects remain negligibleSource quote & editorial note
It was not excited satisfactorily due to the fact that at 100 megacycles the transit time effects were quite noticeable on the fundamental mode.
Editorial note, tabletop extrapolation: Cold measurements scale approximately - eigenfrequencies and field patterns follow geometry, while Q, losses, contacts and probe loading need corrections or direct measurement. Any POWERED model test needs a driver checked for transit angle and loading at the model frequency; otherwise the model exhibits modes the real system never sees, and vice versa.
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In the cited grounded-grid drive chain, phase shift was controlled by making the filament-grid capacity large, so the out-of-phase RF current is large compared with the in-phase electron emission current. MacKenzie's tolerance for the total: shifts around 25 deg 'can be tolerated' but 'can not be increased very much without seriously impairing efficiency' - no functional form is given.
mechanism: I_reactive = V*omega*C_gf >> I_emission reduces the emission-current phase pull (cited circuit)Source quote & editorial note
the shift is reduced by making the filament grid capacity large, so that the out of phase r.f. current will be large compared with the in phase electron emission current. ... Hence we might expect total phase shifts around 25° ... this shift of 25° can not be increased very much without seriously impairing efficiency.
MacKenzie, Preliminary Report on the “Three Quarter Wave” R.F. System for Frequency Modulated Cyclotrons — AECD-1850, University of California (1947) — p. PDF p. 12 (printed 11) for the card's current quote; PDF p. 14 (printed 13) for the ~25° limit
Editorial note, tabletop extrapolation: The mechanism matters for any self-excited tube oscillator on a dee - drive phase error costs efficiency - and padding the input capacity is a candidate fix, not a free one: the added reactive current changes loading, bandwidth and possibly parasitic resonances, so verify the full input network after the change. Check total drive phase with an incident/reflected-wave measurement.
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Verify target areal-density uniformity before quantitative use: Harvard located the tail of the Bragg ionization curve at points across the target to map local density (the sensitivity, gradient figures and the pyrolytic-graphite decision are the report's account - re-read queued).
local areal density from range (Bragg-tail position) of a collimated beam through the target; sensitivity here 0.2%Source quote & editorial note
The density of various parts of the target was found ... by searching for the tail of the Bragg ionization curve.
Harvard University Cyclotron Laboratory, Quarterly Progress Report, 1 June – 31 August 1964 — p. 4
Editorial note, tabletop extrapolation: A range-based (or transmission-based) density map of the actual target spot belongs in the error budget of a yield measurement WHEN the required precision or the material's provenance makes nonuniformity plausible - stock and process vary, so let the required precision decide whether to map, and state the stopping-power and composition assumptions the map rests on.
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Check the transient, not just the equilibrium: beam suddenly applied to cold material heats it at dT/dt = P/(m*c) before radiation/conduction respond - 1300 C/sec for Corwin's 11 ug spot. At 1.9 turns/sec each part of the target sits in the beam only 29 ms and rises only 39 C per pass; the moving-target temperature is a sawtooth (65 to 105 C in his example). The spot's thermal recovery timescale is tau ~ r_b^2/alpha, alpha = k/(rho*c) (0.83 s in the example).
dT/dt = P/(m*c) initially; per-pass rise = (dT/dt) x dwell time; tau ~ r_b^2/(k/(rho*c)) - an order-of-magnitude diffusion timescale, coefficient geometry-dependentSource quote & editorial note
the temperature can rise only 39 C before that part of the target is out of the beam.
Editorial note, tabletop extrapolation: Sets the rotation-speed design check: compute the per-pass peak excursion (P/mc x dwell) against the allowable rise, and where the revisit period is not long compared with tau, run a periodic transient-heat calculation - the pulse train settles to a periodic steady state whose peak, not a simple ratchet criterion, is what must clear the material limit.
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Corwin's practical rotator: three targets on a fully adjustable, chamber-independent rotator turning 1.9 turns/sec through an O-ring shaft seal (a ferrofluidic feedthrough allows faster); reconciling Yntema's observations he notes carbon foil life improves both with motion AND with heating to ~400 C, foils thin above 450 C and thicken when cooler, and suspects damage is worst "when there is radiation from a single spot only".
Source quote & editorial note
The lifetime of carbon foils is enhanced both by motion and by heating to about 400 C. Also, carbon foils have been observed to get thinner above 450 C and thicker when cooler. ... These facts suggest that perhaps the foil is damaged when there is radiation from a single spot only. ... It is fully adjustable, holds three targets, is chamber independent, and takes up limited space. It turns the targets at 1.9 turns per sec which is adequate for most experiments; it could easily go faster by using a Ferrofluidic mechanical feedthrough instead of an O-ring feedthrough.
Editorial note, tabletop extrapolation: A rotating target holder is 1950s-shop technology (motor, gears, O-ring feedthrough at ~2 rev/s); the same shaft can carry several targets so a fresh one rotates into the beam without breaking vacuum.
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Roll metals inside a stainless-steel sandwich (Adair & Kobisk): consolidate the reduced metal into a bead, flatten in a hydraulic press, then roll between stainless sheets — the sandwich keeps the foil from adhering to the mill rolls and permits much thinner foils than bare rolling. Rolled foils are typically 1 x 1 inch.
Source quote & editorial note
the metal is placed in a stainless steel sandwich for rolling which prevents the material from adhering to the rolls of the mill and enables a much thinner foil to be prepared. ... Rolled foils are usually 1 x 1 in.
Editorial note, tabletop extrapolation: A jeweler's rolling mill plus shim-stock sandwich makes durable self-supporting metal targets (typically 1 x 1 in per the source) - the natural route to robust backing foils. Whether a rolled foil can serve as a beam STOP depends on the projectile's range: check stopping areal density against the actual beam energy first; the source's thickness tables cover what each metal reached, so cite the row, not a blanket range.
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Evaporate expensive material from tubular crucibles (carbon, Mo, W, Ta) chosen for chemical compatibility with the evaporant, and expect only ~1% collection efficiency in ordinary geometry (Adair & Kobisk); electron-bombardment guns or RF heating serve the refractory and reactive cases, and vacuum reduction-distillation converts oxides directly to metal films.
Source quote & editorial note
evaporation efficiencies of only 1% are obtained.
Editorial note, tabletop extrapolation: Budget isotope/material mass from the geometry: the ~1% collection efficiency is the source apparatus's ordinary-geometry result, and the right transfer is to estimate your own geometric collection fraction (solid angle of substrate at the source), then verify with a witness coupon or charge/substrate mass accounting; crucible-evaporant chemistry (carbide formation, alloying) is chosen per material, not per convenience.
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Weighing discipline (Adair & Kobisk): the NBS sequence-weighing scheme - sample and standard weights of similar mass weighed in a set order - cancels balance zero-point drift; an interlab check on 200+ boron and lithium crystals of 50-300 ug agreed better than +/-1% in almost every case.
NBS sequence weighing (Pontius, NBS TN 228 / Monograph 103); drift cancels, balance sensitivity extracted from the sequenceSource quote & editorial note
In almost every case the agreement was better than +-1%.
Editorial note, tabletop extrapolation: A used microgram-precision balance plus the free NBS protocol is a strong target-mass QA capability - budgeted honestly: 1 ug of combined uncertainty is already 2% of a 50-ug sample, and a deposited mass obtained by difference doubles the exposure, so write the mass-dependent uncertainty budget (readability, repeatability, calibration, buoyancy, static) before promising sub-percent numbers at the light end. The protocol removes drift; it cannot remove the balance's floor.
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Quartz crystal monitors are in-situ process gauges; the ultimate measurement remains direct mass determination of the target after removal from the vacuum system (the calibration practices, cooling threshold and rotating-wheel extension are the proceedings' supporting material - scan re-read queued).
Source quote & editorial note
the ultimate measurement remains the direct mass determination of the target after it has been removed from the vacuum system.
Editorial note, tabletop extrapolation: Treat the QCM reading as rate-and-range control during deposition and take the certified number from pre/post weighing with the deposited area defined - a QCM calibrated in a stable thermal environment can be good, but radiant load from the source shifts its frequency exactly when the reading matters most, so the removal-and-weigh check is the arbiter.
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Measure self-supporting film thickness by charged-particle energy loss (Adair & Kobisk): collimated alphas through the foil, spectrum shift on a calibrated MCA; for small losses W ~ dE/S(E), and for thicker films integrate - W = INT dE/S_m(E) from E_out to E_in - since stopping power changes as the alpha slows. The era's stopping data carried ~+/-10% accuracy, which bounded their absolute results.
thin limit: W = dE/S(E); general: W = INT_{E_out}^{E_in} dE/S_m(E); alpha sources cover ug/cm2 to mg/cm2, fission fragments resolve ultrathin foils, beta transmission covers thick stockSource quote & editorial note
most of these data have an accuracy of ~ +-10%.
Editorial note, tabletop extrapolation: The one thickness method that needs no balance and works on a mounted film - with a surface-barrier detector and MCA. Quote absolute thickness no tighter than CURRENT stopping tables allow at the actual energies, combine straggling/calibration/fit uncertainties, and remember the alpha source is a regulated sealed source, not generic bench stock.
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Quick semi-quantitative gauges (Adair & Kobisk): a calibrated light densitometer reads carbon foil areal density at low thickness but the method stops being useful above about 40-45 ug/cm2 for carbon; low-geometry counting of radioactive deposits is the proceedings' companion assay method (its accuracy and geometry figures - scan re-read queued).
Source quote & editorial note
light intensity change is not a very useful technique for carbon films of thickness greater than 40 or 45 ug/cm2.
Editorial note, tabletop extrapolation: A photodiode and lamp sort carbon stripper/backing foils into thickness bins as an incoming-inspection tool - calibrated against weighed foils and RE-checked periodically, since optical response drifts with lamp, alignment and film morphology; expect it to saturate out near the source's 40-45 ug/cm2 carbon ceiling.
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Map uniformity, not just mean thickness (Adair & Kobisk): scan the foil with a collimated alpha beam position by position and draw a thickness topograph; for 0.5-500 mg/cm2 targets beta particles serve the same purpose (their Fig. 19 profiles a rolled 58Ni foil with a 204Tl source), and radioactive deposits are scanned with a small aperture and a silicon detector.
Source quote & editorial note
The uniformity of thin foils can be determined by scanning the foil with a collimated beam of alpha particles. ... For targets having a thickness in the range of .5 to 500 mg/cm2, beta particles can be used to determine the target thickness profile ... Figure 19 illustrates a target thickness profile obtained by scanning a 58Ni rolled foil with beta-particles from a 204Tl source. ... For radioactive sources the surface of the sources can be scanned using a small collimating aperture and a silicon solid state detector
Editorial note, tabletop extrapolation: The same alpha energy-loss rig with an XY-translated collimator becomes a uniformity mapper. What it maps is AREAL DENSITY variation - a single-point thickness number hides the wedge or large-scale nonuniformity; fine crystallite structure below the aperture scale needs a straggling measurement instead (dg-1190).
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Sputter from rolled isotopic foils when film properties matter (Adair & Kobisk): IRML adapted a commercial sputtering system to accept small rolled isotope foils as sputter sources - a very reproducible process - trading deposition speed for material economy (the electrode dimensions are the proceedings' detail - scan re-read queued).
Source quote & editorial note
this method has proved to be a very reproducible process.
Editorial note, tabletop extrapolation: Shrinking the source electrode to match the available material is the transferable move for scarce isotopes; how far down the stock can go depends on cathode geometry, erosion track, clamping and utilization - establish the minimum for the actual gun by test rather than assuming milligram-scale grace.
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Thompson's laboratory technique: an aluminum foil held at -300 V above an open 228Th bottle collects recoil-ionized 220Rn, which decays to 212Pb (10.6 h half-life), giving alphas at 8786, 6090 and 6050 keV - a fresh, essentially massless recoil-implanted source after ~10 h activation, useful for ~24 h.
228Th -> 224Ra -> 220Rn(+) collected at -300 V -> 212Pb (T1/2 = 10.64 h) -> alphas 8786 / 6090 / 6050 keVSource quote & editorial note
A large portion of the 220Rn gas is created as positive ions which are attracted by the -300 volt collecting potential
Editorial note, tabletop extrapolation: The physics is elegant - the 2.7 MeV spread between the 212Pb lines self-calibrates a spectrometer with no external standard - and the procedure is not an amateur recipe: an open 228Th container means thoron gas, plated-out daughters and removable contamination, and possessing 228Th in usable quantity is licensed activity in most jurisdictions (/legal/). For the program's spectrometer calibration the appropriate form of this idea is a commercial sealed or electroplated check source.
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Calibrate with two peaks and measure only shifts (Thompson): spread the 6050 and 8786 keV lines across the analyzer with a biased amplifier, compute keV/channel from their separation - the energy-scale SLOPE is all the calibration needed, since only shifts are of interest and the absolute intercept drops out - then read target thickness from the channel shift of each peak. His rig held vacuum below 1e-4 torr because the detector bias can strike a glow discharge at higher pressure and damage the detector.
Ec = (8786-6050)/(B-A) keV/ch; dE = (A-A')*Ec; thick targets by piecewise sum T = (dE/N) * sum 1/S(E-(i-1)dE/N)Source quote & editorial note
This is all the calibration which is necessary since now only energy shifts are of interest. ... the vacuum must be maintained at a pressure of less than 10-4 torr to avoid a glow discharge caused by the detector bias voltage. Such a discharge can damage the detector.
Editorial note, tabletop extrapolation: The whole rig is a surface-barrier detector, preamp, biased amp and a stable, linear MCA - Thompson wrote it up precisely so small labs could build it. Estimate fractional channel positions from adjacent-channel counts (peaks are Gaussian) and state the resulting channel uncertainty; whole-channel reading of a small shift is coarse. The pressure threshold for bias-induced glow depends on voltage and geometry - treat 1e-4 torr as his operating requirement and verify your own.
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Free diagnostics of the alpha-loss method (Thompson): peak broadening beyond the no-target width can flag nonuniformity once straggling and instrumental width are accounted for, and small UNSHIFTED satellite peaks flag pinholes - unattenuated paths through the film; the quantitative limits (minimum-thickness formula, upper range, Bragg additivity for compounds) are the paper's framework (scan re-read queued for the formulas).
Tmin = 1.22*(30 + A) ug/cm2 (10%, half-channel, 512 ch); S_compound = (1/M) * sum Ni*Ai*Si (Bragg additivity)Source quote & editorial note
They show up as small unshifted peaks in the energy spectrum.
Editorial note, tabletop extrapolation: One spectrum yields thickness plus uniformity and open-area evidence - run it on every target before installation. The unshifted peak measures unattenuated FRACTION, not a hole count; converting to open area needs the beam profile. Re-measuring after beam exposure quantifies damage - after the radiation survey and handling review that any post-irradiation work gets.
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Seeding rescued difficult condensers in the MicroMatter practice: zinc and cadmium - poor stickers on bare amorphous substrates - condensed uniformly and with very high sticking coefficients onto seeded surfaces (the seed materials, dose and dual-boat procedure are the paper's recipe - re-read queued).
seed layer ~1 ug/cm2 Be or Bi; dual boats so seed and evaporant deposit in one pump-downSource quote & editorial note
Zinc and cadmium condensed uniformly and with very high sticking coefficients.
Editorial note, tabletop extrapolation: When a film refuses to stick or beads up, a nanometer-scale nucleation layer of a compatible metal is the trial to run - material-specific, verified on a witness slide; note the crystal-structure story is looser than the folklore (Bi and Sb are rhombohedral, not hcp like Zn/Cd/Mg/Be), so pick seed candidates from the literature for the actual evaporant rather than from a structure-matching slogan.
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Reduce oxides in the evaporation boat with graphite (Heagney & Heagney): mix the oxide with spectroscopic-grade graphite, press to a pellet, and heat - the pressure gauge gives an indication of the rate of reduction as gas evolves (the material list, times and pressure ceiling are the paper's details - scan re-read queued).
carbothermal reduction, material-specific chemistry: products may be CO, CO2 or carbides depending on oxide and temperature - balance the actual reaction before relying on itSource quote & editorial note
the pressure gauge gives an indication of the rate of reduction
Editorial note, tabletop extrapolation: Lets a target come straight from a stable oxide powder with no separate metallurgy step. The total-pressure gauge is a qualitative process indicator only - it cannot identify the gas or prove completion; use temperature measurement, and an RGA or a validated endpoint where gas identity matters.
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Soften the roughing sequence where fragile foils live: in ANL's new commercial evaporator, an abruptly opened roughing valve went POOMPF and blew every thin carbon substrate off its frame (the calcium-reduction chemistry and short-throw boat geometry are the paper's separate content - re-read queued).
CaCO3 + heat -> CaO + CO2; 2CaO + Zr -> ZrO2 + 2Ca; closed Ta boat, 3 cm throwSource quote & editorial note
the valve opened with a POOMPF and all the carbon substrates disappeared.
Editorial note, tabletop extrapolation: Every pump-down and vent of a chamber holding fragile foils needs a throttled soft-start path - the foils die from the pressure transient and gas-flow forces, not the vacuum. Short-throw closed-boat geometry remains the milligram-economy move, with collection efficiency verified for the actual source and collimator rather than assumed pure 1/d^2.
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Sputter-yield scale (Scaife, Hanley & Purser): at focused-ion-beam energies, yields between 2 and 10 atoms per argon ion are typical - and unlike evaporation rates, yields rarely spread between materials by more than about an order of magnitude (the detailed energy-curve shape and Kr/Xe multipliers are the paper's account - scan re-read queued).
yield max ~25 keV (conductors) / 50-60 keV (dielectrics); 2-10 atoms per 20-keV Ar+; Kr ~2x, Xe ~3x the Ar yield on conductorsSource quote & editorial note
At focused ion beam energies, sputter yields between 2 and 10 atoms per argon ion are typical.
