Design Guide › Cyclotron general
General cyclotron design rules
78 of the guide’s 1878 rules carry the cyclotron-general tag.
Whole-machine design points and budgets: complete parameter sets for student and tabletop machines, power allocations, and the honest headline numbers a small cyclotron can claim.
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 and on the
all-in-one guide. Where an editorial note says
“the reference machine”, its parameters are on the
guide’s front page.
By applicability level: level 1 (9) · level 2 (35) · level 3 (26) · level 4 (6) · level 5 (2) — levels rank breadth, never license to skip (method). Related domains, by shared rules: Magnet (19), Project management (17), RF (10), Beam dynamics (9), Beam measurement (9). To combine tags or levels, open this domain in the filterable view.
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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A workable student-cyclotron design point for ~1.5 MeV protons: 10-inch pole faces, 17,000 gauss, 25.68 MHz RF, 10-14 kV dee-to-dee at 2 kW RF, giving 2 uA of beam (about 1.3e13 protons/s).
10 in poles, 1.7 T, 25.68 MHz, Vdee 10-14 kV, 2 kW RF, 2 uA, 1.5 MeVSource quote & editorial note
Size: 10-inch pole diameter ... Dee voltage: 10,000 to 14,000 volts dee-to-dee; R.F. power: 2,000 watts; R.F. frequency: 25.68 megacycles ... Magnetic field strength: 17,000 gauss
McGuire, The Iowa State University 1.5 MeV Undergraduate Cyclotron (1961) — p. 9
Editorial note, tabletop extrapolation: The closest historical analogue to a next machine's target: same pole diameter as the reference machine, and the ~3x field buys the ~10x energy (E ~ B^2*r^2 at fixed radius). The ~10x dee voltage buys turn count, phase margin and beam survival at that field - not the energy ceiling itself.
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A 1.2 T tabletop cyclotron design point: 15 cm flat pole faces with the chamber in place giving a 3.81 cm pole-tip separation, 1.28 T at 70 A, water cooled at 18 C and 0.8 gallon/min at 50 A.
15 cm poles, gap 3.81 cm, 1.28 T at 70 A (1.16 T at 50 A); cooling 18 C water at 0.8 gpmSource quote & editorial note
With the chamber in place, the separation between the pole tips is 3.81 cm, giving a maximum magnetic field of 1.28 T at 70 A ... requiring 18 C water flowing at 0.8 gallons per minute (at 50A)
Editorial note, tabletop extrapolation: A purchasable-magnet benchmark almost exactly at the reference machine's scale. The 0.8 gpm is a flow figure, not a chiller spec: size the chiller from coil dissipation and allowable temperature rise (P = flow x heat capacity x dT - the magnet-power calculator's territory), with the flow number as the plumbing constraint it is.
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Accept that the honest headline number for a small machine is small: Houghton's best was ~0.1 uA at a B/3 resonance (the paper's figure), and 3 pA at the highest proton energy reached - 160 keV at 796 mT and 12.1 MHz; the paper names more magnet current, cooling and RF frequency as what higher energy would take.
0.1 uA best (B/3 resonance); 3 pA at 160 keV, 796 mT, 12.1 MHz; 400 keV theoretical needs more magnet current, cooling, and higher RF frequencySource quote & editorial note
The highest proton energy obtained so far is about 160 keV, with a 3 pA peak near the correct magnetic field of 796 mT for 12.1 MHz.
Editorial note, tabletop extrapolation: Calibrates expectations exactly at the reference machine's operating point (~150 keV): currents fall steeply near a machine's energy limit, and the gating items the paper lists are the ordinary ones - magnet current, cooling, RF range.
Cited in: Choosing Your Machine
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A commercial-class 10 MeV PET-cyclotron power budget (CYC2016 design): 1.5 kW internal PIG ion source against 26 kW magnet coil and 14 kW RF consumption; simulated beam after the third accelerating gap ~197 uA at 190 keV from a 40 kV gap voltage.
P_ion_source ~ 1.5 kW (commercial); ~4% of machine wall powerSource quote & editorial note
Coil Consumption Power [kW] 26 ... RF Consumption Power [kW] 14 ... Ion Source Power [kW] 1.5 (Table 1) ... Cavity loss power was calculated 12.7 kW to generate an electric field with 40 kV gap voltage ... Beam energy and current was checked 190 keV, 197 uA after third accelerating gap
Editorial note, tabletop extrapolation: Context datum, not a scaling law: the reference machine's ~0.1-0.2 kW source budget is a deliberate derating of this class of design, but beam current does not scale with source power - capture, acceptance and extraction losses dominate - so estimate current from measured source output and capture efficiency.
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Reduce cross-coupling before closing control loops: once the three dees were isolated electrically by adjusting the neutralizing loops, the machine behaved like three separate single-phase systems, each controllable with its own small amplifier and servo.
Source quote & editorial note
Once the three dees are isolated electrically by adjusting the neutralizing loops the machine behaves like three separate single-phase systems.
Smith, A Three-Phase Radiofrequency System for Cloverleaf Cyclotrons — UCRL-3153 (1955) — p. 18
Editorial note, tabletop extrapolation: The architectural moral - decouple where practical, then control each loop as SISO - applies to a next machine's interacting adjustments (tuner vs coupling vs amplitude); measure the residual interaction after decoupling, and where it stays significant use coordinated control rather than fighting coupled loops one at a time. The programme burned months servoing the coupled system first (ucrl-3187 p.5-6, 11).
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The variable-energy argument for electrical extraction elements: the source's system - with tunable frequency AND gradient - eliminates the difficulties fixed magnetic extraction systems have on variable-energy machines, where static perturbations set into the pole geometry cannot follow a changing energy and field.
tunable (f, E) replaces fixed (B-bump geometry) for variable-energy operationSource quote & editorial note
The possibility of changing the electrical frequency and gradient to match operating conditions eliminates difficulties arising in magnetic extraction systems for variable-energy machines.
Stubbins, Radiofrequency System for Extracting Particles from a Cyclotron — UCRL-8578 (1958) — p. 4
Editorial note, tabletop extrapolation: Supports the next machine's plan-of-record (electrostatic deflector, no fixed magnetic channel) in spirit: an educational machine running several field/energy points wants extraction strength on a knob. A plain electrostatic deflector carries the voltage knob - not the source system's frequency knob - and that adjustability is exactly what a fixed B-bump lacks.
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Budget real machine runs for beam characterization: in the 86-inch's post-modification quarter, 15 of 50 tabulated bombardments (30% by run count) were beam-profile or energy-measurement runs - characterization scheduled as work, not squeezed in as overhead.
~1/3 of runs devoted to beam profile + energy measurement after any major changeSource quote & editorial note
The bombardments are tabulated below: Beam profile 10, Isotope production 8, Experimental 16, Energy 5, Physics 7, Radiation damage 4.
Editorial note, tabletop extrapolation: A quarterly cadence in miniature for the reference machine: after any change (RF upgrade, source rebuild), the run log should show dedicated profile and energy runs alongside the physics runs - the ORNL table records the proportion by count; durations and ordering it does not give, so import the habit, not a timeline.
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Sequence commissioning around your shielding, using a heavier/slower species first: Davis deliberately declined to accelerate protons until the shielding vault was complete, doing all early beam work with H2+ and alphas whose lower velocity and yield kept radiation manageable.
Source quote & editorial note
We have not attempted to obtain particle beams for the cases discussed here as we do not plan to accelerate protons until the shielding vault is completed.
Editorial note, tabletop extrapolation: Directly relevant to the plan's shielding gate: species choice is a radiological control. Commissioning on H2+ at the same B*rho halves the total kinetic energy and quarters the per-nucleon energy versus protons - same tuning fields, gentler consequences - and the proton program waits until the vault or survey case is ready. Davis's sequencing is the model; the record itself says only that they deferred protons until shielding was complete.
Cited in: Shielding a Small Cyclotron
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The unit costs that drive magnet optimization could, in the source's judgment, only be truly determined after years of operation - so the first-pass optimization uses estimates, and refining it beyond the accuracy of those inputs is wasted effort.
Source quote & editorial note
It appears that the unit costs can only be determined after the cyclotron has been in operation for several years, so estimates must be employed.
Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 30
Editorial note, tabletop extrapolation: A 1952 statement of the plan's own doctrine, applied with modern tools: use estimated lifecycle costs with a sensitivity check on the uncertain inputs, update from quotations and commissioning actuals as they arrive, and avoid polishing the spreadsheet past its input accuracy.
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There is an optimum operating field for a given beam energy (bigger magnet at low field vs smaller at high field); it follows from balancing the marginal cost of scale (C = C3*S^3 + C2*S^2 + C1*S + C0, with E ~ S^2) against the marginal cost of excitation - and it cannot be pinned down without a model magnet close to final form.
C = C3*S^3 + C2*S^2 + C1*S + C0; E = E'*S^2; optimum where d(cost)/d(energy) via scale equals d(cost)/d(energy) via field (Eqs. 137-145)Source quote & editorial note
This field strength depends on the design and the size of the magnet and cannot be determined without a model magnet.
Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 33-38
Editorial note, tabletop extrapolation: The steel-vs-power tradeoff behind "how hard to push B" - for a fixed 757-lb-class magnet the answer comes off the real excitation curve, not theory; FEMM plays the role of the model magnet for first passes.
Cited in: Choosing Your Machine
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Model the whole vacuum system as an electrical equivalent circuit - every duct, orifice and perforation a conductance (resistance = 1/S), combined in series/parallel down to a single effective speed AT THE LOCATION THAT MATTERS (inside the dee, where the beam and source live), not at the pump flange.
Source quote & editorial note
the term "resistance" is used there to indicate the reciprocal of the conductance. The use of resistance presents perhaps a clearer picture through the use of an electrical analog.
Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 132
Editorial note, tabletop extrapolation: The report's method in one sentence - their 32-in pumps' 13,700 l/s collapsed to 8,300 l/s effective inside the dee (air; the report's own worked numbers). The size of that collapse is the reason to budget from the source outward, not the pump inward - compute the conductance chain for the actual geometry rather than assuming any fixed fraction survives.
Cited in: The Vacuum Budget of a Cyclotron
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Never quote an internal-target beam energy from the B-rho calculation alone: ORNL's 86-inch measurements indicated the proton energy might deviate as much as +/-10% from the H-rho value, and the energy of maximum intensity varied by several hundred keV under MINOR adjustments of ion-source position, dee voltage, magnetic-field tuning, and oscillator frequency.
observed: E(measured) - E(B-rho) up to +/-10%; dE(max intensity) ~ several hundred keV vs everyday tuning parametersSource quote & editorial note
Measurements of the internal beam of the ORNL 86-inch cyclotron very early indicated that the energy of the proton beam might vary as much as +/-10% from H-rho calculations. ... The energy of maximum intensity was found to vary by as much as several hundred kilovolts with minor adjustments of the ion source position, dee voltage, magnetic field tuning, and oscillator frequency.