Editorial note, tabletop extrapolation: A keV-range ion gun is a plausible deposition tool - sized honestly: take measured or calculated yield curves for the actual ion-target pair, energy and angle, then work out rate from beam current and collection geometry, plus thermal load and neutralization. Gas choice (Ar vs Kr/Xe) is a rate-vs-cost trade to quantify per material, not a fixed multiplier.
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Pressure sets what sputtered atoms arrive with (Scaife et al.): at 1e-3 torr the mean free path is about 1 cm, so glow-discharge-pressure transport suffers gas collisions; at 1e-6 torr the path is meters and atoms arrive with their emission energy and directionality intact - though working-gas incorporation is still measurable at high vacuum (the source reports 100 ppm Xe in xenon-sputtered tantalum).
mean free path ~1 cm at 1e-3 torr vs ~meters at 1e-6 torr; residual gas incorporation: 100 ppm Xe in Xe-sputtered TaSource quote & editorial note
At 10-3 torr, the mean free path in the vacuum chamber is about 1 cm ... At 10-6 torr, the mean free path is of the order of meters
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.103 (printed p.87) for the 1e-3 torr sentence; it completes on PDF p.104 (printed p.88), which also carries the 1e-6 torr / meters sentence and the Xe figure
Editorial note, tabletop extrapolation: For a small sputter rig the choice is real but not one-sided: a differentially pumped gun with a high-vacuum deposition region preserves arrival energy and directionality; glow-discharge and magnetron processes at millitorr nonetheless make dense, adherent films through substrate heating and plasma bombardment. Choose by what the film needs and measure adhesion, structure and gas incorporation on the result rather than assuming pressure decides quality.
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Working numbers for a focused-ion-beam sputter rig (Scaife et al.): a von Ardenne-type duoplasmatron with einzel lens delivering mA-class 20-25 keV Ar+, with a typical deposition rate of 20 ug/cm2/min of titanium at 2.5 cm; usable targets from ~10 mg of source material - NOTE an internal inconsistency: the paper's ~50 ug/s erosion figure would need ~50 atoms/ion at 2 mA, versus its own typical 2-10 (which gives 2-10 ug/s), and the 20 ug/cm2/min at 2.5 cm itself implies ~6.5 ug/s from a cosine lobe. [2026-09-06 page-image re-read: the page prints 'micrograms/second' unambiguously - the inconsistency is the source's own, not an OCR artifact.]
erosion = I*Y*M/(N_A*e); at 2 mA Ar+ with Y = 2-10: 2-10 ug/s of Ti - the printed 50 ug/s does not reconcile (dg-501 pattern); deposition falls ~1/d^2, lobe slightly narrower than cosineSource quote & editorial note
A typical deposition rate for substrates located 2.5 cm from the sputtering source is 20 ug/cm2/min. of titanium. ... total erosion rate averages 50 micrograms/second when operating with 2 mA of 20 keV argon.
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.114 (printed p.98) for the deposition rate and the gun parameters; the 50 ug/s erosion rate is on PDF p.100 (printed p.84); the ~10 mg source quantity is on PDF p.110 (printed p.94)
Editorial note, tabletop extrapolation: Calibration point for sizing a home sputter-deposition scheme - mA and tens of keV is small-accelerator source technology, not exotic hardware. Time a boron run from a boron yield (measured or from tables) and the actual collection geometry, not from the titanium calibration.
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Contact evaporation for maximum recovery (Reynolds & Morgan): the substrate sits directly on a resistance-heated tantalum tube source with stacked tantalum mesh discs inside as a multi-point source - achieving at least 90% material recovery with ~10% uniformity over the cm2-scale area, on 200-ug-class isotope charges; heat gently (~450 C) and cool slowly so the glass slide does not crack.
tantalum tube + 50-mesh Ta discs as diffuser; recovery >= 90%, uniformity ~10% / cm2Source quote & editorial note
a uniformity of 10% over an area of cm2 with a recovery of at least 90% of the material.
Editorial note, tabletop extrapolation: The zero-throw geometry is the method of interest when the feedstock (separated isotope, exotic compound) costs more than one-at-a-time labor - its recovery advantage over open evaporation is large, and exact areal densities follow from the actual charge, recovery and area (at 90% recovery, 200 ug over 1 cm2 is 180 ug/cm2 - quote the arithmetic, not a nominal).
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Vacuum storage beats atmosphere for degradable targets: ANL's storage-and-transfer system (Worthington, Jedlowski & Thomas) kept hygroscopic and rapidly oxidizing targets under vacuum from evaporator to beamline via valved transfer hardware (the wheel capacity, pressures, baffle temperature and interlock details are the paper's - scan re-read queued).
storage < 5e-7 torr; interlock volume < 0.05 torr before valve openingSource quote & editorial note
Some targets may be hydroscopic, while others may oxidize rapidly.
Editorial note, tabletop extrapolation: The load-lock principle scales down to one target: a valved transfer pot REDUCES atmospheric exposure for Li, Ca or boride targets - how much depends on its achievable pressure, residual water and oxygen, pump backstreaming and valve sequencing, so qualify the pot against a sacrificial target before trusting it with the real one.
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The parting agent, not the evaporation, can set target nonuniformity (Abele et al.): Braski's electron microscopy gave parting-agent crystallite sizes of 100-2000 A and surface roughness 50-1000 A - the same order as a 10 ug/cm2 carbon or 100 ug/cm2 gold film (~500 A) - so 'however uniform an evaporation may be, the parting agent produces an inhomogeneous target', and the source states these nonuniformities are NOT detectable by the standard thickness-profile method.
crystallite size 100-2000 A ~ film thickness; effective-thickness spread grows with 1/cos(tilt) plus crystallite-plane geometrySource quote & editorial note
His analysis gave average crystallite sizes between 100 A and 2000 A and average surface roughnesses from 50 A to 1000 A depending on various parameters as parting agent material, temperature of the substrate, rate of evaporation, thickness of the parting agent. Recalling that carbon foils of 10 ug/cm2 or gold foils of 100 ug/cm2 have a thickness of nearly 500 A, one notices that the size of such a crystallite structure and the target thickness are of the same order of magnitude. This means that, however uniform an evaporation may be, the parting agent produces an inhomogeneous target. These nonuniformities are not detectable in a measurement of the target thickness profile with the standard method
Editorial note, tabletop extrapolation: If a target will sit tilted to the beam or feed a spectrometer, the release-agent choice is a resolution decision, not a convenience. Energy-straggling width is the sensitive test the source used; microscopy or profilometry can also reveal the structure - what cannot see it is a mean-thickness scan at aperture scale.
-
Choose low-crystallite organic parting agents for resolution work (Abele et al.): among the tested release agents, Teepol - and nearly, alanine - kept measured straggling near the ideal-target prediction at high tilt, while NaCl and betaine replicas broadened it severely; the source's QA method: pass monoenergetic alphas through the finished target and compare the straggling width to the Vavilov prediction, checking target resolution without expensive beam time.
fit the measured spectrum as the convolution of the Vavilov distribution, the detector/source response, and a thickness distribution; quadrature FWHM subtraction only after validating that a Gaussian approximation holds for the actual caseSource quote & editorial note
all targets should be produced with the use of Teepol as parting agent, or ... an organic parting agent with very little crystallite structure
Editorial note, tabletop extrapolation: Detergent-film release over salt release wherever the condensing metal tolerates it; and the alpha-straggling comparison is a bench-top RESOLUTION metric using the thickness-measurement rig - one axis of target quality, with adhesion, pinholes, large-scale uniformity and durability still needing their own checks.
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Match the e-beam spot to the evaporant droplet (Maier-Komor): the most efficient energy transfer comes at beam diameter = droplet diameter - larger wastes power on the cooled crucible, smaller saturates in the dense vapor above the impact point; for their small charges, roughly half the beam power was lost to backscatter off the high-Z melt (Kanter/Sommerkamp Ta-sphere data: ~49% absorbed).
beam spot ~ droplet diameter; power absorption ~49% (Ta sphere); backscatter loss rises with Z and with incidence angleSource quote & editorial note
the most efficient energy transfer is achieved, when the electron beam and the molten droplet have the same diameter.
Editorial note, tabletop extrapolation: Small-charge e-gun work is a spot-placement problem, and the transferable warning is that rated gun power is not deposited melt power - the deficit depends on electron energy, Z, geometry and what the chamber recaptures, so estimate absorption for the actual configuration instead of applying the Ta-sphere 49% as a universal factor of two. Never size a gun from evaporation enthalpy alone.
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Regulate the e-gun supply or re-aim at every power change (Maier-Komor): drooping supplies sag up to 25% at full load, and with magnetic deflection the spot radius follows sqrt(V), so the spot walks off the evaporant - the source's own example says nearly 7 mm for its gun. Find the true spot by melting a hole in a copper foil laid in the crucible, or by maximizing crystal-monitor rate versus deflection. Use water-cooled copper crucibles, cleaned of oxide, one per isotope.
r ~ sqrt(V): a 25% droop at r = 25 mm computes to 25*(1 - sqrt(0.75)) = 3.4 mm of radius change. [2026-09-06 page-image re-read: both printed numbers verified exactly; the source's 'nearly 7 mm' reconciles as the landing-point displacement, ~2x the radius change (6.7 mm) - read its figure as spot walk on the evaporant, not radius change.]Source quote & editorial note
the output voltage can fall off by as much as 25 % at the maximum load ... assuming a deflection radius of 25 mm ... the beam spot will shift nearly 7 mm when the power supply is fully loaded
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.228 (printed p.211)
Editorial note, tabletop extrapolation: Any home-built or surplus e-gun needs a stiff regulated HV supply before it needs more power; the copper-foil melt-hole trick is the free beam-alignment diagnostic.
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Manage charge on insulating substrates during e-gun runs (Maier-Komor): the parting-agent-coated substrate is an insulator, so start at a very low evaporation rate so the growing layer can discharge - otherwise 'sparks will occur, destroying the parting film and the thin isotope layer by hairline cracks'; the wider charging discussion is the paper's (scan re-read queued).
Source quote & editorial note
sparks will occur, destroying the parting film and the thin isotope layer by hairline cracks.
Editorial note, tabletop extrapolation: Grounding topology inside the evaporator is part of the recipe - and the same charging physics will bite any deposition or beam system with floating fixtures near keV electrons: bond fixtures deliberately rather than assuming they find ground.
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Budget substrate heating from condensation and source radiation (Maier-Komor): condensation releases ~6e5 J/g-atom for low-vapor-pressure metals - so heating rate = (mass flux)*(6e5/M) with the evaporant's molar mass M in the equation - and radiant load at equal vapor pressure follows source temperature (Mo radiates ~10x what Au does); the only ways out are cooling the substrate or periodically interrupting the evaporation.
q_dot = (g/cm2/s flux) * 6e5/M [the 6e5/M molar-mass form is our algebraic restatement - the paper works the criterion as a condensation rate: 5e-8 g/cm2.s keeps a 50 ug/cm2 NaCl parting layer under 10 C per second at ~10 cm crucible-substrate distance]; contamination criterion = ratio of residual-gas impingement flux to deposition flux (NOT a source-pressure ceiling - slower evaporation at fixed background makes films dirtier; the paper's 1e-6 Torr applies to the residual vacuum)Source quote & editorial note
the energy impinging on the substrate is ten times as large for Mo than for Au. Here the only way to avoid destruction of the targets is to cool the substrate or to periodically interupt the evaporation process
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.236 (printed p.219)
Editorial note, tabletop extrapolation: Substrate meltdown during deposition is the same radiation/conduction bookkeeping as beam heating (Corwin, this volume) with condensation enthalpy as the source term; refractory evaporants punish the substrate through radiation long before the film is thick.
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Sulphide (and volatile-compound) evaporation is a cleaning-and-preheat protocol, not just a boat temperature - Peck's protocol (Queen's): abrasive-clean the substrate (gently on gold - buried grit mimics a Si contaminant), water then ethanol rinse, pump while still alcohol-wet, chimney-topped boat, substrate pre-warm.
Source quote & editorial note
The cleaning process is of utmost importance ... The substrate must first be cleaned with a mild abrasive powder ... The water is removed with Ethyl Alcohol and while still wet with alcohol is immediately placed in the evaporator and pumping started.
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.257 (printed p.240); the pre-warm step and the colour chart are on PDF p.258 (printed p.241)
Editorial note, tabletop extrapolation: Template for any compound that dissociates or splashes: pelletize the charge, chimney the boat, pre-warm the substrate with the source itself - and treat any color-temperature chart as a coarse process indicator only (color-to-temperature conversion is unreliable; a thermocouple wins when the number matters). Valve off the diffusion pump so compound vapor does not load the pump oil.
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When forming a target compound by heating a deposit on a substrate, beware the high side: too high a temperature diffuses the reactant into the substrate - nitrogen into the tantalum, in the cited N-15 work - leaving a target with poorly defined thickness (the specific temperature window is the paper's recipe - re-read queued).
TiN nitriding window 750-800 C (optical pyrometer, uncorrected for emissivity)Source quote & editorial note
too high a temperature can cause nitrogen diffusion into the tantalum substrate resulting in a target with a poorly defined thickness (Stinson, "The Preparation of Nitrogen-15 Targets")
Editorial note, tabletop extrapolation: Any reacted-layer target (nitride, oxide, deuteride) on a metal backing needs its own temperature study - the failure modes differ by system (substrate diffusion here; desorption or decomposition for deuterides) - and a smeared depth profile shows up downstream as degraded resonance width or energy resolution, which is the cheap check that the window was respected.
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Hydrogen tube-furnace reduction converts many common target oxides to metal with modest equipment, per the report's two-page per-element table (temperature, reductant, boat); the boat must be chemically compatible - the quote's trap: iron in a graphite boat forms carbide - and the report's apparatus dries and deoxygenates the H2 and guards the vent flame with an oil trap.
per-element reduction table (temp, reductant, boat) at PDF pp.102-103; Vycor tube to 1000 C, quartz to 1300 CSource quote & editorial note
Iron forms a carbide if a graphite boat is used (Heagney & Heagney, "Reduction Techniques for Isotopic Materials")
Editorial note, tabletop extrapolation: The route from purchased oxide powder to rollable or evaporable target metal - consult the per-element table before buying any element as oxide. A hot hydrogen furnace is its own hazard class: inert purge before and after H2, flow and flame management, and per-element vapor and hydride toxicity are prerequisites the table assumes rather than teaches; the report's apparatus description is the checklist seed, not the whole checklist.
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Electrolytic reduction conserves scarce material: in the cited practice, usually better than 90% of the metal deposited on the cathode (the bath chemistry, current density and volumes are the paper's parameters - re-read queued).
Zn, Cd plating at 5-10 mA/cm2; bath volume 1-5 ml scaled to isotope quantitySource quote & editorial note
Usually better than 90% of the metal can be deposited on the cathode (Heagney & Heagney, "Reduction Techniques for Isotopic Materials")
Editorial note, tabletop extrapolation: For milligram-scale enriched material the deciding metric is END-TO-END recovery fraction, not speed - cathodic deposition is one term in it (dissolution, transfers and electrode handling take their shares), so weigh the whole chain for each candidate route rather than assuming electrolysis beats furnace reduction whenever plating works.
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Cool a fragile target in use by conduction through its edges: the cited mercury targets connected the target edge to a chilled copper block with silver paint (the block and target temperatures are the discussion's figures - re-read queued).
edge conduction via silver paint; block -80 C -> target ~-50 C (~30 K rise through the joint and film)Source quote & editorial note
They are cooled from the edges by connecting to a copper block with silver paint (Maier, discussion of "Preparation of Isotopically Enriched Mercury Targets")
Editorial note, tabletop extrapolation: The simplest conductive-cooling geometry for a target that cannot be water-backed - a cold finger to the frame plus a conductive-paint joint. What temperature the target actually runs at is beam power times the total thermal resistance: compute it or measure it in beam; the joint and film resistance can be anywhere from negligible to dominant, so no stock kelvin budget applies.
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In reduction-distillation, pick a reductant of MODERATE oxygen affinity - by the oxide dissociation-pressure diagram - so reaction speed stays controllable by furnace temperature: tungsten powder reduces HgO smoothly (the paper's 500 C, ~10 min run), while thermodynamically stronger reductants (Zr, Th) run into explosion and scatter the charge.
choose reductant by oxide dissociation-pressure diagram; W + HgO controllable at 500 C, Zr/Th explosiveSource quote & editorial note
the reaction with mercury oxide runs into an explosion (Friebel et al., "Preparation of Isotopically Enriched Mercury Targets")
Editorial note, tabletop extrapolation: Strongest is not best in metallothermic reduction: a controllable reaction that completes in minutes beats a violent one that contaminates the product. Mercury adds its own layer - at these temperatures Hg is mobile, toxic vapor, so the paper's sealed-retort integrity, condensation path and exhaust handling are part of the method, and mercury work sits behind fume containment at any scale.
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Thick targets from powder, per the cited practice: press the powder between two polished stainless ferrotype plates at about three tons per square inch (the charge masses, disc size, binder wash and glove-box handling are the paper's procedure - re-read queued).
~3 ton/in2 between polished plates -> 100-150 mg/cm2 discs; 1 mg/ml polyethylene-xylene binder wash for fragile discsSource quote & editorial note
the powder was pressed between two stainless steel plates (Premier Brand Ferrotype) at about three tons per square inch (Minamisono & Ramsay, "Thick Targets for In-Beam Hyperfine Structure Study")
Editorial note, tabletop extrapolation: The no-evaporator route for activation and yield work: a hydraulic press and polished plates. Compute the areal density from measured mass over measured area (300-400 mg on a 2-cm disc runs ~95-127 mg/cm2), and verify 'beam-stopping' against range data for the actual ion and energy rather than by adjective.