Editorial note, tabletop extrapolation: The direct historical support for this collection's energy-convention discipline: the reference machine's '150 keV-class computed' is a convention, not a measurement, and its own discrepancy must be measured, not assigned ORNL's +/-10%. For a next machine's B11(p,alpha) work, where yield vs energy is steep, measure energy AT the target (absorber stack in front of the PIPS, or foil methods) every time tuning changes.
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Distrust beam diagnostics taken with the machine deliberately detuned to reach diagnostic-friendly intensity — the operating conditions differ enough from normal running that the measured energy distribution may not be the operating one; state the caveat with the result.
Source quote & editorial note
the cyclotron operating conditions are so different from those used in normal operation that it may well be that the energy distribution is not the same.
Editorial note, tabletop extrapolation: Methodological honesty that transfers directly: IF detector protection forces attenuated or otherwise-configured beams for a measurement, log the machine state (dee voltage, field, frequency, source position, attenuation method) alongside every energy measurement so diagnostic-mode and run-mode data are never silently mixed - attenuation need not mean detuning, so record what actually changed.
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Set beam energy as an explicit compromise among cost, the physics value of higher energy, and the fraction of beam you can extract - the source's three axes; current they set separately, from what the research program needed.
Source quote & editorial note
The beam energy is really a three way compromise between cost, the advantages of higher energy, and the ability to extract a large fraction of the beam.
Oak Ridge National Laboratory, A Proposal for the Mc² Isochronous Cyclotron — ORNL-3540 (1963) — p. 20
Editorial note, tabletop extrapolation: Directly transferable process rule (their answer, 810 MeV / 100 uA, is not): write down the compromise axes for a next machine's energy point instead of inheriting a number.
Cited in: Choosing Your Machine
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A risk-retiring model's charter, in the source's words: examine practicability, reveal any unexpected phenomena, and demonstrate the feasibility of the riskiest subsystem - the purposes their electron analogue was conceived for.
Source quote & editorial note
conceived as an experimental device to examine the practicability of isochronous acceleration ... to reveal any unexpected phenomena ... and finally, to demonstrate the feasibility of a high efficiency beam extraction system.
Oak Ridge National Laboratory, A Proposal for the Mc² Isochronous Cyclotron — ORNL-3540 (1963) — p. 263
Editorial note, tabletop extrapolation: The three-purpose charter is scale-free for any model or prototype a program chooses to build; whether to build one at all is a cost-versus-risk call - FEMM plus the tracker is the tabletop program's cheap analogue. The keV-electron stand-in trick itself needs more than matched T/mc^2 to be faithful (rigidity and geometry must scale together).
Cited in: Choosing Your Machine
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When rejecting alternatives in a trade study, name each one's defects - the source's own practice in the quoted line: 'all suffer from one or more of the following defects', followed by the list.
Source quote & editorial note
All suffer from one or more of the following defects: excessive space requirements, lack of terminal space, lack of terminal auxiliary power, and lack of flexibility for future uses.
Oak Ridge National Laboratory, A Proposal for the Mc² Isochronous Cyclotron — ORNL-3540 (1963) — p. 149
Editorial note, tabletop extrapolation: Their injector shoot-out (tandem vs open-terminal vs pressurized vs Van de Graaff) models the documentation style for any subsystem selection in mark2_design_notes open decisions.
Cited in: Choosing Your Machine
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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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Provision probable future additions now and keep their cost out of the baseline - the quoted split: 'provisions have been made in all plans to make the addition of the medical facility as simple and as economical as possible' while 'the cost of the medical facility is not included in the initial cost of the project'.
Source quote & editorial note
Provisions have been made in all plans to make the addition of the medical facility as simple and as economical as possible ... The cost of the medical facility is not included in the initial cost of the project
Oak Ridge National Laboratory, A Proposal for the Mc² Isochronous Cyclotron — ORNL-3540 (1963) — p. 22
Editorial note, tabletop extrapolation: Scale-free scoping discipline for the business plan: design the educational-machine baseline with hooks for upgrades (extraction port, shielding growth, second station) without loading their cost onto gate-one.
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Put scheduling detail where the novelty is: the ORNL project network-planned the machine and beam handling - 'the major novelties and complexities' - and left the building and shielding out of that programming exercise, relying on conventional construction planning for them.
Source quote & editorial note
Because the major novelties and complexities of the project lie in the area of the machine and the beam handling, these areas were programmed. The building and shielding portions of the project were not programmed
Oak Ridge National Laboratory, A Proposal for the Mc² Isochronous Cyclotron — ORNL-3540 (1963) — p. 252
Editorial note, tabletop extrapolation: Scale-free effort allocation: plan the risky subsystems (source, RF, field mapping) at fine grain; conventional logistics still get milestone-and-dependency tracking - procurement lead times, lifting, electrical and shielding milestones - just not fine-grained networks.
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Treat the first schedule as a hypothesis: when the critical path gives an unacceptable duration, re-evaluate every activity on it and resequence - ORNL completed the vault and building first so magnet assembly could begin earlier, cutting the ~8-year-10-month initial estimate substantially (figure sighted in the scan; the resequencing decision is the quoted mechanism).
Source quote & editorial note
All activities on the critical path were then re-evaluated ... It was decided that the cyclotron vault and cyclotron building could be completed first, to allow the magnet assembly to begin at an earlier date.
Oak Ridge National Laboratory, A Proposal for the Mc² Isochronous Cyclotron — ORNL-3540 (1963) — p. 258
Editorial note, tabletop extrapolation: Scale-free: iterate the schedule, overlapping long-lead assembly with remaining construction. Note what sat on their critical path per the report's activity lists - field plotting, re-plot analysis, iron alignment rechecks - field mapping is schedule, not an afterthought, at any scale.
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The pole iron is the durable identity: ORNL's 1949 test cyclotron was the '22-inch' by maximum orbit, and after the rework it was 'more appropriately identified as the 44-in. cyclotron' - renamed for its equivalent pole diameter, the report's own naming logic.
Source quote & editorial note
Inasmuch as the equivalent diameter of the pole pieces is 44 in., the machine is more appropriately identified as the 44-in. cyclotron.
Editorial note, tabletop extrapolation: The reference machine's H-frame is the analogous asset: energy upgrades - gap, shims, dees, RF power - can stage around the same 757-lb iron for years. The platform reading is the editorial lesson drawn from ORNL's staged reuse of one magnet line (1.5 MeV, then 5 MeV, then proposed heavy ions); the quote itself carries the renaming.
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A variable-energy cyclotron is a credible Van de Graaff alternative in the 5-10 MeV band: ORNL's study concluded feasibility, with energy definition better than +/-10 keV achieved by collimation plus magnetic analysis of the deflected beam - selection, not correction: the analyzer transmits a narrow band and discards the rest, trading current for resolution - and 1-10 uA deflected.
energy definition < +/-10 keV via deflected-beam collimation + magnetic analysisSource quote & editorial note
such a cyclotron is feasible, that an energy definition of less than +/-10 kev could be achieved, and that deflected beams would be in the range of 1 to 10 ua
Editorial note, tabletop extrapolation: Direct prior art for the plan's educational variable-energy concept: vary energy with field/frequency plus a movable target (cf. the 44-inch spacer), and buy energy DEFINITION with a simple analyzed beamline - accepting the current it costs - rather than machine perfection.
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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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Scaling datapoint - the revised ORNL 44-inch as specified: 6400 oersteds in a 13.5-in. gap, 9.7 Mc/sec, up to 100 kV dee-to-dee, giving 1.5-MeV protons at 11-in. radius or 4.9 MeV at 20 in.
B = 6400 Oe, f = 9.7 Mc/s, V_dd <= 100 kV; E = 1.5/4.9 MeV at r = 11/20 in. (nonrelativistic check: 0.64 T gives ~1.5 MeV at 11 in)Source quote & editorial note
Beam radius, in. 11 / 20; Proton energy, Mev 1.5 / 4.9; Magnetic field, oersteds 6400; Magnet gap, in. 13.5; Maximum dee-to-dee potential, kv 100; Frequency, megacycles/sec 9.7 (spec table, condensed)
Editorial note, tabletop extrapolation: The nearest professional sibling to a next machine in this collection - same ~0.64 T field class and ~9.7 MHz as the reference machine's 0.59 T / 9 MHz. Use it to sanity-check B-f consistency; note the 100 kV (vs ~1.3 kV) buys energy per turn and fewer turns - less phase slip and interception - while the energy-radius relation stays set by the field.
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Commission in a designed-in reduced-energy state: the rebuilt 44-inch's 14.5-in spacer moved the dees back from the field center so the machine could run at ~1.5 MeV for test operation at very high proton currents, before removal for full 5-MeV running.
Source quote & editorial note
This spacer moves the dees back from the center of the magnetic field so that the machine can be operated at approximately 1.5 Mev for test operation at very high proton currents.
Editorial note, tabletop extrapolation: Mirrors staged-gate logic - plan a low-energy high-current commissioning configuration as a mechanical state, not an improvisation, so beam-physics problems are separated from full-energy behavior. Reduced energy closes many reaction channels but not all: thresholdless capture (12C(p,gamma), 14N(p,gamma)) and light-element targets remain live, and very high current makes small cross sections and thermal loads consequential - so each commissioning state still gets its own reaction check, survey and beam-loss budget.
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Design subsystems as a reusable kit: the proposed 44-to-48-inch conversion needed only a new magnet and vacuum tank because the oscillator, dee system, vacuum system, ion source, target probe, and power supplies were all judged reusable — subsystem modularity is what makes a machine upgradable into a different machine (44-inch cyclotron).
Source quote & editorial note
All other components of the present 44-in. cyclotron, oscillator, dee system, vacuum system, ion source, target-probe, and power supplies, would be utilized.
Editorial note, tabletop extrapolation: A strong argument for clean interfaces between a next machine's subsystems: ORNL could contemplate a new machine class for the price of iron and a tank because everything else was JUDGED reusable - the judgment is the quote's; the adaptation cost of the reuse is not on this card. Design interfaces so the same judgment could be true of your machine.
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Adapting existing equipment mortgages the machine: ORNL's own five-point verdict on the 63-inch - built fast from adapted parts, it ended up unshieldable, with marginal field (median plane drifts, hard to keep shimmed), dee-to-ground capped at ~40 kV by its bushing insulators, a 6-in. gap half of what was needed, and a single-species rf system — and none of the five "can readily be corrected".
Source quote & editorial note
a large amount of existing equipment was adapted for use in the accelerator, and many design compromises were accepted. Consequently, this machine lacks the versatility and reliability which are essential ... which cannot readily be corrected: 1. The cyclotron is not and cannot be shielded ... [the dee stems] must enter the vacuum through bushing insulators. This limits the maximum dee-to-ground potential to about 40 kv ... 4. The magnetic field gap is only 6 in., less than half of what it should be to obtain the desired output.