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Pack-rolling craft: 3-5 mil polished tungsten sheet makes a hard reusable pack (but not for the very thinnest foils); spring-steel sheet works alongside stainless; and when a soft metal (Pd) welds itself to the pack below ~500 ug/cm2, make three to five passes at the SAME mill setting before reducing further.
W sheet 0.003-0.005 in packs; Pd anti-weld = 3-5 passes per setting; U limit ~1 mg/cm2 with electropolish (H2SO4) between rolling stages, minimal heatSource quote & editorial note
In addition to stainless steel, spring steel sheet has been found useful for pack rolling. Tungsten sheet, 0.003 to 0.005 in., is good for pack rolling, is very hard with a good polish, and can be used many times. Tungsten is not suitable for rolling very thin targets because of its crystal structure. Palladium: A problem is welding of palladium to the pack when trying for less than 500 ug/cm2. This can be avoided by making three to five passes at the same setting before going thinner. Uranium: 1 mg/cm2 is about the limit. Since oxidation of U limits its rollability, it is useful to roll, electropolish (sulfuric acid removes oxide), roll again, (or roll in Ar). Be careful not to generate too much heat in rolling.
Editorial note, tabletop extrapolation: The same-setting-passes trick (plausibly work-hardening the surface before the next bite - our hypothesis, not the source's) and the electropolish-between-stages cycle for oxidizing metals are the two non-obvious moves in amateur pack rolling.
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Heating and moving a stripper foil multiplied its life in the cited experiment (carbon foils under intense 3-MeV Kr+): holding foil and frame at 450+-150 C gave about 4x lifetime, orbiting the foil ~3x, both together ~6x - and the failure signature changed, cold foils breaking suddenly while heated ones tore gradually from an edge.
x4 (heat 450+-150 C), x3 (orbit 1 rpm), x6 (both); baseline reduced lifetime 0.4-0.5 min for 3-MeV Kr+ at 0.125-0.2 p-uA/mm2 (Table I, PDF p.29)Source quote & editorial note
Heating the carbon foil and graphite support frame to an ambient temperature of 450 +-150 C increased its lifetime by about a factor of 4 (Thomas, DenHartog, Bicek & Yntema, "Lifetimes of Carbon Stripping Foils")
Editorial note, tabletop extrapolation: A heater ring or slow rotation stage on a foil holder is a cheap candidate life-extender - for carbon under heavy beams it has a strong record; for other target materials, adhesives and beams, heating can as easily hurt (oxidation, adhesive failure, evaporation), so test it with heat-load and vacuum checks rather than booking a multiplier. The gradual-tear behavior of heated carbon is a bonus where it holds: warning instead of sudden loss.
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Beam duty-cycling extends foil life only if the off-periods are long enough: equal on/off periods of 60 s produced encouraging results while 6-s periods showed very little improvement - the source's reading being that longer cycles may afford the foil a relaxation time, which may also contribute to the gains from moving foils.
60 s on/off helped, 6 s did not (3-MeV Kr+ on ug/cm2-class carbon stripping foils; the previously printed 5 mg/cm2 was a unit slip - the paper's foils run 5-120 ug/cm2)Source quote & editorial note
Periods of sixty seconds have produced encouraging results while six second periods showed very little improvement in foil lifetimes. The longer cycling times may afford the foil a relaxation time. This relaxation time may also be a contributing factor in the increased lifetimes for foils which are moved.
Editorial note, tabletop extrapolation: Relevant to any interlock or chopping scheme meant to spare a target: two time points bracket, but do not measure, the relaxation constant - if chopping is the plan, scan the off-time on the actual foil rather than assuming tens of seconds is the magic number.
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Rolling feedstock should be a clean solid bead (Kellner & Maier-Komor): pressed-and-sintered powder shows severe disadvantages - grain-boundary defects end rolling early - and arc melting loads the bead with gaseous impurities; their route melts 50-500 mg portions with an electron gun in a water-cooled copper crucible, lets the drop solidify slowly from the cooled side so impurities concentrate in a last-frozen 'stalagmite' that is cut off, repeating ~10 times for uranium.
e-beam zone refining by slow solidification + stalagmite cutting, ~10 cyclesSource quote & editorial note
The older method of pressing the metal powder and sintering it under vacuum shows severe disadvantages. The defects at the grain bounderies [sic] set an early limit during the rolling process. Arc melting has disadvantages too, there may be many gaseous impurities in the processed metal bead ... The metals are melted in portions from 50 to 500 mg in a water cooled copper crucible with an electron gun keeping the temperature just above the melting point. ... the drop solidified starting with the zone nearest to the water-cooled crucible. The part of the drop which solidified last was formed like a stalagmite and was highly enriched with impurities. After venting with argon this stalagmite can be cut away and the procedure can be repeated. For Uranium we did this about 10 times.
Editorial note, tabletop extrapolation: Explains why bought powder pressed into a pellet resists rolling thin (porosity and grain-boundary defects - fully densified stock is the exception); the repeated directional solidification rejects the impurities whose segregation behavior is favorable, not all of them - the authors themselves found true zone refining fails on uranium (surface tension) and used this slow-solidification variant instead.
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Pack (sandwich) rolling jacket spec: bright-annealed, temper-passed stainless of 0.5 mm or thinner, LOW carbon (<0.03%, low grain disintegration) for most metals, or ~0.1%-C spring steel for metals less ductile than nickel; use vacuum-melted stainless for the inner jacket — ordinary cold-rolled band carries ingot-scale texture lines that slice thin foils into strips along the rolling direction.
jacket <=0.5 mm, surface roughness 0.05-0.1 um; low-C Cr-Ni stainless (or spring steel for brittle metals); vacuum-melted sheet for inner jacketSource quote & editorial note
For rolling metals with a ductility lower than nickel or iron one should take as sandwich material a stainless steel with a high carbon content named spring steel band. This material has a higher temper due to its carbon content of about 0.1%. All other stainless steel sandwiches should be made of a Chrom-Nickel steel with extreme low carbon content. There are some materials available with a carbon content below 0.03%. ... We noticed that material with a thickness of 0.5 mm or below gave the best results. ... This material should be bright-annealed in an inert gas atmosphere and be dressed in a temper pass mill, to get a highly polished oxide-free surface. The surface roughness for the best quality material is of the order of 0.05 to 0.1 [um] ... These lines are strictly parallel and always along the texture of the sheets ... The source of these inhomogeneities are the scales which remained on and in the ingot before machining it to cold rolled band steel. Vacuum melted stainless steel does not have these impurities. ... We use it for the inner part of our double sandwich.
Editorial note, tabletop extrapolation: The foil replicates the jacket's flaws (the source's central claim, conditioned on an accurately designed mill) - jacket steel selection is the dominant quality variable in pack rolling once the mill itself is true; roll finish, alignment and reduction schedule still matter on amateur equipment.
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Pack-rolling schedule for the cited uranium/molybdenum work (Kellner & Maier-Komor): reduce about 3-10% per pass, and when the jacket has grown to about twice its size, transfer the foil to a fresh jacket (the double-sandwich variant and its thresholds are the paper's further detail - scan re-read queued).
3-10% reduction/pass; re-jacket at 2x elongation; double sandwich (0.1-0.2 mm inner) below 5-10 mg/cm2Source quote & editorial note
reduced by about 3 to 10% per pass. When the jacket increased its size by approximately a factor of two the foil is placed in a new jacket (Kellner & Maier-Komor, "Rolling Thin Uranium Foils")
Editorial note, tabletop extrapolation: A worked schedule showing sub-mg/cm2 rolling is a craft with rules, not heroics - transfer the discipline (small reductions, fresh jackets on elongation) and expect each metal to demand its own trials: permissible reduction, annealing needs and attainable thickness are material-specific.
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Anneal rolled foils between resistively-heated tantalum sheets in good vacuum for ~30 min at a temperature chosen below the metal's phase transition (uranium: below 930 K at 1e-7 torr, to stay in the alpha phase); etch the oxide first with highest-purity dilute nitric acid, because a reactive foil picks up reducible metal contaminants from a dirty acid. [Corrected 2026-08-23: earlier text said the foil 'getters every metal impurity', which overstates the chemistry.]
anneal ~30 min, 1e-7 torr, T below phase transition (U < 930 K)Source quote & editorial note
If oxidation on the surface of the Uranium foil is observed it should be etched with diluted nitric acid of the best quality, because all metal impurities in the acid will be catched by the Uranium foil due to its very negative electro-chemical potential of -1.8 volts. After cleaning in oxygen free distilled water and ethanol the foil is annealed between two Tantalum sheets which are heated by an alternating current. The annealing lasts for about half an hour in a vacuum of 10-7 Torr at a temperature below 930 K, which was chosen to prevent phase transitions.
Editorial note, tabletop extrapolation: Interpass and final annealing is what keeps a work-hardened foil rollable and flat. The phase-transition ceiling is the uranium-specific reason here; for any other allotropic metal choose the anneal from its own phase diagram and the phase or texture you want - some iron and titanium treatments deliberately cross a transformation. [Note revised 2026-08-23: earlier note generalised 'below any phase transition' to all allotropic metals.]
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Reactive sputtering produces even, tough, adherent nitride films with easy thickness control (Stinson): DC sputtering of Ta or Ti in low-pressure N2 - with the paper's own numbers carrying an internal transposition: it rates TaN at 1-1.5 and TiN at 3-4.5 ug/cm2-min, yet its examples make 36 ug/cm2 of TaN in 8 min (4.5) and TiN in 32 min (1.1) - the material labels on the rates and the examples cannot both be right (dg-501 pattern; scan re-read queued).
DC sputtering ~3 kV / 30 mA at ~80 um N2; rates TaN 1-1.5 ug/cm2-min, TiN 3-4.5 ug/cm2-min; 36 ug/cm2 TaN in 8 minSource quote & editorial note
Even, tough films, easy thickness control and production of self supporting targets are other advantages inherent to the process (Stinson, "Nitrogen Targets Produced by Reactive Sputtering of Tantalum and Titanium") ... Tantalum nitride targets with a thickness of 36 ug/cm2 were produced by sputtering for eight minutes. Titanium nitride targets of the same thickness required 32 minutes. ... the sputtering rates range from 1 to 1.5 ug/cm2.min for tantalum nitride, and from 3 to 4.5 ug/cm2.min for titanium nitride.
Editorial note, tabletop extrapolation: Sputter deposition is the durable-target counterpart to the ORNL-3021 evaporation recipes - slower, but the film adheres and survives beam heating; backing choice and beam-power suitability still get verified per design rather than assumed from the process name.
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An uncooled sputtering cathode heats up during long runs and the sputter rate climbs with it, so deposited thickness is NOT linear in time — either water-cool the cathode or calibrate thickness against weighed samples rather than clock time.
rate spread 1-1.5 (TaN) and 3-4.5 (TiN) ug/cm2-min attributed to cathode heatingSource quote & editorial note
the longer sputtering times required for thick targets produce higher temperatures, and higher rates (Stinson, "Nitrogen Targets Produced by Reactive Sputtering")
Editorial note, tabletop extrapolation: Applies to any deposition where the source drifts hot — time-based thickness control needs either thermal steady state or an in-situ monitor (quartz crystal, witness plate).
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Refractory-metal evaporation practice from the cited tungsten work (Ellsworth): electron-bombardment heating of an outgassed isotope ball on a tungsten pedestal in a water-cooled crucible; higher evaporation rates gave LESS stressed targets, and tank pressure above 4e-6 torr made the films brittle with short shelf life.
6 kV / 130 mA loop-filament e-bombardment; pressure ceiling 4e-6 torr; NaCl on 10-mil stainless at 400-600 F; 0.1-0.3 mg/cm2 self-supporting from 300-500 mg of isotopeSource quote & editorial note
Tank pressure above 4 x 10-6 torr made the targets more brittle and shortened their shelf life (Ellsworth, "Preparation of 3/4-in Dia. Self Supporting 182W and 184W Targets for Cyclotron Bombardment")
Editorial note, tabletop extrapolation: Transfer the method - control pressure, rate and substrate temperature, then calibrate stress, adhesion and shelf life on the actual material - not the tungsten numbers: the 4e-6 torr boundary and the rate-stress trend are that process's results, and residual stress can move the other way in another material/substrate system.
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Mount curl-prone foils on frames pre-coated with Canada Balsam dissolved in xylene: once the solvent dries the balsam stays tacky indefinitely at low vapor pressure and retains foils that would otherwise curl off on drying; keep a cover frame over freshly floated films until dry.
Canada Balsam in xylene, applied to frame, solvent dried before pick-upSource quote & editorial note
The Balsam remains tacky and retains foils indefinitely. It also has a low vapor pressure (Riel, "Gallium Rich Ga2O Targets for Use at Room Temperature")
Editorial note, tabletop extrapolation: A tacky mounting adhesive solves the foil-jumps-off-the-frame failure of float-mounting; pairs with the ORNL-3021 float-off recipes. 'Low vapor pressure' is the source's claim for their chamber - run an outgassing/base-pressure test (and consider beam-induced decomposition near the spot) before trusting balsam in a tighter vacuum budget.
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Rollability of chromium is set by chemistry (Friebel et al.): small impurities of nearly all metals at the few-hundred-ppm level largely enhance brittleness - so the reduction route chosen upstream fixes the ductility available downstream (their route choice and processing thresholds are the paper's account - scan re-read queued).
few-hundred-ppm impurities embrittle Cr; ductile fragments 10-15 mg; interpass anneals above 1 mg/cm2; minimum reached 700 ug/cm2Source quote & editorial note
small impurities of nearly all metals in the order of magnitude of a few hunderd [sic] ppm largely enhance the brittleness (Friebel, Frischke, Grossmann & Maier, "Preparation of Isotopically Enriched, Self Supporting Chromium Targets")
Editorial note, tabletop extrapolation: When a foil cracks in the mill, suspect chemistry before technique - assay or provenance-check the stock before burning days on rolling variables. The few-hundred-ppm sensitivity is chromium's measured result; treat other brittle metals as innocent until their own data convict.
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Derive the gas-purity spec for hydrogen reduction from equilibrium thermodynamics (Friebel et al.): for their Cr2O3 + H2 process the equilibrium maximum tolerable water content of the hydrogen was 540 ppm - with the practical spec set well below it for workable kinetics (their temperature, working ppm and furnace time are the paper's recipe - scan re-read queued).
p(H2O)/p(H2) equilibrium ratio 5.4e-4 at 1400 K (Cr2O3); working spec <=10 ppm; 6 h at 1400 K for completionSource quote & editorial note
in equilibrium the maximum tolerable water content of the hydrogen atmosphere is 540 ppm (Friebel et al., "Preparation of Isotopically Enriched Chromium Targets")
Editorial note, tabletop extrapolation: The template for judging whether tank-grade gas is good enough for any reduction or annealing atmosphere: compute the equilibrium H2O/H2 ratio at the furnace temperature before blaming the furnace - then verify the DELIVERED atmosphere (dew point or oxygen potential at the work zone), since a purifier's outlet spec says nothing about downstream leaks and outgassing.
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Thick carbon foils (1-8 mg/cm2) need no evaporator (Lozowski): settle 325-mesh graphitized powder from an air suspension onto carbon-coated glass, then press at ~14 tons/in2 into a lustrous flexible film (uniformity <10%); the tested amorphous powder was rejected - it would not bind, and its low thermal conductivity and high resistivity made it a poor choice for their accelerator targets.
325-mesh graphitized (2500 C) powder; 14 ton/in2 (1.93e8 N/m2) between carbon-coated glass; 1-8 mg/cm2, uniformity <10%Source quote & editorial note
additional properties of low thermal conductivity and high electrical resistivity reveal it to be a poor choice for accelerator targets (Lozowski, "A Dry Powder Technique for the Preparation of Carbon Foils")
Editorial note, tabletop extrapolation: Beam-stopping carbon from a powder blower and a hydraulic press - plus the selection principle that a target material must conduct heat and charge away. The amorphous-carbon verdict belongs to that powder and process: evaporated amorphous-carbon foils serve routinely as accelerator targets and strippers, so judge each carbon form on its measured conductivity and binding, not the category.
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Electrodeposited platinum targets proved less fragile in beam than evaporated ones in the cited work (Saettel), with ~250 mA/cm2 the workable compromise (higher densities gave spongy deposits) and a deposition rate of ~3.6 ug/cm2-min. The paper's '20% yield' is platinum recovery from the bath charge (10 mg charged; ~18% ends up across the nine deposits), not a Faradaic current efficiency - with that reading the printed current density and rate stand together. [2026-09-06 page-image re-read: 250 mA/cm2 verified at 600 dpi; the earlier Faradaic-efficiency contradiction dissolves under the bath-recovery reading, which the abstract and the bath arithmetic both support.]
Pt at 250 mA/cm2 deposits ~3.6 ug/cm2-min (15-90 min gives 60-305 ug/cm2); '20% yield' = bath-recovery fraction, vs 85% Faradaic-class plating for Fe/Ni/ZnSource quote & editorial note
a constant current density of 250mA/cm2 ... the deposition rate is about 3.6ug/cm2. min. ... the yield in the case of platinum is about 20%. However, it happens that platinum is lost as a residue in elementary form in the bath.
Proceedings of the Sixth Annual Conference of the International Nuclear Target Development Society — LBL-7950, Lawrence Berkeley Laboratory (1978) — p. 133 (printed = PDF) for the quoted conclusion; the numbers are on 131-132
Editorial note, tabletop extrapolation: Electroplating joins rolling on the durable side of the durable-vs-evaporated divide, and it works at milligram scale with a beaker and a regulated supply - for platinum by this process on this evidence; other metals earn the durability label with their own beam tests.
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Optical transmittance calibrates surface density for evaporated METAL films too (Al, Cr, Cu, Au, Ag, Sn, Ti; ~+-20% at 546.1 nm) — but gravimetric calibration fails on slides coated with soap-like parting agents, which lose weight in vacuum; reactive metals (Ti, Al, Cr) reproduce worst because of oxide/gas uptake.
transmittance vs ug/cm2 curves at 546.1 nm, +-20%; Al/Cr/Sn/Ti useful to ~50-80 ug/cm2, Ag/Au/Cu to ~300 ug/cm2Source quote & editorial note
For evaporated metal coatings (Al, Cr, Cu, Au, Ag, Sn, and Ti) we have developed curves of optical transmittance vs surface density that can be used to estimate surface densities to within about +-20%. ... measured at 5461 A ... it was not possible to carry out accurate measurements with slides that had been coated with a soap-like parting agent, since these would lose weight upon being placed in vacuo. ... It is certain that all of our coatings were contaminated either by oxide layers, burial of residual gas, and/or adsorption of active molecules. The curves indicate such effects by the extent of their non-reproducibility, most serious for the active species
Editorial note, tabletop extrapolation: Extends the carbon transmittance gauge to the metals a small lab actually evaporates; weigh calibration slides bare, never soaped — the parting agent is part of the tare and it evaporates.
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Load titanium with hydrogen by heating in sub-atmospheric purified gas (Gursky & Sherwood): outgas at 800 C in vacuum first, absorb at ~650 C, pass the gas through a deoxygenating cartridge AND a liquid-nitrogen trap - the trap is essential; the gas is not absorbed otherwise - and meter uptake as the pressure drop in a known volume (via n = d(PV/RT), converting to STP volume afterward if wanted); reversible by pumping at 800 C.
absorb at ~650 C sub-atmospheric; outgas 800 C; uptake = dP * V_system at STP (example - 0.817 of available gas absorbed, 130 cm3 per cone)Source quote & editorial note
The trap is essential; the gas is not absorbed otherwise (Gursky & Sherwood, "Hydriding of Titanium Cones for a Sputter-Ion Source")
Editorial note, tabletop extrapolation: The bench recipe for Ti-H or Ti-D loaded pieces - executed as a hydrogen process, not a casual one: hydrogen-rated containment and plumbing, leak checking, ventilation and ignition control, and a trap that gets inspected (an LN2 trap can concentrate oxidants if purification fails). Tritium is a different world entirely - licensed containment, monitoring and recovery - and is not an amateur variant of this recipe.
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Sandwich low-melting-point target metals between carbon layers - GSI practice for Pb and Bi on high-current wheel targets, e.g. C/Bi/C at 0.03/0.5/0.03 mg/cm2 - extending stability and lifetime under bombardment.
C/metal/C sandwich, typ. 0.03 / 0.5 / 0.03 mg/cm2 - i.e. 30 ug/cm2 of carbon per side, 60 totalSource quote & editorial note
Low melting-point elements like Pb or Bi are sandwiched between C layers for the use on target wheels, thus extending the stability and life-time
Editorial note, tabletop extrapolation: A demonstrated construction for Pb/Bi-class soft metals; for another soft metal, run the compatibility, adhesion and beam tests before promoting it to recipe. Budget the carbon honestly - 60 ug/cm2 total is real material in a sub-MeV beam's energy-loss budget - and credit the skins with mechanical containment first; the thermal mechanisms are plausible but unquantified here.
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Multi-layer overcoats buy target lifetime through conduction: the 1983 heavy-ion discussion recorded that metal/carbon overcoat layers appear to enhance thermal and/or electrical conductivity, shunting both thermal gradients and accumulated charge to the heavy frame around the target - significantly increasing lifetime; energy accumulation showed up as local melting, evidenced by broadening of scattering peaks.
Source quote & editorial note
Additional features of such multi-layer targets appear to be their enhanced thermal and/or electrical conductivity. Both thermal gradients and electrical charge generated in or on the target during bombardment appear to be shunted to the relatively heavy frame surrounding the target. This improved energy transfer tended to significantly increase target lifetime under bombardment. Accumulation of energy was also reported to cause local melting of the target material as evidenced by significant broadening of scattering peaks.
Editorial note, tabletop extrapolation: Two transferable ideas: treat the frame as the heat sink and design the film-to-frame conduction path deliberately; and watch the elastic-scattering (or yield) peak width online as a degradation warning - broadening flags trouble worth investigating (melting is one cause; thickness change, roughening, charging and detector drift are others).
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Protect reactive target metals with a thin sacrificial overcoat, sized by experiment: Argonne reported lithium (500 ug/cm^2 on pinhole-free Ni) protected by ca. 500 ug/cm^2 of copper — possibly as thin as 100 ug/cm^2 — which held oxygen/moisture attack off for about five minutes of air exposure; gold at 30-40 ug/cm^2 gave only marginal protection.
Cu overcoat ~100-500 ug/cm^2 on Li; ~5 min air handling windowSource quote & editorial note
Representatives from Argonne National Laboratory indicated their partial success using a thin layer of copper (ca. 500 ug/cm2 or less). With this protection, it was observed to take five minutes before any significant amounts of oxygen or moisture were detected. The minimum thickness of copper required was indefinite, but 'it could possibly be as thin as 100 ug/cm2'. The overcoating was successful with lithium layers of 500 ug/cm2 on pin-hole free nickel substrates. ... others in the group indicated only marginal success with gold coatings. The thickness suggested for the gold layer was 30-40 ug/cm2.
Editorial note, tabletop extrapolation: Sets the realistic SCALE for air-handling of reactive targets - minutes, not hours - from one measured case (Li under Cu, with 'partial success' and detection-limited timing): use inert transfer where possible, validate each target/overcoat pair, and remember overcoat nuclei scatter too, so the coating choice is coupled to the experiment.
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Make elemental Si from enriched SiO2 by magnesium reduction in a closed crucible (Hinn) - SiO2 + 2Mg -> Si + 2MgO - avoiding a large excess of Mg, which forms Mg2Si instead of Si (the full recipe - charge masses, firing cycle, leach and outgassing - is the paper's procedure; scan re-read queued, including reconciling its ~70% yield against the ~93 mg theoretical Si from 200 mg oxide).
SiO2 + Mg reduction; 200 mg oxide to 170 mg Mg; ~70% yieldSource quote & editorial note
A large excess of Mg must be avoided to preclude formation of Mg2Si instead of Si.
Editorial note, tabletop extrapolation: The metallothermic pattern (reductant choice, closed crucible, acid leach of the oxide by-product) is the standard route from affordable oxide feedstock to a solid target. Boron-from-oxide is its own chemistry with its own purification and hazards - parallel in shape, not in recipe.
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Foil flatness is an orbit-quality parameter: ripples increase the effective source thickness and thereby degrade performance - the flatness requirement Chalk River states for its in-dee stripper-foil system (the chain-changer mechanism, lifetimes and magazine details are the paper's description - re-read queued).
Source quote & editorial note
foils must be flat since ripples increase the effective source thickness and thereby degrade the performance.
Editorial note, tabletop extrapolation: The cleanest statement in this collection that foil flatness is physics, not cosmetics - applicable to any internal foil in proportion to how its incidence geometry turns ripple into path-length spread; and the Chalk River system stands as an existence proof that in-vacuum consumable-changers can share space with a live dee structure (details per the re-read).
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The saddle-field source ran cold in the cited setup: a cold filament producing a temperature rise of the evaporant of only ~10 C (the beam-neutral fraction, focus size and insulator capability are the paper's further characterization - re-read queued).
Source quote & editorial note
a cold filament which produces a temperature rise of the evaporant of only ~ 10 C
Editorial note, tabletop extrapolation: A candidate route to boron and refractory films without an e-gun - qualified in place: a small bulk temperature rise does not preclude local sputter damage to a substrate or release layer, so verify with witness pieces; the commercial gun class is bench-scale, and its insulator/neutral-beam claims come from the re-read source, not the summary.
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Saddle-field sputter-gun geometry (Thomas, ANL): the gun at thirty degrees to the target surface and about 5 cm from the sputter source - steeper angles back-sputter material into the gun (the operating pressures, current and alignment notes are the paper's account - scan re-read queued).
30 deg incidence, 5 cm standoff, ~1e-5 Torr, ~2 mA @ 6 kVSource quote & editorial note
the gun be at a thirty degree angle to the horizontal surface and about 5 cm from the sputter source.
Editorial note, tabletop extrapolation: Useful geometry prior-art for a sputter gun in a diffusion-pumped bell jar of exactly the archive's class - commissioned as HV apparatus, not from a recipe card: engineered enclosure, current limiting and bleeders, grounding, door and pressure interlocks, and the pump's own precautions come before first beam; the visible beam then makes alignment easy.
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Budget time, not power, for sputtered targets: the reported saddle-field rates ran about 4-44 ug/cm2 per hour by material (Au ~44, Sn ~14, W ~12.5, Ni 5-13, Fe 4-10, Si ~4), with about half an hour to stabilize; the cited rig then ran virtually unattended for days with only slight adjustments.
Au ~44, Sn ~14, W ~12.5, Ni 5-13, Fe 4-10, Si ~4 ug/cm2/hr - schedule per material: 1 mg/cm2 is ~23 h at the Au rate, ~250 h at the Si rate (verify rate linearity at thickness)Source quote & editorial note
it can be left virtually unattended overnight and usually for several days with only slight adjustments.
Editorial note, tabletop extrapolation: Schedule per material from the actual rate - Au-class films are an overnight job, Si-class a couple of weeks - or reserve sputtering for thin layers and adhesion coats. Unattended running was the cited lab's practice; an amateur HV/vacuum rig earns that only with interlocks that fail safe.
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Focused-ion-beam sputtering economizes scarce isotopes: GSI consumed only 2.3 mg of Zr in preparing five 0.1 mg/cm2 targets (1 mA / 10 kV Ar+ focused ~1 mm, Sletten-type apparatus); self-supported rare-earth sputter layers were routine after dissolving a copper substrate.
2.3 mg Zr -> 5 targets x 0.1 mg/cm^2Source quote & editorial note
only 2.3 mg of Zr were consumed in the preparation of 5 targets of 0.1 mg/cm2
Editorial note, tabletop extrapolation: An economy benchmark in the sense of an existence proof - milligrams in, several targets out. For boron or another feedstock, the efficiency is its own measurement (yield, cathode fabrication losses, coated area and recovery all move it); compare candidate routes by measured end-to-end material balance rather than by the Zr anecdote.
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With adequate care for cleanliness, high-quality RDM targets and stoppers can be produced reliably and easily - the cited conclusion of the Argonne foil-stretcher practice, which draws fragile foils taut over an optically polished reference surface via O-ring compression (the construction, success rates, beam tests and capacitive gap verification are the paper's account - re-read queued).
Source quote & editorial note
with adequate care to ensure cleanliness, high quality RDM targets and stoppers can be produced reliably and easily
Editorial note, tabletop extrapolation: The mounting lesson: flatness comes from a polished reference surface plus elastomer-mediated even tension, with cleanliness setting achievable quality. Capacitance-vs-distance is a fine nonmagnetic gap gauge between conductive, near-parallel, calibrated surfaces - with a vacuum-rated elastomer when used in vacuum.
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Metallize plastic films gently and in stages: Chalk River's attempts at single-step evaporation to the needed coating thickness ruptured the polypropylene foil through radiant heat damage - staged deposition with cooling pauses was the fix (the stretch-temperature profile, undercoat and per-layer recipe are the paper's process - re-read queued).
stretch 105/115/125 C; CN 10 + Cr 5 (2 steps) + Au 20 ug/cm^2 (3 steps)Source quote & editorial note
Attempts at single step evaporations to these thicknesses were unsuccessful because of rupturing of the foil due to heat damage.
Editorial note, tabletop extrapolation: Stretched polypropylene is a workhorse thin window for gas counters and low-energy vacuum isolation, and the step-and-cool discipline is the transferable method - applied to another polymer as a trial with its own thermal and adhesion checks, not as a universal recipe.
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Store hygroscopic and oxidizing targets under vacuum with out-rush protection: Argonne's computer-controlled target store (Nardi & Worthington) keeps 100 targets in a vacuum chamber with transfer under vacuum to the experiment; on recovery from a fault it roughs through a restrictor valve first, specifically to prevent target damage by gas out-rush, and its legacy failure list is instructive — plugged water-cooling pipes, loosening thermocouple connectors, a valve slamming on the transfer rod.
Source quote & editorial note
This prevents target damage by gas out-rush.
Editorial note, tabletop extrapolation: Even a desiccator-scale target store benefits from the transferable habit: throttled first venting/roughing near fragile foils (the source's restrictor-valve recovery). The legacy failure list is instructive where the corresponding hardware exists - IF the store or target uses water cooling, monitor flow and let a hazard assessment decide whether the monitor must interlock beam or heating rather than just alarm.
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A solid target in a stored (circulating) beam is thickness-capped by heating and thermal runaway: the IUCF Cooler design tolerated only ~1-1.5 ug/cm2 with the beam traversing the target ~1e6 times per second; proposed solid-target routes were grazing the beam edge and fiber/whisker substrates.
stored-beam bookkeeping: crossing rate = N_stored * f_rev, target current = q*N_stored*f_rev - this IS the circulating current (times intercepted fraction); the turn multiplier applies against stored inventory and injection rate, never a second time against circulating currentSource quote & editorial note
thermal runaway would occur and the stored beam would be lost.
Editorial note, tabletop extrapolation: Directly relevant to the synchrotron campaign, not the cyclotrons: compare target heating with the circulating current and intercepted fraction - a nanoamp of circulating current is a nanoamp at the target - and apply the traversal multiplier where it belongs, to how fast the stored inventory or injected charge is consumed.
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Chemical vapor deposition makes thick refractory films from milligram feedstock (Gallant, Chalk River): dilute H2 + WF6 over a heated susceptor at ~500 C - WF6 + 3H2 -> W + 6HF - gave good tungsten films over 2 mg/cm2; only the susceptor reaches reaction temperature, so very small metal quantities serve. Flagged as nearly absent from target-lab practice at the time.
WF6 + 3H2 -> W + 6HF (susceptor ~500 C; films > 2 mg/cm2); the by-product is hydrofluoric acid gas, not a vague 'fluorine'Source quote & editorial note
very small quantities of metals such as tungsten, tantalum, and molybdenum can be used in miniature systems
Editorial note, tabletop extrapolation: The one route in the volume to thick refractory targets without an e-gun or rolling mill - and an institutional corrosive-gas process, full stop: WF6 is acutely toxic and makes HF on contact with moisture, the exhaust is HF, and the carrier is hydrogen. Compatible closed plumbing, gas cabinets, leak detection, scrubbing and trained operation are the entry fee; Ta and Mo have their own precursor chemistries, not this one with substitutions.
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Durable self-supported oxide targets by cation-loaded cellulose decomposition: Quinby (ORNL) soaked purified carboxy-methyl-cellulose (dialysis-tubing) membrane in a boiling nitrate solution of the element, then decomposed it flat in staged heating (weighted teflon/copper/quartz sandwich under a heat lamp, 230 C oven, then furnace oxidation); films of 100 ug/cm^2 to several mg/cm^2 were strong, near-transparent, weighable, and frame-mountable — cohesion attributed to chemical bonding of cations in the polymer, well below sintering temperatures.
Source quote & editorial note
relatively high strengths and in some cases were virtually transparent.
Editorial note, tabletop extrapolation: A genuinely low-tech thick-oxide route - solution chemistry plus an oven, no vacuum plant - for the metal-cation nitrate systems the source demonstrated (rare earths and similar), where elemental form is not required. Loading adjusts with solution concentration within the membrane's ion-exchange capacity. Boron is NOT a drop-in: borate chemistry doesn't cation-load cellulose the same way, so a boron oxide target needs its own sourced procedure.
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Sparker circuit values that worked on the cited 27-inch machine: 500 pF charged through 700 kilohm from a 30 kV supply into an air spark gap (~0.22 J per spark), the gap spacing set for roughly two sparks per second - and ordinarily a single spark started the oscillator.
E = C*V^2/2 = 0.5*500e-12*(3e4)^2 ~ 0.22 J per spark; repetition rate is a gap-breakdown setting, not the RC timeSource quote & editorial note
The spark gap is adjusted so that the sparking rate is roughly two per second. Ordinarily a single spark will cause oscillation to commence.
Editorial note, tabletop extrapolation: A sub-joule impulse sufficed on a 27-inch machine; what a smaller system needs follows from its dee capacitance, coupling efficiency and the voltage the kick must reach - calculate or measure it rather than scaling by size. The 30 kV charger is the one nontrivial part, and it must be a properly engineered, current-limited supply with the right polarity and isolation - a bare NST or flyback is a starting component, not the finished charger.
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Interlock an impulse starter so it can only fire when wanted: charging supply energized only while oscillator power is on AND dee voltage is absent, de-energized automatically the moment dee voltage appears — so the operator gets no new control to manage; he presses the normal "on" button, hears a spark if the start hesitated, and the oscillator starts.
Source quote & editorial note
automatically turned on when the oscillator power is on and there is no dee voltage, but which is automatically turned off as soon as dee voltage appears.