Editorial note, tabletop extrapolation: The counterweight to thrift - surplus-equipment compromises in shielding provisions, magnet gap, and insulator ratings are the ones a finished machine cannot shed. When designing a next machine around salvaged parts, check each against this five-item list; anything on it deserves new hardware.
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A major rebuild of even a small, staffed machine runs about two years decision-to-tested-assembly: 44-inch revision design underway Mar 1953 (ORNL-1531), design essentially complete Mar 1954 (ORNL-1670), assembly approaching completion Sep 1954 with contractor rework (ORNL-1795), assembled and vacuum-tested but NOT yet on beam Mar 1955 — with ion source, oscillator auxiliaries, and shimming still open.
timeline: design start +12 mo = design done; +6 mo = assembly (blocked on contractor); +6 mo = assembled/vacuum-tested, beam still pendingSource quote & editorial note
The major components have been assembled and vacuum-tested (see Fig. 5).
Editorial note, tabletop extrapolation: Schedule realism, one datapoint thick: a professional division with machine shops took about two years from revision concept to vacuum-tested assembly, with outsourced fabrication the long pole (dg-951). A home program's periods stretch and compress differently; the census's one-to-six-year first-beam spread is the wider base rate.
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Retire RF-system risk with a scaled electrical model before cutting full-size metal: build the complete RF circuit at reduced scale (frequency scales inversely with size), verify tuning range, voltage distribution, and power on the bench, then commit to full-scale construction on the model dimensions. The 184-inch followed a three-stage chain: calculation (MacKenzie BP-140), half-scale model (this report), full-size bench test before installation.
half-scale resonates at ~2x full-scale frequency, and characteristic impedance is scale-invariant - for geometrically similar structures in the same mode with the same dielectric; lumped parts, couplers, losses and joints break exact similarity, so the model verifies the geometry-dominated partSource quote & editorial note
Performance of the model is considered sufficiently satisfactory to proceed with the full scale design and construction based on the model dimensions.
Anderson, Half-Scale Model Tests on the Three Quarter Wave R.F. System — UCRL-31 (1947) — p. 16
Editorial note, tabletop extrapolation: A next machine's dee/stem/tank is already benchtop-sized, so the transferable form is the mockup itself — a cheap RF-only copy (no vacuum) of the dee-liner geometry, swept with a VNA before the vacuum parts are machined. Same lineage as UCRL-64 and MDDC-1045 already in this collection.
Cited in: Choosing Your Machine
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Keep an availability ledger: divide every scheduled hour into operating (beam-on-target / beam adjustment / target setup / development) and outage by cause, each as a percentage of scheduled time. A professionally staffed national-lab cyclotron logged only 60.1% operating and 39.9% outage over a half year.
scheduled time = operating (beam-on + adjustment + setup + development) + categorized outage; NRL Jul-Dec 1969 = 1382.5 h, 60.1%/39.9%Source quote & editorial note
Total Operating Time 831.3 ... 60.1 ... Outage Total 551.2 ... 39.9 ... Scheduled Operating Time 1382.5
Editorial note, tabletop extrapolation: A run log that records why each session ended, in fixed categories, turns anecdote into a failure Pareto within a year. The NRL 60/40 split is one professionally staffed machine's half-year - a sobering calibration, not a forecast: build the spare-time machine's own ledger and let it set expectations.
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Rank downtime by category and spend reliability effort by the ranking: NRL's half-year outage Pareto put power supplies at 10.2% and vacuum at 9.3% of ALL scheduled hours, far ahead of RF (1.6%) and ion-source/filament changes (1.0%).
NRL outage by category (% of scheduled): power supply 10.2, vacuum 9.3, electrical 3.3, mechanical 2.7, RF 1.6, source/filament 1.0Source quote & editorial note
Vacuum 128.6 ... 9.3 ... R. F. 22.1 ... 1.6 ... Power Supply 140.4 ... 10.2
Editorial note, tabletop extrapolation: The transferable content is the Pareto METHOD on your own log, not NRL's ranking: on that machine in that period, unglamorous supply and pump maintenance was where uptime was bought - a small machine's ranking may differ, so measure before allocating effort.
Cited in: The Vacuum Budget of a Cyclotron
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Budget for transition overhead: in NRL's 1382.5-hour schedule, start-up/shutdown consumed 5.6% and beam tuning another 4.0% - together roughly a tenth of scheduled time spent getting into and out of running condition.
NRL: start-up/shutdown 77.5 h (5.6%) + beam tuning 55.0 h (4.0%) of 1382.5 scheduled hoursSource quote & editorial note
Beam Tuning 55.0 ... 4.0 ... Start Up and Shutdown 77.5 ... 5.6
Editorial note, tabletop extrapolation: Pump-down, filament conditioning, and field settling are largely per-session costs on a small machine; if your own log confirms that, batching experiments into fewer, longer sessions raises the beam-on fraction - measure the local session overhead first rather than assuming NRL's accounting transfers.
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Develop in parallel with operation, and expect major changes to require shutdown: NRL ran development alongside cyclotron operation, with major modifications waiting on machine shutdown (the shutdown-scheduling specifics are the report's account - re-read queued).
Source quote & editorial note
In most cases development is in parallel with operation of the cyclotron. However, major changes may require shut-down of the cyclotron for these modifications to be effected.
Editorial note, tabletop extrapolation: Grouping every open-the-chamber job (seal replacement, source work, new feedthroughs) into one planned vent-and-rebuild window costs one pump-down and one reconditioning instead of many - sound practice on its own logic, whatever NRL's exact schedule was.
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Latch and store the location of every fault: some faults (magnet overtemperature) clear themselves before the operator can find the tripping sensor - the quoted need for 'a device... which could detect and store the location of a large number of possible faults'.
Source quote & editorial note
This may happen before the operator can determine the sensor causing the fault condition. Therefore, a device was needed which could detect and store the location of a large number of possible faults.
Editorial note, tabletop extrapolation: Any interlock chain needs fault capture - latching relays, or a logged timestamp per sensor; per-sensor timestamps also give first-out ORDERING, which turns a cascade of consequential trips back into its primary cause. Without capture, intermittent faults (thermal, flow, vacuum burps) become undiagnosable ghosts that waste sessions.
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Classify faults into two tiers: priority faults that must be corrected before operation continues (annunciation cannot be cleared while the fault stands) and non-priority faults that may be acknowledged and bypassed (a failed roughing pump) while their indication stays displayed until fixed.
Source quote & editorial note
One is assigned as priority faults, errors which must be corrected to continue cyclotron operation ... The other is non-priority faults, such as the failure of a mechanical vacuum pump which may be bypassed and operation continued.
Editorial note, tabletop extrapolation: Hard-wire the chains whose failure is immediately hazardous - radiation monitors, HV enclosure, cooling on powered elements, vacuum-envelope and arc faults, as the machine's own hazard analysis identifies them - so they cannot be acknowledged away, and give genuinely operational faults a bypassable alarm that stays displayed until fixed. The design insight survives: a system where every fault stops the machine trains its operator to defeat interlocks. The tier assignment comes from the hazard analysis, never from a fixed list.
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The NRL machine gated its beam by dropping dee voltage to approximately 50% of normal - below that machine's acceleration threshold - rather than unkeying the RF, keeping the tuning and regulation loops engaged for clean recovery.
beam-off dee voltage ~50% of normal (below threshold but above regulation-loop dropout); switched via the d.c. reference of the dee voltmeter in the regulator loopSource quote & editorial note
the R. F. dee voltage was lowered to approximately 50% of its normal value which is less than the threshold voltage.
Editorial note, tabletop extrapolation: The concept transfers as an experiment, not a guarantee: measure the machine's own beam-versus-dee-voltage curve first (reduced RF can merely move the loss radius inward rather than extinguish ions), verify with a detector that the gated state is beam-off to the level the measurement needs, and check where the residual beam goes. Where true interruption matters, gate the source. Stepping the regulator's dc reference is the clean actuator either way.
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Utilization benchmark from a mature research cyclotron: 1,680 hours of operation in one quarter - about 18 hours per day - with the reported unscheduled losses being three days to a cold-trap refrigerator failure and one day to low diffusion-pump oil.
1680 h / 92 days ~ 18.3 h/day operatingSource quote & editorial note
the cyclotron was in operation 1680 hours, or about 18 hours per day. Three days were lost due to failure of the refrigerator for the cold-trap above the diffusion pumps. Another day was lost because of inadequate oil levels in the diffusion pumps.
Harvard University Cyclotron Laboratory, Quarterly Progress Report, 1 June – 31 August 1964 — p. 1
Editorial note, tabletop extrapolation: An upper anchor for what sustained cyclotron utilization can look like - useful against the NRL 60% figure only as a rough contrast, since the two reports account time differently (Harvard reports operating hours and lost days; NRL a full scheduled-time ledger). Note both of Harvard's losses were vacuum-auxiliary failures - cold-trap refrigeration and pump oil - not accelerator physics.
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Support equipment can dominate an outage: in the Harvard quarter, failure of the refrigerator serving the cold trap above the diffusion pumps cost three operating days.
Source quote & editorial note
Three days were lost due to failure of the refrigerator for the cold-trap above the diffusion pumps.
Harvard University Cyclotron Laboratory, Quarterly Progress Report, 1 June – 31 August 1964 — p. 1
Editorial note, tabletop extrapolation: Chillers, trap refrigeration, and compressed-air auxiliaries deserve the same spares-and-monitoring attention as the pumps they serve - on any system whose operation actually depends on them: where a warm trap means contamination or lost vacuum margin, the machine is down as surely as if the pump died.
Cited in: The Vacuum Budget of a Cyclotron
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The Harvard quarter's reported planned outage was a single ~1-week scheduled shutdown that installed the internal-beam pulsed-deflection apparatus.
Source quote & editorial note
A scheduled shutdown of about one week was required to install apparatus for pulsed deflection of the internal beam.
Harvard University Cyclotron Laboratory, Quarterly Progress Report, 1 June – 31 August 1964 — p. 1
Editorial note, tabletop extrapolation: Conditional batching guidance, not a demonstrated result: when several tasks require opening the same vacuum boundary, combining them into one planned shutdown saves repeated venting, pump-down, leak-checking and conditioning cycles - the same pattern as NRL's engineering shutdown, at a smaller scale.
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Keep the driving coils as close to the air gaps as possible - the quoted reason: less spreading and bowing of the field, and the largest usable fraction of gap area; the report's design discussion builds its order of operations around this (gap, field and uniformity first, then iron topology - full sequence: scan re-read queued).
Source quote & editorial note
With the size and proportions of the gap selected from the foregoing considerations and the required field strength and uniformity determined, several magnet types could be conceived which might satisfy the requirements. ... After the type of magnet has been selected, it is possible to calculate approximately the weight of copper and steel
Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. quoted principle on PDF 25 (printed p. 15) as cited; the order-of-operations sequence is on PDF 24 (printed p. 14), Sec. 6 'GENERAL DESIGN PROCEDURE'
Editorial note, tabletop extrapolation: Coils-near-gap is the reason cyclotron coils hug the poles rather than the yoke; the usable-fraction-of-pole-area argument is exactly the good-field-radius economics of a small machine.