Editorial note, tabletop extrapolation: DIRECT automation pattern: gate the starter on (RF enabled) AND (dee pickup below threshold) - a dee voltage pickup is standard monitoring hardware, and where one exists it is exactly the signal needed. The same gate makes stalls detectable: a starter that keeps refiring means the machine is not coming up, so alarm on repeated firings, with the rate threshold chosen at the machine.
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Decouple an auxiliary coupling loop from steady-state operation by geometry: with its plane oriented for minimal flux linkage to the operating mode, the sparker loop saw very small induced RF even at full dee voltage, and sparks during operation caused no perceptible change on the cited machine.
Source quote & editorial note
Because the loop is oriented at right angles to the axis of the cavity, the RF voltage induced in the loop is very small, even with full dee voltage.
Editorial note, tabletop extrapolation: General principle for any starter or diagnostic coupling on a resonator: orient it weakly coupled to the operating mode - remembering reciprocity: a true null for pickup is a null for drive through the same port, so the impulse works through the residual coupling (and other current paths), which is fine because the required kick is small. Verify the coupling both ways, and rate the spark circuitry for the transients it will still see.
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A shock start did not depend on the oscillator tube's ACTIVE state on the cited machine: dee response to the sparker was unchanged with plate power or filament on or off, while retuning the grid circuit changed the spark-induced amplitude severalfold - the impulse reaches the dee through the passive resonant system, with considerable capacitive current through the (passive) tube.
Source quote & editorial note
Changing the tuning of the grid circuit changed the amplitude of spark-induced dee oscillation severalfold, which seems indicates the flow of considerable capacitative current through the oscillator tube.
Editorial note, tabletop extrapolation: Two consequences, one caution: every branch circuit hanging on the resonator participates in the ring, so commission the starter at the operating tune, not on the bench. And the tube's passive capacitances were part of the tested path - a solid-state driver changes that path AND is far less transient-tolerant, so model the coupling with the PA's output network, isolate or disconnect the devices for first tests, and check transient ratings before calling the method transferred.
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For an add-on impulse coupler, the cited team chose inductive over capacitive coupling to the dee - partly convenience in a crowded dee chamber, partly expecting less RF-pickup trouble; the energy-transfer efficiency was 'extremely small' and still adequate, with tighter coupling available as an upgrade they never needed.
Source quote & editorial note
partly because it was more convenient in our case since the dee chamber is rather crowded, and partly because we thought that the RF pickup problem would cause less trouble with inductive coupling.
Editorial note, tabletop extrapolation: A useful trade note, not a theorem: in a small chamber where every square inch near the dee is contested, try a loop near the dee stem (outside the beam region) first - then MEASURE steady-state pickup and impulse coupling before fixing the location; whether inductive actually beats capacitive depends on the local field geometry and the mode.
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Double gaskets with a pumped interspace, everywhere possible: UW used "Berkeley standard double groove gaskets with pump outs ... on all joints" of the tank, and double gaskets with pump-out space wherever possible throughout the 4800-liter envelope; single stuffing-box gaskets only around water lines, ion-gauge tubes, RF-loop insulators, viewports. Materials: Garlock style 8474 hycar rubber, molded hycar sandwich gaskets, standard O-rings; chevron seals on moving shafts (O-rings on small ones). The leak record vindicates the ranking: leaks appeared in two stuffing-box seals and one flat gasket (rubber failure) — none in the double-gasket joints.
Source quote & editorial note
Double gaskets with a pump-out space between the two gaskets are used wherever possible for making seals at the joints in the system.
Editorial note, tabletop extrapolation: Same guard-vacuum doctrine as ornl-1196/anl-5907: on a tabletop machine the pumped interspace is most worth its complexity on the largest lid and any joint opened often. Material translation: the 1951 Hycar parts are the nitrile (Buna-N/NBR) family; Viton/FKM is a DIFFERENT modern option chosen on temperature, chemistry, permeation and compression-set grounds, not a synonym. UW's leak record (two stuffing-box seals, one flat gasket, zero double-gasket joints) is favorable single-system experience for the ranking, not proof.
Cited in: Cyclotron Vacuum Chamber Design and Sealing · The Vacuum Budget of a Cyclotron
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Dee construction pattern for water-cooled copper dees: 1/8-in electrolytic high-conductivity copper skin with 1/4, 3/8 and 5/8-in copper tubes silver-soldered on the back for cooling; each dee and stem SPLIT longitudinally so halves separate for repair; joining surfaces of liner sections silver-plated for RF contact; the movable shorting "spider" that tunes the resonant line held at ~100 lb per lineal inch of contact pressure, with spring-loaded gear- and cable-driven fingers, externally controlled. Dees 53 in dia on 9.75-in OD stems inside a 31-in ID liner.
Source quote & editorial note
The skin is of electrolytic high conducitvity copper with 1/4, 3/8, and 5/8" copper tubes silver soldered on the back side for water cooling.
Editorial note, tabletop extrapolation: The construction vocabulary transfers as a menu, not a mandate: EHC copper skin with cooling sized from computed RF loss (a tabletop dee at tens of watts may need none), silver-plated joints where measured contact resistance warrants, high-pressure sliding contacts only on genuinely movable RF joints, and split-for-repair weighed against the RF seam it adds. Same contact-pressure concern as the nyo-9683/ornl-2648 sliding-contact rules when a movable short exists.
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Ground the anode DC and float the filament for a big-tube oscillator, and the cooling plumbing simplifies: UW runs the ML 354 with the plate at d-c ground (shunt feed), "so that no insulation is required in the water lines," cooling water flowing through the plate line's inner conductor; the filament sits at high negative voltage, its transformer insulated for full plate voltage to ground, and deliberately of high-reactance design so the cold-filament inrush is limited to 500 A — the tube's own safe limit — with 13 V / 225 A normal rating.
Source quote & editorial note
the plate is operated at d-c ground potential so that no insulation is required in the water lines.
Editorial note, tabletop extrapolation: Solid-state amps moot the HV plumbing, but two doctrines survive: pick the grounding scheme that minimizes what the coolant circuit must insulate - DC-grounding the plate removed the DC insulation requirement, while RF potentials, leakage control and water quality stay on the checklist - and use source impedance (here transformer reactance) as passive inrush protection where a component's own rating allows it.
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Deflector doctrine from the UW study, anchored on its phase analysis: a minimum of 80 kV dee-to-ground RF was calculated necessary so ions never enter decelerating phase within the dees (the 70-degree geometry, DC-supplement thresholds, channel dimensions and energy-spread figures are the study's design narrative - scan re-read queued, including which electrode is RF-energized in their plate-at-RF-ground scheme).
UW: 70-deg deflector from 60 deg past gap; >=80 kV RF floor; DC supplement below ~120 kV dee; selective channel 0.90 cm -> ~1.5 MeV spread at 21 MeVSource quote & editorial note
a minimum of 80 kv dee to ground r.f. potential is necessary in order that the ions do not enter the region of decelerating phase at any time within the dees.
Editorial note, tabletop extrapolation: Two transferable ideas for any future extraction study: run the phase-floor analysis BEFORE cutting metal (the computation this collection's deflector cluster expects), and consider using the machine's existing RF field for deflection with DC as supplement - after resolving the geometry from the re-read, since a deflection field needs a potential difference and the as-summarized grounded-plate-vs-grounded-dee-edge description cannot be right as written.
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Construction cost structure of a university-built 60-inch, 1948-1951: total ~$642,000 to April 15, 1951, excluding University of Washington overhead and staff salaries; the report's accounting (allocation figures sighted in the scrambled scan - verbatim re-read queued) puts buildings at ~$225,000 against machine materials ~$201,500, with visible payroll only ~$14,000 - most machine labor being institutional or donated (Navy-supplied machine tools, supplier assistance).
Buildings $225k > machine materials $201.5k; visible payroll only $14k of $642kSource quote & editorial note
Total expenditures to date from all sources, excluding University of Washington overhead and staff salaries, has been $642,000.
Editorial note, tabletop extrapolation: A historical cost-accounting example that corroborates the plan's assumption from the construction side: facility/infrastructure rivalled machine materials HERE, and reported totals understate true cost by the labor the institution absorbed - for an educational-accelerator business, price materials PLUS the labor a customer cannot donate. One project's ratio is context, not a law.
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Tune the fault-detector delay as a physics compromise, and Smith gives the number: the interlock signal is deliberately RC-slowed so the discharge persists about a millisecond — "long enough to vaporize the foreign material which initiated the spark. If the circuit is made too fast, it takes too long to bake the resonators in. If it is made too slow, the spark damage to the dee and liner surfaces will be excessive. Experience indicates that 1 msec is about the right delay." (Overcurrent faults in tube anode/grid circuits bypass this delay and open the hard-tube modulator in ~10 us.)
Spark dwell before interrupt: ~1 ms (conditioning); tube overcurrent path: ~10 usSource quote & editorial note
The signal from the rf-dc interlock is slowed down by an RC circuit, so that the discharge will persist for about a millisecond. ... Experience indicates that 1 msec is about the right delay.
Smith, The RCA 6949 as a Self-Excited Cyclotron Oscillator — UCRL-9435, Lawrence Radiation Laboratory (1960) — p. PDF p. 7 (printed -7-)
Editorial note, tabletop extrapolation: A protection spec you cannot derive from electronics alone: the dwell is chosen so each spark finishes cleaning the spot that caused it. The compromise transfers; the number does not - Smith's ~1 ms suits his machine's stored energy and electrode scale, so a tabletop supply picks its own dwell from its fault energy, starting shorter and lengthening only if conditioning stalls. Amplifier-device faults still trip as fast as the electronics allow: two speeds, two purposes.
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A cyclotron resonator's vacuum envelope relieves the stray-RF problem 'somewhat' - the quoted qualifier: the chamber that must be vacuum-tight is thereby RF-tight over its solid surfaces, and what escapes does so at the penetrations and the drive side.
Source quote & editorial note
the resonator has to be vacuum-tight, automatically making it rf-tight.
Editorial note, tabletop extrapolation: Comforting for a residential machine, with 'somewhat' doing real work: the metal chamber contains the dee's RF well, and the leakage paths are feedthroughs, viewports, gauge ports and the amplifier chain - gasket and shield those, then VERIFY with a receiver walk-around. Quiet neighbors' radios are a measurement, not a promise.
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To switch a pi-filter resonator between two frequencies an octave apart, short a series inductor with a vacuum relay: COLUMBUS runs 24 uH + 8 uH in series (32 uH total) at 2.82 MHz; the relay shorts the 24 uH coil, leaving 8 uH for 5.64 MHz. An ordinary switch cannot be used at this node - the book requires a vacuum relay.
f = 1/(2*pi*sqrt(L*C)); L_total = 32 uH (2.82 MHz) or 8 uH (5.64 MHz) - consistent with ~100 pF effective C; expect retune after relay/lead parasiticsSource quote & editorial note
Mit Hilfe eines Relais kann die Spule mit L = 24 µH in Serie zu der 8 µH-Spule [geschaltet werden] ... Zieht das Relais an und schließt den Kontakt, wird die 24 µH-Spule kurzgeschlossen, so dass nun nur noch die Induktivität von 8 µH wirksam ist. ... kann für diese Umschaltung kein Schalter verwendet werden, vielmehr muss sie mit Hilfe eines Vakuumrelais erfolgen [tr.: a relay puts the 24 uH coil in series with the 8 uH coil; when the relay closes, the 24 uH coil is short-circuited so only 8 uH remains effective; no ordinary switch may be used for this switching - a vacuum relay is needed]
Editorial note, tabletop extrapolation: A 4:1 inductance ratio gives the 2:1 frequency ratio at nominally constant capacitance, covering H+ and H2+ on one network - as an ideal-LC starting point: relay contact capacitance and lead inductance shift both points, so retune and re-measure at each setting, and rate the relay for the RF voltage and current at its node.
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Quote which mean-free-path form a number uses: the stationary-background form l = 1/(n*sigma), or the Maxwell sqrt(2) form l = 1/(sqrt(2)*n*sigma) - the latter being the result for IDENTICAL molecules in a Maxwellian equilibrium gas, as the book applies it.
l = 1/(sqrt(2)*n*sigma) (identical-Maxwellian-gas result); fast ion in thermal gas: l ~ 1/(n*sigma_loss(E)) - the stationary form with the ENERGY-DEPENDENT loss cross-sectionSource quote & editorial note
Nach einem Ansatz von Maxwell wird dies durch einen Faktor √2 im Nenner berücksichtigt [tr.: following Maxwell this is accounted for by a factor sqrt(2) in the denominator]
Editorial note, tabletop extrapolation: For a beam ion crossing slow gas the stationary form is the better physical model (relative speed ~ ion speed) - but only with the right sigma: gas-kinetic hard-sphere values are not loss cross-sections, so a beam-loss budget needs sigma_loss(E) from evaluated data (dg-460), whatever the sqrt(2) bookkeeping.
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A coiled filament (3-5 turns, as on COLUMBUS) generates its own magnetic field that binds part of the emitted electron cloud by the Lorentz force, so not all emission reaches the chimney.
Source quote & editorial note
Bei einer Spulengeometrie (3–5 Wdg. wie bei Columbus) erzeugt dieses ein Magnetfeld, das die Elektronen infolge der Lorentz-Kraft bindet [tr.: a 3-5 turn coil produces a field that binds the electrons]
Editorial note, tabletop extrapolation: When comparing source geometries (coil vs hairpin vs straight, AC vs DC heating), meter EMISSION at the anode, not filament current - the self-field confinement is one reason the two differ. To estimate the self-field, B ~ mu0*N*I/(2R) needs the coil radius, not just turns and current; compute it against the electron Larmor radius at the actual energy before crediting or blaming it.
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Small commercial diffusion pump as-built datum (Innovac R220), Dow Corning 704 silicone oil heated by a 120 VAC element with the pump wall chilled by a water-cooled copper tube wrapped around the outside, supplied with 0.75 L/min of chilled water; the printed heater draw of about 0.5 A (roughly 60 W) is image-verified as what the thesis prints, but is anomalously low for a diffusion pump heater and is best read as a source-level misprint.
Source quote & editorial note
silicon oil is heated by an electrical heating element at 120 VAC, drawing about .5 A
Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 31
Editorial note, tabletop extrapolation: The external wrapped-coil water jacket and DC-704 fill are transferable STARTING points for a self-built vapor pump (validate boiler power and temperature for the actual geometry - the diff_pump project's own design work governs there). The printed '.5 A' at 120 VAC implies ~60 W, low for this pump class: REPORTED BUT UNVERIFIED - check the R220 manual or a nameplate before treating it as datum or misprint.
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Structure a teaching-scale orbit simulation in three layers — an input layer holding three parameter groups (ion properties, experiment settings, machine geometry), a simulation engine, and a presentation layer whose plot modules (XY orbit plot, intensity plot, spectrometer plot) each also export data to file for external processing.
Source quote & editorial note
As shown in Fig. 1 the simulation consists of three sections, the input-layer, the simulation-layer and the presentation-layer. … The input-layer incorporates three groups of parameters which define the ions, the experiment and the geometry of the cyclotron. So the simulation can be easily adapted to different situations. … The simulation engine described above has three modules for the evaluation: XY-Plot, Intensity-Plot and Spectrometer-Plot. Every module - apart from the graphical output - allows also a data export to a file so that the measured values can be processed by external programs.
Editorial note, tabletop extrapolation: Separating ion, experiment, and geometry parameter groups lets one code serve several machine configurations and several experiments; the data-export hook is what allows direct overlay of simulated and measured detector scans.
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An as-printed (uncleaned) hybrid printed-and-welded connector measured only slightly worse than a conventional stainless connector of the same type in a 24 h pressure-rise test — 7.39*10^-7 versus 5.25*10^-7 mbar*l/s combined leak-plus-outgassing rate — so print provenance is not, by itself, a vacuum disqualifier at high-vacuum level.
Source quote & editorial note
the 3D-welded KF-SC DN-40 in the uncleaned state behaves slightly worse than a conventionally manufactured component KF-SC DN40 made of stainless steel. … Table 2: Leakage Rates … 3D Welded KF-SC DN40 uncleaned … 7.39·10-7 … Edelstahl KF-SC DN40 … 5.25·10-7 [Leakage Rate column, mbar·l/s]
Editorial note, tabletop extrapolation: The penalty for a printed part fresh from post-processing is a factor of about 1.4 against wrought stainless in this 24 h test; whether that matters in a given system is a gas-load-budget question, not a constant.
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Exploit additive manufacturing's function integration for vacuum vessels by printing a network of flow channels directly into the chamber wall, shaped with a CFD program for good flow; the same channels heat the vessel during evacuation (bake) and cool it during later operation.
Source quote & editorial note
Through the flow channels, the recipient can be heated during evacuation and alternatively cooled when needed in operation. The exact shape of the channels was determined by a CFD-program to ensure optimal flow conditions.
Editorial note, tabletop extrapolation: Integrated wall channels give a small chamber bakeout and cooling with no external jacket or brazed lines - a capability that is expensive to add to a one-off machined chamber - at the price of fluid connections and a leak qualification of the channel walls against the vacuum volume.
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Measured resonance-curve width exceeded the simple phase-integral prediction on the ISU 1.5 MeV cyclotron (1961): about 150 gauss full width at half maximum at 9 cm target radius versus 115 gauss theoretical. The companion Mueller calculation attributed the excess width to protons with negative initial phase reaching the target — ions its model assumed were all lost to electric defocusing ('probably', its own hedge; see dg-1593).
Source quote & editorial note
Fig. 1 shows the theoretical and experimental shapes of the resonance curve at a target radius (r2) of 9 cm ... The two experimental curves are practically identical. They are about 150 gauss wide at half-maximum intensity. The theoretical curve (1), shown in broken lines, is quite a bit narrower-115 gauss at half-maximum intensity.
Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: a measured tuning curve broader than the phase-window model predicts is not necessarily a field or metrology error — simplified phase-acceptance assumptions bias the prediction narrow. Treat a width discrepancy as a prompt to examine the phase-acceptance assumptions and other broadening mechanisms, not as evidence that a machine's field tolerances are looser than computed.
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Activation-analysis experiment design from ISU (1961), C12(p,gamma)N13: set the target radius so proton energy is only slightly above what the source calls the reaction's 'threshold' [the reaction is exothermic, Q about +1.9 MeV — the operative point is the practical yield onset under Coulomb suppression], keeping the activity shallow so positrons escape the sample; bombard machined dry wafers of spectroscopic carbon (1 mm) for about half an hour; then count off-line — 15-second counts each minute for half an hour on an NaI counter in a lead house. Measured half-life 10.3 plus or minus 0.3 min (three runs) against the then-published 10.1 min confirmed the N13 identification (modern value 9.97 min).
slope of ln(count rate) vs t = -0.693/T_half [the source prints '0.693/T1/2' without the sign; the decay slope is negative]Source quote & editorial note
The samples to be bombarded were machined (dry) in the form of thin wafers (1 mm thick) from spectroscopic carbon. The target radius was set so the energy of the protons would be only slightly greater than the threshold energy for the reaction. This was done to minimize the absorption of the β+-particles leaving the sample, thus providing the maximum flux at the counter. The sample was then bombarded for about one half-hour. After bombardment, the activated sample was removed from the machine and taped to a two-inch NaI crystal scintillation counter located in a lead house for minimum background. The counting was done for fifteen-second periods every minute for one half-hour ... A plot of the natural logarithm of the counting rate versus elapsed time has a slope equal to 0.693/T1/2, where T1/2 is the half life for the decay ... gave T1/2 = 10.3±0.3 min. The average value of three such determinations also yielded a half life close to 10.3 min. for the N13. This is in reasonable agreement with the published value of 10.1 min.
Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: off-line activation counting decouples the measurement from accelerator-correlated pickup — the machine only has to run for the bombardment, and a known half-life gives a self-grading answer. Barely-above-onset bombardment as a technique for keeping activity near the surface is a subtle, transferable target-design trick.
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Positron endpoint-energy cross-check (ISU, 1961): the measured 1.1 MeV maximum positron energy from N13 versus the published 1.2 MeV was reconciled by two identified absorbers - the aluminum foil over the NaI crystal and self-absorption in the carbon since most N13 lies below the surface. Discrepancies were traced to physical absorbers rather than averaged away.
Source quote & editorial note
The difference can be accounted for by the absorption of the aluminum foil covering the NaI crystal, and also by the fact that most of the N13 atoms are located below the surface of the carbon
Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: window and source-layer energy loss can significantly bias an MeV-class endpoint measurement — model each layer's areal density between source atom and scintillator, alongside detector resolution, calibration and backscatter, before doubting the physics. Listing the absorbers explicitly is the difference between a validated measurement and a shrug.
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Initial-condition sampling for axial-motion studies (ISU, 1963): start orbits at an apogee; represent initial axial position and velocity as a phasor za of angle sigma_z', and since the linearized axial equation is linear (amplitude units arbitrary), a uniform distribution is represented by eight runs at sigma_z' = N*pi/8, N = 0..7 — other integral N repeat with a possible sign reversal, and the source's own caveat stands: the true axial motion is 'not quite simple harmonic, but this gives a reasonable distribution approximation'. Radial/angular motion being independent of z in this model, one radial solution serves all eight axial cases. Output was recorded at physically meaningful events — apogees, perigees, extrema of z, selected gap crossings — as functions of angle rather than time, since those relations carry the experimental significance.
Source quote & editorial note
The magnitude of za is the amplitude of the axial oscillations. Note that Equation 5 is linear; therefore, the units of za are arbitrary. Hence, only the direction of za is significant in forming a uniform distribution ... values of σz′ were chosen to be σz′ = Nπ/8 where N = 0, 1, 2, ... 7. Eight calculations were performed while only σz′ was varied. Other integral values of N would give the same results with a possible reversal in sign. The true axial motion is not quite simple harmonic, but this gives a reasonable distribution approximation ... the computer outputs r and φ at apogees and perigees in radial positions. It gives z and φ at maxima of |z|. It also outputs r, φ and θ at selected dee gap crossings ... their relations to one another are more useful to study since these have more experimental significance ... only one graph of r versus φ is needed when variations in σz′ are considered
Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: exploiting linearity and symmetry collapsed a two-parameter scan to eight runs on a 1962 vacuum-tube computer — the same economy matters when scanning initial conditions with a desktop tracker today, and event-based output (turn-by-turn at gaps and extrema) is what maps directly onto probe measurements. Eight phase samples suffice under the linearized model; a nonlinear tracker needs a denser scan.
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Twin large-radius resonances resolved by trajectory integration in the ISU cyclotron (1963): the omega_r = 2*omega_z coupling at n = 0.2 (r = 10.1 cm) and a second coupling at n = 0.25 (r = 10.3 cm) driven by orbit shifts from the electric accelerations - only about 0.2 cm apart, so observed axial-amplitude growth could not be attributed to either alone; at the resonance region axial oscillations also phase-localized (initially staggered phases pulled nearly into step), and in one case the coupling reduced amplitude instead.
Source quote & editorial note
Note the amplitude expansion of axial oscillations in the region of 10.1cm. This is the predicted resonance at n = 0.2. Also at r = 10.3cm where n = 0.25 (ωz ≈ 2φ̇) there is a coupling due to the shifting of the orbit as a result of the electric accelerations. Since the two resonances are only about 0.2cm apart, the amplitude expansion cannot be considered as a result of only one of the two factors. In one plot of z the coupling had the opposite effect by reducing the amplitude of axial oscillation ... At the region of resonance, some of the oscillations have encountered phase localization; that is, all but the reduced oscillations are very nearly in phase.
Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: in the ISU geometry these two resonances crowded within 0.2 cm and their effects could not be separated — a warning that on a steep-edged small pole distinct resonances can overlap, making single-resonance analysis of beam loss underdetermined there. For another machine, locate each resonance from its own field map and track them separately and together before deciding whether they form one overlapping loss region.
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Radiation-environment design assumption stated in the IUAC coil epoxy specification — the coils are treated as sitting in a high ionization radiation area with a total absorbed dose of approximately 2 MGy over a 10-year operating lifetime, and the casting epoxy must be shown (by manufacturer dose-rate data sheet, approved before use) to sustain that dose.
Source quote & editorial note
The coils will work in high ionization radiation area. Total absorbed dose in coil shall be approximately 2 MGy in its lifetime of 10 years of operation. Epoxy resin should be able to sustain the above mentioned radiation dose. Technical data sheet of radiation dose rate for the offered epoxy should be provided to IUAC.
Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: a rare explicit statement of the radiation dose a design team budgets for organic insulation next to an MeV-class cyclotron gap over a decade of teaching use. Long-lived small machines should treat coil insulation as a radiation-exposed component, not just a thermal one — and note a manufacturer dose-rate data sheet alone is thin qualification: survival depends on total dose, species, dose rate, atmosphere and the property retained, so prefer total-ionizing-dose test data for the actual resin.
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Universal digital LLRF architecture demonstrated at IUAC — one SoC-FPGA hardware set covers RF structures from 12.125 to 97 MHz and serves as sawtooth generator, generator-driven-resonator controller and self-excited-loop controller without FPGA reprogramming, using a wideband analog front-end for up/down conversion, an on-board DDS, EPICS IOC remote control, and the motorized frequency-tuner logic hosted in the same FPGA.
Source quote & editorial note
IUAC, New Delhi, India, operates accelerators with RF structures in the range of 12.125-97 MHz, in both normal and superconducting modes ... this controller has been tested as a Sawtooth Waveform Generator for the Multi-Harmonic Buncher (MHB), as a generator-driven (GDR), and as a self-excited loop (SEL)-based LLRF for various RF cavities at IUAC ... It is a compact, frequency-reconfigurable, standalone device controlled by an EPICS IOC ... The main feature of our design is the hardware configuration, which remains the same regardless of the cavity type, without the need for FPGA reprogramming. In addition to the LLRF algorithm, the same FPGA contains logic for the motorized Frequency Tuner Control, considerably lowering the system's cost ... The major blocks of the system as shown in the overall physical block diagram (Fig. 1a) are a wideband Analog Front-End (AFE), microcontroller programmed PLL Multiplier, and a SoC-FPGA-based digital board.
Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: one reconfigurable digital controller replacing a zoo of structure-specific analog LLRF chassis is exactly the maintainability trade a small lab faces. Folding the mechanical tuner drive into the same FPGA as the feedback loop removes a separate controller box — the motor's power stage still exists, but its logic does not need its own electronics.
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Commodity-hardware basis of the IUAC universal LLRF — the digital board is the commercial Red Pitaya STEMlab 125-14 (the paper's reference 13), with the design argument that standalone non-crate systems beat VME/cPCI/microTCA backplane solutions on cost, bulk and adaptability for a multi-accelerator lab; a Si5356-based PLL multiplier generates the LO and the 125 MHz FPGA system clock, with an on-FPGA digital PLL mitigating experimentally observed long-term sub-millihertz-level errors traced to manual setting of the chip's phase increment word.
Source quote & editorial note
Several implementations invoke backplane-based methods, such as VME, cPCI, and microTCA. These solutions are often costly, bulky, and difficult to adopt due to a customized design goal. Standalone, non-crate-based systems provide a more versatile, fast, and cost-effective alternative ... The local oscillator signal for the mixer is generated by a Si5356-based I2C-programmable PLL multiplier, synchronized with an external reference signal. Apart from the LO signal, it is used to generate a 125 MHz system clock signal for the FPGA ... This board [13] houses the main signal processing algorithm ... [reference 13:] Red Pitaya, "Red pitaya STEMlab 125-14" ... A lightweight digital PLL (DPLL) ... helps the Si5356-based PLL multiplier mitigate long-term sub-millihertz-level errors which were experimentally observed and caused by accuracy issues with the manual setting of its phase increment word
Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: a national accelerator centre building its cyclotron LLRF around a hobbyist-priced software-defined-radio board shows amateur-accessible hardware can anchor serious RF field control at these frequencies — as one component of a system whose performance also hangs on the analog front end, clock reference, firmware and interlocks. The DPLL fix for the clock chip's long-term drift (sub-millihertz-level, from manual phase-increment setting) is a practical gotcha worth knowing before trusting a cheap synthesizer unsupervised.
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Machine attribution and stated design energy from a partner-institute report — a 1.2 MeV proton cyclotron proposed by Prof. P. C. Deshmukh is described as currently under development at the Inter-University Accelerator Centre, New Delhi, with the proposal developed by CAMOST members plus affiliate members and student internships on the facility anticipated (design intent; the machine has no demonstrated beam).
Source quote & editorial note
1.2 MeV proton cyclotron proposed to be built in India by Prof. P. C. Deshmukh is currently under development at the Inter-University Accelerator Center, New Delhi. The proposal was developed by CAMOST members plus affiliate members, including Prof. G. Aravind, Prof. C. Vijayan, and Prof. T. S. Natarajan. Students from IISER/IIT Tirupati can go to IUAC and do internships using this facility.
CAMOST (IIT Tirupati / IISER Tirupati), Annual Report 2022–2024 — p. 16
Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: pins the machine's stated design energy in one primary source — and institutional coverage of the same pre-beam machine varies between this 1.2 MeV figure and roughly 1 MeV-class elsewhere, a spread preserved rather than resolved, and a caution for anyone citing energies of in-progress machines. The declared purpose (student internships on a teaching cyclotron) marks the pedagogy use-case for this machine class.
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The Rutgers 12-inch three-hole chimney experiment machined three identical apertures, one in the median plane and one 2.5 mm above and below it, to give ions deliberate initial betatron amplitudes; the intensity of the three sources declined with distance from the filament but the off-plane apertures varied only +/- 7% from the median-plane aperture, so the observed differences in beam survival were attributable to optics rather than to unequal source strength.
Source quote & editorial note
A chimney with three identical apertures was machined, one aperture was in the median plane as is typical of the normal ion source, and an aperture placed 2.5 mm above and below the median plane aperture. In addition to experiencing the vertical electric field the off-plane apertures gave the ions initial betatron amplitudes. The cyclotron was brought up to typical operating values – this time three stacked purple glows appeared fanning into the face of the DEE (figure 3). The intensity of the three apertures declined as they moved away from the filament, as plotted in figure 4. The off-plane sources intensity varied only +/- 7% from the median plane aperture.
Koeth, Hanebuth, Hoffman & Schneider, Rutgers 12-Inch Cyclotron Ion Source Studies: Part II (2007) — p. 2
Editorial note, tabletop extrapolation: A cheap, highly copyable experiment: one extra chimney with three apertures (median plane, ±2.5 mm) turns the source into a deliberate initial-condition generator, and the glow-intensity profile (Fig. 4) is the control — the off-plane sources matched the median one within ±7%, so survival differences are attributable mainly to optics, at that level of control. Pick your own offsets from your machine's modeled or measured vertical acceptance and the betatron amplitude you want to launch, not by scaling 2.5 mm to your gap.
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On the Rutgers 12-inch the fluorescent-screen image is only analysable over a limited energy window: the authors could resolve two distinct betatron paths for about 1.5 betatron periods, between 185 keV and 325 keV, after which reduced turn-to-turn spacing and betatron damping merged the traces; within that window a calibrated pixel measurement gave a 47 degree phase difference between the two waveforms.
Source quote & editorial note
quickly losses the ability to distinguish the two different betatron paths. For a region of about 1.5 betatron periods (between 185 keV and 325 keV) the fluorescent screen intensity and turn to turn spacing were sufficient to capture an image useful for analysis. Calibration of the horizontal pixels indicates that the horizontal spacing of the two prominent betatron waveforms corresponds to a phase difference of 47 degrees.
Koeth, Hanebuth, Hoffman & Schneider, Rutgers 12-Inch Cyclotron Ion Source Studies: Part II (2007) — p. 3
Editorial note, tabletop extrapolation: Realistic expectations for photographic beam diagnostics: this image was analyzable for about 1.5 betatron periods (185-325 keV) — below that the glow was too faint, above it the turns crowded together — and within the window a calibrated pixel measurement resolved a 47-degree phase difference between the two launched waveforms. Pixel calibration against a known internal dimension (here the 0.25-inch chimney) is the enabling trick; find your own machine's usable window empirically, since it belongs to the screen, exposure and beam intensity, not the class.
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Historical puller-geometry data point cited by the Rutgers group from Livingston, Holloway and Baker (Rev. Sci. Inst. 10, 63, 1939): for a 0.0625 inch diameter aperture, pullers with a vertical 1/4 inch gap residing 1/4 inch away from the aperture yielded best results; the Rutgers authors note this parameter space had not yet been explored on their own machine.
Source quote & editorial note
Optimization of the puller placement and vertical gap needs further investigation. Livingston found that for a 0.0625 inch diameter aperture that pullers with a vertical ¼ inch gap residing ¼ inch away from the aperture yielded best results. [7] This parameter space for our cyclotron has not yet been explored. It is clear from figure 12 that the ions initial radius is very large, thus the pair of pullers plates could be replaced with by a single solid plate with just an aperture in it.
Koeth, Hanebuth, Hoffman & Schneider, Rutgers 12-Inch Cyclotron Ion Source Studies: Part II (2007) — p. 5
Editorial note, tabletop extrapolation: A historical calibration point rather than a recipe: Livingston, Holloway and Baker's 1939 optimum for a 1/16-inch capillary aperture was a 1/4-inch puller gap at 1/4-inch standoff — quoted approvingly here by authors who explicitly had NOT explored that space on their machine. Scan or model gap and standoff for your own extraction voltage, field and aperture. The memo's single-apertured-plate suggestion is an untested option for cases where trajectory calculation shows the first-turn radius clears the plate — verify, don't assume. (The quoted passage begins on p.5 — where the 0.0625 inch figure appears — and concludes on p.6.)
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Insulator and HV-connection practice on the Rutgers 12-inch deflector: the electrode was supported from behind by the stems of two T-shaped Teflon insulators whose arm-tip bosses seated in detents in the top and bottom plates, the stems deeply counter-bored and finished with a blank through hole; the electrode was secured to the insulator bases with Nylon screws, and electrical connection was made by seating the HV ceramic vacuum feed-through conductor directly into a third clearance hole in the back of the electrode, captured by a set screw.
Source quote & editorial note
It was supported from the back by stem of two T-shaped Teflon insulators. Bosses were machined in the tips of each arm of the T-insulators, the bosses were seated in detents in top and bottom plates. The T-insulator stems were deeply counter-bored and finished with a blank through hole. Two tapped holes on the rear of the HV electrode, and Nylon screws secured the electrode to the base of the T-insulators, which can be seen in place in Figues 3 and 4. Electrical connection was made to the HV electrode by directly seating a HV ceramic vacuum feed-through conductor into a third and final clearance hole in the back of the electrode, and is captured by a set screw.
Editorial note, tabletop extrapolation: Three compact construction choices from a working HV-in-vacuum assembly, with their plausible rationales: the deeply counter-bored insulator stem (surface-path length — verify creepage on the actual geometry), Nylon fasteners in the high-field region (less grounded metal near the electrode), and the feedthrough conductor seated directly into the electrode (no in-vacuum HV wire to dress). None is a proven remedy on its own; qualify the PTFE, Nylon and feedthrough for voltage, temperature, charging and outgassing, and check the fields the real geometry makes.