Cited in: Choosing Your Machine
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Copy a proven machine when one exists at your scale: the UW 60-inch worked from a complete set of Berkeley Crocker plans, followed 'closely on the magnet design', drew sustained advice from the originating lab, and reached assembled-ready-for-test in three years - a schedule the report credits to exactly that inheritance; original design effort went to the subsystems where the precedent was silent.
Source quote & editorial note
We have had available for our use a complete set of the Berkeley plans which was kindly placed at our disposal by Professor E. O. Lawrence.
Editorial note, tabletop extrapolation: The strategy transfers directly: for any new machine, start from the closest documented working design - this corpus and the builds census exist to make that possible - and spend novelty only where the precedent is silent.
Cited in: Choosing Your Machine
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Know the fixed-frequency niche boundary: a 60-inch pole at ~15 kG is "about the optimum dimensions in which deuterons may be accelerated profitably without resorting to frequency modulation" — beyond this scale relativistic phase slip forces FM/synchro operation. Below it, constant-frequency operation buys large beam currents.
Source quote & editorial note
A magnet of this size when used with detuerons, is about the optimum dimensions in which deuterons may be accelerated profitably without resorting to frequency modulation.
Editorial note, tabletop extrapolation: Any tabletop proton/deuteron machine sits far inside the fixed-frequency regime: phase slip there is dominated by field shaping and dee voltage, not relativity. Fix small-machine beam loss with shimming and volts-per-turn first (dg-273's summed-slip check), and reserve frequency modulation for the relativistic regime this rule bounds.
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Control-system requirements worth copying whole: (1) EVERYTHING interlocked "in such a manner that serious damage cannot occur" for ANY fault — operator error, water failure, vacuum leak; (2) all major equipment startable from the control room in a definite sequence; (3) pilot lights showing both the exact operating state and THE REASON any unit failed to operate; (4) wiring arranged so units can be added with minimum rework (UW: cross-connect terminal boards in each room, one master schematic kept up to date, books of vacant terminals/wires/relay contacts). Operationally: gang-switched start sequence; paired on/off pushbuttons whose green READY light means the interlock chain ahead is satisfied; the LAST button in the chain applies oscillator plate voltage; on shutdown a time delay keeps cooling water, towers and oil pumps running ~5 minutes.
Source quote & editorial note
it should be completely interlocked in such a manner that serious damage cannot occur due to any failure of the operator or of equipment such as water failure or a vacuum leak.
Editorial note, tabletop extrapolation: A strong SEED for a tabletop control panel or PLC - the quoted requirement (no serious damage from ANY single operator or equipment failure) plus their sequence logic - to be completed rather than copied: the 1951 scheme is equipment protection, and a modern chain adds the personnel-safety layer on top (access, radiation, e-stop: dg-1065, dg-1072, dg-1075).
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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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Cyclotron RF differs from industrial RF in ways to design for from day one - the report's headline differences: (a) the resonator is a sparking load that can deliver large energy into the electronics; (b) multipactoring, 'common in the field of particle accelerators, rarely occurs in other industrial applications' (the quoted item); (c) frequency agility where the machine class needs it.
Source quote & editorial note
(b) the multipactoring problem, common in the field of particle accelerators, rarely occurs in other industrial applications
Editorial note, tabletop extrapolation: The checklist for adapting any industrial or ham RF gear (an LDMOS pallet included) to a cyclotron: add spark protection, add a multipactor start plan, and only then worry about power. Fixed-frequency tabletop machines are spared only (c).
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THE SELF-EXCITED POSITION (design tension with the MOPA position of ornl-2403): Smith's 88-inch runs the resonator as the frequency-determining element - 'hence it is called a self-excited oscillator' - with the report's implementation figures (AFC, regulation) as its own record (scan re-read queued for those numbers).
Source quote & editorial note
In this type of system the resonator is the frequency-determining element of the system; hence it is called a self-excited oscillator.
Editorial note, tabletop extrapolation: The live architecture decision for a next machine. An LDMOS chain driven by a synthesizer is a MOPA — it inherits ornl-2403's virtues (frequency authority, instrumentation) AND the self-excited literature's start-up disease (nyo-9359): the synthesizer holds frequency while multipactor holds the dee at zero. Smith's phase-discipline logic (feedback phase correct across the whole operating range) is the checklist item either way. High-SWR argument p.6.
Cited in: Driving the Dee: RF Coupling
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Before dimensioning anything, draw the dependency diagram of the five subsystems (magnet, acceleration, ion, vacuum, detector) and separate the given inputs (pole radius, maximum orbit radius, nominal pumping speed, flux density, pole gap, gap width, dee amplitude, specific charge) from the quantities calculated from them (cyclotron frequency, rigidity, final velocity and energy, first-orbit radius and velocity, number of accelerations, total path length, effective pumping speed, mean free path, final pressure, permissible gas load).