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Current-limiting resistor packaging on the Rutgers 12-inch deflector: the 150 megaohm resistor for the Bertan 205A-50N 50 kV supply was housed in an acrylic tube capped at both ends and externally covered with a grounded copper mesh, and the housing was installed in a relatively inaccessible location at the top and backside of the magnet yoke.
Source quote & editorial note
Subsequently, a surplus Bertan 205A-50N 50 kV power supply was ordered and installed. This supply was also only a constant voltage supply requiring a 150 MΩ current limiting resistor. The resistor was housed in an acrylic tube, capped at both ends, which was then externally covered with a grounded copper mesh. The resistor housing was installed in a relatively inaccessible location at the top and backside of the magnet yoke.
Editorial note, tabletop extrapolation: This is the source's own construction practice for a stack of HV resistors on a small machine: an insulating tube for standoff plus an outer grounded screen so the assembly presents a defined, grounded surface rather than a floating one, and physical placement out of casual reach. Reported here as what they did, with their numbers.
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Energy-resolution estimate for the Rutgers 12-inch deflection channel: with V = 28 kV, rho = 4.125 inches, d = 0.31 inches, delta-rho = 2.757 inches and epsilon_r = 0.118 inches, the channel admits an energy band of delta-T = 25 keV on a nominal 500 keV proton beam, i.e. 5% — and the authors state the real resolution will be worse because the entire finite-width entrance slit admits ions that may also have an angular component.
T_nom = (V*rho/(2*d))*(1 + rho/delta_rho); delta_T = T_+ - T_- = (V*rho^2/(2*d))*(2*eps_r/(delta_rho^2 - eps_r^2))Source quote & editorial note
For the 12-Inch Cyclotron values, V=28 kV, ρ=4.125 inches, d=0.31 inches, ∆ρ=2.757 inches, εr=0.118 inches, we arrive at a ∆T=25 keV for a nominal 500 keV proton beam, a 5%. The resolution will be worse than this figure, as the entire entrance slit is admitting ions, which may have an angular component as well. These effects will be thoroughly studied in a future deflector document.
Editorial note, tabletop extrapolation: For anyone whose internal deflector doubles as an energy diagnostic: apply the formula to YOUR channel — the ~5% here belongs to the listed Rutgers parameters, and the authors themselves call it optimistic (finite slit, angular spread). Worked checks: T_nom = (28 kV × 4.125)/(2 × 0.31) × (1 + 4.125/2.757) = 465 keV, consistent with the quoted nominal 500 keV; and subtracting the paper's own printed T+ and T− expressions yields a 2·εr factor and 24 keV, where the printed combined ΔT expression reads "1 +" — an apparent typesetting slip for "2", flagged here with both computations shown.
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Stated future extraction design intent for the Rutgers 19-inch cyclotron, based on the 12-inch deflector: a scaled version of the 12-inch deflector with the HV potential limited by design constraint to 50 kV (a second 50 kV Bertan supply having been purchased), and with the deflection channel's gap increased through the region of declining magnetic field so as to reduce the extraction field as the extracted beam traverses the rapidly falling vertical fringe field.
Source quote & editorial note
A scaled version of the of the 12-Inch Cyclotron's deflector will be the basis of the 19-Inch cyclotron deflection system. The 19-Inch cyclotron projects has a design constraint limiting the HV potential to 50 kV as a second 50 kV Bertan supply has been purchased. The stated goal is to extract and transport the 19-Inch Cyclotron's beam to a diagnostic and experimental chamber. As such, the extracted beam will need to traverse the rapidly falling vertical fringe field. The 19-Inch extraction design will incorporate an increase the deflection channel's gap, reducing the extraction field, through the region of declining magnetic field.
Editorial note, tabletop extrapolation: The authors' design intent for a machine not yet built, not an achieved result. The transferable idea, stated correctly: an extracted particle crosses the fringe at roughly constant speed, so the magnetic bending force falls locally as B — the channel needs progressively less counter-field on the way out, and widening the gap along the channel is one way to deliver that at a single electrode potential. Derive the gap profile from the measured fringe map plus tracking, not from a scaling law; the B²-type relation (dg-1660) applies to the equilibrium-orbit sizing calculation, not to this traverse.
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Planned automation of the Rutgers 12-inch deflector measurement: an IEEE-488C GPIB interface was purchased for the Bertan HV 205A-50N supply to enable remote computer control, with a planned project to automate sweeping of the cyclotron magnetic field and HV deflector while recording the beam current, effectively turning the cyclotron into a very sensitive accelerator-based q/m spectrometer.
Source quote & editorial note
An IEEE-488C GPIB interface has been purchased for the Bertan HV 205A-50N power supply, enabling remote computer control. There is a planned project to automate the sweeping of the cyclotron magnetic field and HV deflector while recording the beam current, effectively turning the cyclotron into a very sensitive accelerator based q/m spectrometer.
Editorial note, tabletop extrapolation: Stated as a plan, not an achievement. The idea is well matched to a tabletop machine that already has a current-collecting screen: a two-axis sweep of field and deflector voltage recorded against collector current turns the manual photograph-stitching method (Fig. 11) into a quantitative spectrum with no new hardware in the vacuum. Modern equivalents of the GPIB link are trivial by comparison.
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The Rutgers 12-inch spiral AVF geometry is an Archimedes spiral of the form theta = alpha r with alpha = 15 degrees per inch, each of the four vanes 45 degrees in angular width.
Archimedes spiral sector edge: theta[deg] = (15 deg/inch) * r[inch] for this trial design (the paper prints alpha = 15° with the per-inch understood from its coordinate convention)Source quote & editorial note
With acceptable agreement between the measurement and simulation, a spiral sector pole was simulated; again each vane had 45° angular width. The spirals were describe by an Archimedes spiral of the form θ=αr, where α=15°.
Editorial note, tabletop extrapolation: A worked description of the trial spiral: 15 degrees of sweep per inch takes the edge through 75 degrees over a 5-inch ion region — this study's first spiral iteration, described with 45-degree vane widths in the same passage. The built optimized design swept 270 degrees total (AKG270, dg-1717). The number to copy is neither: sweep rate is the knob that trades edge-angle focusing against tune ramp (dg-1697, dg-1698), chosen from your own tune plot.
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To fly the Rutgers 12-inch AVF fields in SIMION the Maxwell 3D field report was generated on a 1 mm grid to match the 1 mm per SIMION grid unit ratio, spanning plus/minus 115 mm in x and y and 53 mm in z — 231 x 231 x 53 rows, over 2.8 million points and more than 500 MB of text — the radius being set by the 4.5 inch deflector interception point.
Source quote & editorial note
The resolution of the imported field has been set at 1 mm to conveniently match the 1mm:1 SIMION grid unit ratio. The M3D report file is a 6-column a comma separated variable file reporting x, y, z, Bx, By, and Bz at each grid point, with a spacing of 1-mm between grid points. To fully cover the ion accessible region in our cyclotron, the field region must span a volume with a radius up to 4.5 inches – the point of interception of deflector. Therefore the extent of the report spans ±115 mm (~ 4.55-inches) X ±115 mm X (~ 4.55-inches) X 53 mm (~ 1.04-inches) which contains 231 X 231 X 53 rows of data, an excess of 2.8 million points - causing the simple text data to become unwieldy, in excess of 500 MB.
Editorial note, tabletop extrapolation: Concrete sizing for a tracker's field-map file: 1 mm resolution over the ion-accessible volume of a 12-inch machine is 231 × 231 × 53 points — 2.8 million rows, over 500 MB as text — so plan a binary or compressed intermediate format from the start. The printed axial figures do not reconcile (53 mm ≈ 2.09 in, yet the parenthetical prints "~1.04-inches", plausibly a half-extent; unresolved in the source — inspect your own file's z bounds rather than inferring). Size the map to cover the COMPLETE tracking domain out through every loss surface and relevant fringe region, not merely the aperture the beam is supposed to occupy.
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Radial trace-space exploration of the Rutgers 12-inch AKG270 spiral field revealed four-sided non-linear contours consistent with sector periodicity four even at 50 keV, and by 250 keV four closed contours had formed in the corners — four off-centre stable orbits in addition to the primary equilibrium orbit.
Source quote & editorial note
The AKG270 radial trace space was explored first to identify the equilibrium orbits in 50 keV increments. Even, at 50 keV, non-linear behavior is noted in the larger stable orbits, exhibiting four-sided contours, behavior which is consistent with pole tips that have a sector periodicity of four. The corners of the four-sided nonlinear orbits become more pronounced and bulbous with increasing energy. By 250 keV four closed contours formed in the protracted corners, displayed in Figure 23. Thus, in addition to the primary Equilibrium Orbit, there are four off-center stable orbits.
Editorial note, tabletop extrapolation: A phenomenon to look for on any sectored machine, from this worked case: the four-sector AKG270's radial phase space showed four-sided nonlinear contours already at 50 keV, sharpening with energy until four closed islands formed by 250 keV — genuine off-centre stable orbits alongside the primary one. Whether YOUR sector count produces islands, and at what energy, depends on the field harmonics and tunes: survey trace space at energy steps fine enough to resolve your calculated resonances (50 keV was this study's choice), and follow with RF-on tracking to learn whether real accelerating beam gets captured by them (a beam parked on an island reads as mis-steered, dg-1793).
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Turn-by-turn axial centroid and envelope signals extracted from the Rutgers 12-inch beam images were fitted with a harmonic signal using a moving-window technique with error weighting (lower weights on points with large beam envelopes, whose centroids are less precisely determined); image-by-image examination showed a 5-point window gave the best results, against a typical signal length of around 15 turns.
Source quote & editorial note
These data were in turn fitted with an harmonic signal using a moving window technique. The fitting technique takes the measurement errors into account: lower weights were associated with the data points corresponding to large beam envelopes, as the determination of the centroid of these data points are not as precise as those were the beam is at a focus. Image-by-image examination of the fit quality showed that the best results are obtained using a 5-point window. That relatively low number of data points allowed to extract frequency information for many radial position as the typical signal length is around 15 turns long.
Editorial note, tabletop extrapolation: Calibration context from the Rutgers analysis: their typical signal was ~15 turns and image-by-image checks favoured a 5-point moving window. On another machine, pick the window by fit residuals and uncertainty (synthetic-signal tests are cheap); the transferable part is the method — error-weighted moving-window harmonic fits with envelope-dependent weights — not the two numbers.
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Deuterated-titanium target preparation on the Rutgers program followed a hydrogen-loading recipe adapted from Livanov et al.: three samples cut from 0.010-inch thick laboratory grade titanium sheet, nominally 10 mm x 20 mm, cleaned with acetone and methanol and precisely massed; a base vacuum of 1x10-6 Torr established in a two-foot quartz tube inside a clamshell tube furnace, the furnace warmed to 900 degrees C with an approximately 3 hour dwell during which the outgassing pressure rose and then fell, and once the pressure had dropped to approximately 2x10-5 Torr the pump was isolated and the tube backfilled and held at one atmosphere of deuterium.
Source quote & editorial note
A recipe for the controlled loading of titanium with hydrogen gas was adopted from Livanov, et al. [6] The loading apparatus consisted of a clam-shell tube furnace capable of reaching 1000°C, into which was inserted a two foot quartz tube connected to a high-vacuum system. The vacuum system consists of a mechanically backed turbo pump that was supplemented with an in-line lN2 cold trap. … Three identical samples were cut from a 0.010-inch thick sheet of laboratory grade titanium. Each sample was nominally 10 mm X 20 mm. They were cleaned with acetone and methanol. Precise mass measurements were made before the loading – these mass measurements included gases already adsorbed. Two of the three samples were loaded into center of the quartz tube, the vacuum system sealed and pumped. The third sample was kept as a reference. A base vacuum of 1x10-6 Torr was established before heating the samples. Pressure measurements, plotted in figure 4, were made as the tube furnace warmed to 900°C and throughout the ~3 hour dwell period. … The pressure slowly dropped during the 900°C dwell. Once the pressure dropped to approximately 2x10-5 Torr, the vacuum pump was isolated and the tube furnace was quickly backfilled and maintained at one atmosphere of deuterium.
Koeth, Neutron Production with a 12-Inch Cyclotron (2017) — p. 2
Editorial note, tabletop extrapolation: A reproducible target-loading procedure using apparatus within amateur reach (tube furnace, quartz tube, trapped turbo pump), with the numbers the source states — 900°C, ~3 hour dwell, isolate at ~2×10⁻⁵ Torr, backfill to one atmosphere of deuterium. The unloaded reference sample is the detail that makes the later mass-gain measurement trustworthy (dg-1761). Not stated in the source and needed anyway: the safety engineering for hot hydrogen isotopes — flammable gas at a hot furnace mouth, quartz failure modes, and ventilation — which the reader must supply before attempting it. (The isolation-and-backfill clause is on p.3.)
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The Rutgers deuterium loading used a water bubbler on the manifold through a check valve, with deuterium flow set to approximately one bubble per second to guarantee slight positive pressure; a notable delay between start of gas flow and first bubbles was taken as the loading period, and the onset of bubbling was taken to mean the titanium targets were saturated and cooling could begin. Audible 'crinkling' sounds were heard from the targets as the deuterium was introduced, and deuterium flow continued until the targets were back at room temperature, locking the deuterium in.
Source quote & editorial note
A water bubbler connected to the manifold through a check valve was used to indicate a slight pressure above atmosphere within the quartz tube. The deuterium flow was set to cause approximately one bubble per second ensuring a slight positive pressure at all times. Audible 'crinkling' sounds were heard from the targets as the deuterium gas was introduced. ... There was a notable delay between the start of the gas flow and the first bubbles. Once the bubbling began, it was assumed that the titanium targets were saturated and cooling could commence.
Koeth, Neutron Production with a 12-Inch Cyclotron (2017) — p. 3
Editorial note, tabletop extrapolation: A zero-instrument endpoint HEURISTIC, reported as the source's own assumption: when the bubbler starts passing gas, they took the targets as saturated. Bubble onset can equally reflect line filling, head pressure or a leak, and cooling under flow does not by itself prove retention — so pair the bubbler with an independent uptake check (before/after mass on an unmounted coupon, flow integration, or a loading curve) before trusting the endpoint. Everything here is still glassware and a check valve.
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Loading two 0.010-inch titanium samples with deuterium at the Rutgers program produced a mass increase of 56 mg each (sample #1 0.61872 g to 0.67515 g; sample #2 0.60395 g to 0.66030 g) and roughly 10% linear swelling, with visible large grain structures and fissures; the authors determine greater than 220% (atomic) deuterium loading and note that compressing the same quantity of gaseous deuterium into the titanium sample's volume would correspond to a pressure of 20,000 PSI, which is why the metal swells and embrittles.
Source quote & editorial note
After the loading, each target was again precisely massed, both indicating an increase of 56 mg. Table 1 summarizes the mass and dimensional increases. It is worthwhile to note that the compression of the same quantity of gaseous deuterium into a volume of the titanium sample would result in a pressure of 20,000 PSI! With that in mind, it is understandable that the titanium would swell. Determined by the mass measurements, greater than 220% (atomic) deuterium loading has been achieved in our samples.
Koeth, Neutron Production with a 12-Inch Cyclotron (2017) — p. 3
Editorial note, tabletop extrapolation: What two real coupons did, not an acceptance limit: 56 mg gained each and roughly 10% linear growth on 10×20 mm, 0.010-inch titanium. Recomputed assuming every milligram gained is deuterium, the two samples give D/Ti ≈ 2.17 and 2.22 — bracketing the stated >220% and close to stoichiometric TiD2 — but mass gain is not deuterium-selective (oxide and adsorbates ride along), so an independent composition check is needed before certifying a load. The swelling is hydride-phase lattice expansion; the source's 20,000 PSI compressed-gas figure is a vividness argument, not the mechanism. The finished target is brittle and dimensionally changed — mount accordingly. Table 1 (p.3) prints 4% for the #2 height change and 10% for the #2 width change, but the tabulated dimensions give ~10% and ~4.7% respectively — the two percentages appear transposed in the source.
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The Rutgers deuterated titanium targets were prepared in February of 2008, mounted to sample holders with silver epoxy, and stored at atmosphere until their use in April 2017; because of the mounting, periodic mass measurements could not be taken and the authors state there is therefore no knowledge of the deuterium retention over that interval.
Source quote & editorial note
The targets were prepared in February of 2008, and were mounted to sample holders using a silver epoxy and were stored at atmosphere until their use in April 2017. Because of their attachment to the target holders, periodic mass measurements could not be taken, thus there is no knowledge of the deuterium retention.
Koeth, Neutron Production with a 12-Inch Cyclotron (2017) — p. 3
Editorial note, tabletop extrapolation: Two lessons for a small target program: these targets, stored at atmosphere for nine years with retention unmeasured, were the ones the same paper's April 2017 runs then used to produce detected neutrons (dg-1763, dg-1767) — so long storage did not kill them, though how much deuterium survived is unknown by the source's own admission. And the mounting scheme is why: silver-epoxied to holders, they could never be re-weighed. Mount so the coupon can come off the holder for weighing, or keep an unmounted witness coupon from the same loading batch.
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Neutron-induced gamma spectroscopy on the Rutgers 12-inch produced two telltale lines identified by the authors: 847 keV from inelastic scattering of neutrons on the magnet's iron nuclei (measured as 847 keV +/- 10% with NaI(Tl)) and 2.22 MeV from proton capture of a neutron — the binding energy released in creating a deuteron — arising in hydrogenous material such as the polyethylene moderator and the rem ball's Bonner sphere. A 6.5 minute HPGe run gated in synchronization with the RF pulse (beam-on only) additionally resolved construction-material lines: 472 and 1015 keV from the aluminum chamber lid, 962 keV from the copper magnet coils, and 140, 198 and 596 keV originating in the germanium of the detector itself.
Source quote & editorial note
Again, the 847keV and 2.22MeV lines are the prominent peaks, the additional gamma ray lines originate in the cyclotron's construction materials, such as 472, 1015keV lines from the aluminum chamber lid, and the 962keV line of copper, from the copper magnet coils. Several gammas lines, i.e. 140, 198, 596keV originate in the germanium of the gamma ray detector itself.
Koeth, Neutron Production with a 12-Inch Cyclotron (2017) — p. 7
Editorial note, tabletop extrapolation: A useful line list for anyone who puts a gamma detector near a small neutron-producing machine: the machine's own aluminium chamber and copper coils show up in the spectrum, so a background-subtracted, beam-gated run is needed to attribute anything. The 847 keV iron line doubles as evidence that fast neutrons are reaching the magnet steel. The Fig. 15 in-figure labels give 598 keV and 1014 keV and 2223 keV where the body text says 596, 1015 and 2.22 MeV; minor internal rounding differences. (The 847 keV +/-10% measurement and the 2.22 MeV proton-capture explanation are on p.6; the HPGe line list is on p.7.)
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Fission was demonstrated on the Rutgers 12-inch by surrounding a spare Westinghouse WL6376A HEU U-235 lined tube (approximately 1 gram of U-235 lining an argon-filled proportional tube, intended for reactor nuclear instrumentation) with moderating polyethylene blocks next to the cyclotron's target region; the detector was biased at +1100 V with signal split off through a preamp and pulse shaping spectroscopy amplifier. After tuning for maximum neutron production with a more sensitive 3He detector, large fission pulses appeared at a rate of approximately 1 fission event per RF pulse.
Source quote & editorial note
The fission chamber used was a spare Westinghouse WL6376A, HEU 235U lined tube intended for reactor nuclear instrumentation. Approximately 1 gram of 235U lined an argon-filled proportional tube. The detector bias and signal are split with a preamp, the HV bias was +1100 V, the signal was conditioned with a pulse shaping spectroscopy amplifier, and distributed to an oscilloscope for observation and scalar/timer for counting. ... These occurred at a rate of approximately 1 fission event per RF pulse.
Koeth, Neutron Production with a 12-Inch Cyclotron (2017) — p. 8
Editorial note, tabletop extrapolation: Reported as the source's own experiment and instrumentation, with no recommendation attached: an HEU-lined legacy fission chamber is specialized regulated material — possession, transfer and disposal rules must be verified for any such device, whatever its surplus provenance. What transfers is the method (optimize with the sensitive detector first, then bring in the insensitive instrument) and the calibrated fact that this complete configuration — this beam charge per pulse, target, moderator and ~1 g chamber — produced about one fission event per RF pulse; the rate belongs to the whole configuration, not to 150 keV alone.
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The Rutgers author's summary of the achievement is that a small 1 MeV proton cyclotron, modified to accelerate deuterons up to 400 keV, generated neutrons through the d(d,n)He3 reaction; the machine's stated forward plans are neutron-activation isotope identification, exploration of other low energy nuclear reactions accompanied by energetic gamma rays, and improved beam intensity and focusing to reduce beam current loss at larger radii and so increase neutron fluence.
Source quote & editorial note
Settling a personal pursuit for the author, a small 1 MeV proton cyclotron, modified to accelerate deuterons up to 400 keV, has demonstrated the ability to generate neutrons through the d(d,n)He3 reaction.
Koeth, Neutron Production with a 12-Inch Cyclotron (2017) — p. 8
Editorial note, tabletop extrapolation: One demonstrated operating point, precisely stated: a nominally 1 MeV proton 12-inch machine, retuned, accelerated deuterons to 400 keV and generated D–D neutrons. Other machines land elsewhere as field, radius, RF voltage and phase acceptance dictate. The listed future work (isotope identification, other low-energy reactions, beam-loss reduction) is the author's stated intent, not accomplished work; the source's printed reaction "F16(p,alpha)O16" is a misprint, the physical reaction being 19F(p,alpha)16O.
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(draft report) The Rutgers/UMD neutron detector for the diffusion measurement was a roughly two-foot-long 3He tube nested within a stack of pure polyethylene blocks, with the two sides and back stacked with neutron absorbing borated polyethylene blocks to set the boundary condition.
Source quote & editorial note
The neutron detector consisted of a ~2-foot-long 3He tube nested within a stack of pure polyethylene blocks. The two sides and back were stacked with neutron absorbing borated poly blocks to set boundary condition.
Koeth, Gilde & Moroch, Measurement of Neutron Diffusion Time from Fast Pulsed Systems (draft, 2020) — p. 3
Editorial note, tabletop extrapolation: A simple, buildable moderator/detector assembly: plain polyethylene where you want thermalization, borated polyethylene where you want the diffusion problem bounded. Reported as this source's construction. Draft report.
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(draft report) A digital oscilloscope set to infinite persistence gave the Rutgers/UMD group a preliminary, non-quantitative demonstration of neutron diffusion: with the rectified RF "on time" reference on one trace and the 3He detector NIM pulses on the other, 5 minutes of acquisition at 100 pulses per second yielded 250 neutron events, the slowest arriving 550 microseconds after production (RF off). The source is explicit that this display is not quantitative, because overlapping detector pulses blur individual arrival times; the exponential fit comes from the TAC/MCA measurement that follows.
Source quote & editorial note
A preliminary demonstration of the neutron diffusion effect is given by a digital oscilloscope set to infinite persistence which recorded the electronic pulses generated from the detection of neutrons over numerous cyclotron pulse events. … The upper yellow trace in figure 4 is the rectified reference of the actual RF “on time” pulse … The lower blue trace displays the pulses from the 3He detector NIM electronics, which are seen to continue to arrive long after the cyclotron RF is off. After 5 minutes of acquisition at 100 pulses per second a total of 250 neutrons events are observed. One can see the slowest neutron took 550us after production (RF off) to reach the 3He detector. This is not a quantitative measurement, since many of the neutron detector pulses overlap and blur their individual arrival times.
Koeth, Gilde & Moroch, Measurement of Neutron Diffusion Time from Fast Pulsed Systems (draft, 2020) — p. 3
Editorial note, tabletop extrapolation: A zero-cost first look before building any timing electronics: infinite persistence on a two-channel scope already shows whether the physics is there — and the source is explicit that this stage is not quantitative. The Fig. 4 caption says "in excess of 500 us" where the text says 550 us. Draft report.
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(draft report) The quantitative neutron thermalization/diffusion measurement used an Ortec model 567 time-to-amplitude converter with a 1 ms full-scale window delivering 0 to 10 V (so a 500 microsecond interval gives a 5 V pulse), started by a TTL pulse synchronized with the beginning of the RF pulse and stopped by the NIM pulse from the 3He detector, with output binned by an Ortec EZMca multichannel analyzer at a conversion gain of 512 channels. Intervals exceeding 1 ms simply reset the TAC without an output pulse, automatically ignoring cyclotron pulses that produced no detected neutron. A ten-point channel-to-time calibration was performed with 70, 100, 200, ..., 900 microsecond intervals from a Tektronix arbitrary waveform generator.
Source quote & editorial note
To quantify the thermalization and diffusion time, an Ortec model 567 time-to-amplitude-converter (TAC) was employed as outlined in figure 5. … In the present case, the full-scale time window was set 1ms. The TAC then delivered a proportional output pulse, ranging from 0 to 10V, corresponding to a time period of 0 to 1ms. Thus, if the period between the start and stop pulse was 500us, then the TAC would then output a 5V pulse. The TAC output was then binned by a multi-channel analyzer (MCA) to generate the temporal profile. The MCA used was an Ortec EZMca set to a conversion gain of 512 channels. If the time between start and stop pulses exceeded 1ms, the TAC simply reset without triggering an output pulse, and awaited a new start pulse, thus ignoring cyclotron pulses that did not result in a detected neutron. A ten-point calibration of MCA channel-to-time interval calibration of the TAC-MCA system was performed with 70, 100, 200, …, 900uS time intervals generated from a Tektronix arbitrary waveform generator. … To perform the measurement of neutron thermalization and diffusion time, a TTL pulse synchronized with the beginning of the RF pulse started the TAC clock, and the NIM pulse arising from the 3He detector registering a neutron provided the stop pulse.
Koeth, Gilde & Moroch, Measurement of Neutron Diffusion Time from Fast Pulsed Systems (draft, 2020) — p. 4
Editorial note, tabletop extrapolation: The source's TAC/MCA timing method, built from ordinary NIM modules. Two behaviours matter: an interval exceeding the 1 ms full scale resets the TAC with no output — which conveniently ignores the ~249 of 250 no-detect pulses, but also truncates any genuine event arriving later than 1 ms — and the ten-point AWG-generated calibration is what makes the histogram's time axis trustworthy. Detector conditioning, discriminator settings and grounding are not in the excerpt; treat this as the method's skeleton, not a complete recipe. Draft report.
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SIMION modelling of the Rutgers four-sector spiral AVF field revealed four off-center stable fixed points surrounding the central equilibrium orbit at 250 keV proton energy (nominal r = 2.75 inches); the islands are a nonlinear consequence of the four-fold symmetry, disappear quickly at higher energy, and appeared to have little effect on stability during acceleration.
Source quote & editorial note
Multiple off-center stable orbits were found at particle energy 250 keV (nominal r=2.75”). … In Fig. 7, four stable fixed points can be seen surrounding the central fixed point. … The off-center islands quickly disappear at higher energies, and seem to have little effect on particle motion/stability during acceleration.
Editorial note, tabletop extrapolation: PDF p.4 = printed p.294. Warns an AVF builder that a low-sector-count spiral geometry can grow parasitic off-center equilibrium orbits at intermediate energy (four of them here at 250 keV, matching the four-fold symmetry). The source's own hedged report: the islands "quickly disappear at higher energies, and seem to have little effect" during acceleration. Practical consequence: a beam that looks mis-steered at mid-radius may be sitting on an island — check with turn-by-turn tracking rather than assuming detrapping is clean.
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Over the Rutgers 12-inch cyclotron's history, 18 junior- and senior-level undergraduates worked on the machine and six went on to accelerator-physics careers; the machine also seeded a one-week USPAS course in January 2013, with a two-week course stated as in preparation for January 2015.
Source quote & editorial note
To date, 18 junior- and senior-level undergraduate physics students have gained experience with this machine … six of them have gone on to pursue accelerator physics careers in both academia and industry. The Rutgers cyclotron was the inspiration for a 1 week course at the United States Particle Accelerator School (USPAS) in January 2013. A second course (2 weeks) is in preparation for January 2015.
Editorial note, tabletop extrapolation: PDF p.5 = printed p.295. A reported program count for a tabletop-cyclotron education effort: 18 upper-level undergraduates to 2013, six of whom went on to accelerator-physics careers — with the machine also seeding a one-week USPAS course (January 2013) and a two-week course then in preparation for January 2015, i.e. stated intent at the 2013 conference, not an accomplished fact. Use it as one program's outcome record, not a student-hours costing benchmark; the paper gives no participation-duration data.
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The Rutgers optical phase/bunch-length method sidesteps RF pickup entirely: a fast (3 ns) phosphor screen on a radial positioner is viewed by a gated camera to build "time sliced" images, a measurement insensitive to dee voltage that can be made anywhere the radial probe reaches, including arbitrarily close to the ion source.
Source quote & editorial note
We have developed an optical based measurement that is insensitive to DEE voltage using a fast (3 ns) phosphor screen viewed by a gated camera to create “time sliced” images which longitudinally profile the beam. The phosphor plate is located on the end of a radial positioner that can sweep the entire chamber radius and hence any ion revolution. … This optical method mitigates measurement difficulties due to interfering RF fields near the accelerating gaps, and enables measurements to be made arbitrarily close to the ion source.
Editorial note, tabletop extrapolation: PDF p.1 = printed p.299 (conclusion on p.3/printed p.301). The central transferable idea: convert a longitudinal measurement that residual RF spoils into an optical one — the paper's own claims are that it mitigates the RF-field interference near the gaps and reaches anywhere the radial probe does, including the central region. A radial positioner already exists on most small machines as a beam probe; the added cost is the fast phosphor and the gated camera, the camera being the expensive item.
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The Rutgers fast-phosphor target is a 0.944-inch diameter ZnO:Ga-doped phosphor deposit layered between a 0.050 inch thick quartz substrate and a 1000 angstrom aluminium coating, with a 1/e relaxation time of 3 ns; the plate rides on an adjustable radial probe and is electrically isolated so it also reads average beam current.
Source quote & editorial note
The 0.944-inch diameter ZnO:Ga doped “fast” phosphor deposit was layered between a 0.050 inch thick quartz substrate and a 1000 Å aluminium coating. The plate, mounted at the end of an adjustable radial probe, was electrically isolated for average beam current measurements. The fast phosphor screen has a 1/e relaxation time of 3 ns
Editorial note, tabletop extrapolation: PDF p.2 = printed p.300. The reported layer stack for a fast beam-imaging target at tabletop scale — named phosphor (ZnO:Ga), quartz substrate and thickness, 1000 Å Al coating — with deposition, thickness of the phosphor itself, and optics not specified. The dual role (image plus isolated current reading) is worth copying where practical, remembering an isolated target reads net collected charge: secondary-electron emission must be suppressed or calibrated before that number is treated as beam current.
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The Rutgers group report that the 1000 angstrom aluminium backing on their fast phosphor attenuated the incident proton beam and reduced light output, and list as improvements either thinning the backing or turning the plate so the beam strikes the imaging side.
Source quote & editorial note
we believe that the aluminium backing attenuated the proton beam and therefore reduced signal from the beam
Editorial note, tabletop extrapolation: PDF p.3 = printed p.301. Directly relevant at tabletop energies: 1000 Å (100 nm) of aluminium in front of the phosphor is a real energy-loss layer for protons near 100 keV, and its fractional effect decreases as energy rises toward 1 MeV. The authors present attenuation as a belief, not a measurement; before copying the fix (thinner backing, or beam-side phosphor), evaluate the layer with PSTAR/SRIM at the actual beam energy.
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The Rutgers optical phase measurement was run at 7.800 MHz with fields around 0.5 Tesla, the frequency chosen as a compromise: lowering it lengthens the RF period so that the camera's fixed 3 ns resolving time buys finer phase resolution, at the cost of maximum achievable proton energy. At 7.8 MHz, 3 ns corresponds to 9 degrees of RF phase and one RF period is 128 ns.
Source quote & editorial note
Operation at 7.8 MHz was a compromise between maximum achievable proton energy and extending the RF period so as to maximize the time resolution
Editorial note, tabletop extrapolation: PDF p.2 = printed p.300. A tabletop machine running at a few MHz is accidentally well suited to this measurement: at lower cyclotron frequency a fixed gate width spans fewer RF degrees (Δφ = 360·f·Δt), so the same 3 ns camera gate buys finer phase resolution. Direct computation gives 3 ns of a 128.2 ns period = 8.42 degrees; the paper's 9 degrees is its rounding of that.
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The Rutgers optical measurement needed 900 camera integrations per 3 ns time step because the phosphor light was weak, and 44 steps to cover one 128 ns RF period (a 132 ns span); at the 20 Hz RF pulse rate a complete run took over half an hour. A light-tight optical transport between viewport and camera was necessary.
Source quote & editorial note
Due to the extreme sensitivity of the camera, and weak light of the phosphor, it was necessary to create a light-tight optical transport between the chamber viewport and the camera … 900 integrations per time step, a complete run of 44 time steps required over half an hour.
Editorial note, tabletop extrapolation: PDF p.2 = printed p.300. A realistic cost-of-measurement anchor: at Rutgers' own settings the arithmetic is 44 steps × 900 integrations / 20 Hz = 1,980 s — 33 minutes of stable operation (source, RF and field all required to stay put). Another machine's run length scales with its signal-to-background ratio, camera and beam current; the light-tight enclosure exists because the phosphor light is weak and the camera extremely sensitive — measure your own signal level before deciding it is optional.
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Measured on the Rutgers 12-inch cyclotron in a weak-focusing field with the plate at 91 mm radius (roughly 100 keV proton termination energy), proton bunch length fell as the magnetic field rose: 38 +/- 4.5 degrees at 0.498 T, 26 +/- 4.5 degrees at 0.534 T (nominal), and 20 +/- 4.5 degrees at 0.566 T.
Source quote & editorial note
we observe a tendency for bunch length to decrease with a rising magnetic field.
Editorial note, tabletop extrapolation: PDF p.3 = printed p.301 (Table 1; the 91 mm probe radius and ~100 keV termination energy are on PDF p.2). Rare published bunch-length numbers for a tabletop machine at almost exactly the 100 keV end of the target class: a beam tens of RF degrees long, with the measured means falling as field rises — the source states this as a tendency. The tabulated ±0.03 T is comparable to the spacing between the three field values; if that uncertainty were independent per row the settings would barely be distinguishable, so either it is largely common-mode (calibration) or ±0.003 T was intended — an unverified hypothesis, reported here as such with the printed value preserved.
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Even at the maximum ion current the nine-inch cyclotron produced, 50 nanoamps, no beam loading of the RF system was observed.
Source quote & editorial note
It is worth noting that even under maximum ion current conditions of 50 nanoamps no beam loading was noticed.
Editorial note, tabletop extrapolation: A useful separation-of-concerns datum: at 50 nA this machine saw no detectable beam loading, so RF tuning and beam tuning decoupled cleanly — expect the same at nanoamp-class currents, as a practical matter rather than a law (loading scales with current and energy gain, and a sensitive enough RF measurement might resolve it). The corollary stands: at these currents beam loading is useless as a diagnostic; a collector is the instrument.