Source quote & editorial note
Bevor man an den Nachbau eines Zyklotrons geht, muss man sich darüber im Klaren sein, was man benötigt. ... Bei den fünf Teilsystemen handelt es sich im einzelnen um das Magnet-System, das das Führungsfeld liefert, das Beschleunigungs-System, das für die Hochspannung sorgt, das Ionen-System, verantwortlich für die Produktion der Ionen, das Vakuum-System, das das erforderliche Vakuum zur Verfügung stellt, und schließlich das Detektor-System, das die beschleunigten Teilchen registriert. ... Die Vorgaben in den grünen Kreisen sind zum einen gerätespezifische Größen. Dazu gehören: der Radius der Magnetpole rp und der maximale Bahnradius ... das Nenn-Saugvermögen SN des Pumpstands [tr.: before building a cyclotron one must be clear what is needed; the five subsystems are the magnet system supplying the guide field, the acceleration system providing the high voltage, the ion system producing the ions, the vacuum system, and the detector system registering the accelerated particles; the givens in the green circles are device-specific quantities - the pole radius, the maximum orbit radius, the pump stand's nominal pumping speed - the calculated quantities in blue circles]
Editorial note, tabletop extrapolation: A small machine has few free parameters; listing which are fixed by hardware (pole radius, pump) and which are design choices (B, gap, U0, species) keeps the sizing chain consistent and exposes circular dependencies early.
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Treat magnetic rigidity zeta = B*rho (T m) as the magnet system's design variable: an ion that reaches radius rho carries p = q*B*rho and, nonrelativistically, E = q^2*(B*rho)^2/(2m) - the field-and-geometry CEILING on energy; dee voltage sets turn count and whether the ceiling is reachable, not the ceiling itself.
p_max = q*B*rho ; E_max = q^2*(B*rho)^2/(2*m) ; v_max = (q/m)*B*rhoSource quote & editorial note
Sie bestimmt die maximal erreichbare Energie der Ionen und diese ist somit nur vom Magnetfeld und dem Radius der Austrittsbahn abhängig [tr.: energy depends only on field and exit radius]
Editorial note, tabletop extrapolation: For 0.5 T and 10 cm usable radius, zeta = 0.05 T m gives ~120 keV protons; doubling either B or rho quadruples the ceiling. Low dee voltage doesn't lower it - but capture, phase acceptance and losses can keep the beam from ever reaching rho, which is the caveat behind 'regardless of dee voltage'.
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Below a rigidity of about 0.3 T m (protons: 0.31 T m, 4.7 MeV, v = 0.1c) the source treats the machine as non-relativistic; the relativistic regime would demand fields of 3-6 T on 50-100 mm poles and is out of reach for small magnets. The boundary is a tolerance statement, not a switch: at beta = 0.1 the cyclotron frequency is already ~0.5% low.
zeta_rel = m*(0.1c)/q = 0.31 T m (H+), 0.63 T m (H2+)Source quote & editorial note
Für ζ ≤ 0,3 Tm ist man demnach im nichtrelativistischen Bereich [tr.: for zeta <= 0.3 T m one is in the non-relativistic regime]
Editorial note, tabletop extrapolation: A tabletop proton machine (zeta ~ 0.03-0.12 T m) sits comfortably below the bound - by a factor of 2.5 at the top of that range, not an order of magnitude. Constant-mass orbit codes are fine for geometry, but check the RF phase budget: even the ~1e-3-class frequency shift at 0.12 T m accumulates over hundreds of turns, so run the accumulated-phase check alongside the field-shape one rather than crediting all slip to field errors.
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When both H+ and H2+ are present, COLUMBUS plans the RF so both species come into resonance by changing the FIELD rather than the frequency - at fixed 2.82 MHz, protons resonate near 185 mT and H2+ near 370 mT - the book judging it easier to double the field than the frequency.
f_cyc = (q/m)*B/(2*pi) ; H2+ needs 2*B of H+ at the same fSource quote & editorial note
Es ist nämlich leichter, das Magnetfeld von 185 mT auf 370 mT zu erhöhen als die Frequenz von 2,82 MHz auf 5,64 MHz [tr.: easier to raise B from 185 to 370 mT than f from 2.82 to 5.64 MHz]
Editorial note, tabletop extrapolation: A fixed-frequency resonator plus a 2:1 field range covers both hydrogen species IF the machine works at both fields - field quality, source output and capture must each hold at both points, so verify rather than assume. Two peaks at B and 2B are consistent with H+/H2+ but not unique to them (q/m degeneracy, dg-1432); use them as a species INDICATION to confirm.
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Record operating points by species and status: at B0 = 370 mT protons resonate at 5.64 MHz (~32 keV at full radius) while H2+ - whose period is twice as long - needs 2.82 MHz (~16 keV); the published experiments run at 2.82 MHz with 1000 V amplitude, the proton runs at roughly half the design field (~187 mT peak).
370 mT: H+ at 5.64 MHz (~32 keV) OR H2+ at 2.82 MHz (~16 keV) - same radius, species-dependent frequency; operated: 2.82 MHz / 1000 V; ~187 mT peak for the proton experimentsSource quote & editorial note
Mit einer Beschleunigungsspannung der Frequenz von 5,64 MHz werden Protonen in einem Magnetfeld von B0 = 370 mT resonant beschleunigt. Unter diesen Bedingungen wäre für die H2+-Ionen die Umlaufdauer doppelt so groß; sie würden dann den ersten Halbkreis im Dee nicht phasenrichtig zum elektr. Wechselfeld verlassen. ... Als Frequenz der Beschleunigungsspannung wählt man 2,82 MHz mit 1000 V Amplitude [tr.: at 5.64 MHz accelerating frequency, protons are resonantly accelerated in a 370 mT field; under these conditions the H2+ orbital period would be twice as long and they would leave the first semicircle out of phase; for the accelerating voltage one chooses 2.82 MHz with 1000 V amplitude]
Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 37-39, 70-71
Editorial note, tabletop extrapolation: The design-vs-operated distinction this card exists for: conference-paper numbers are usually design values - cite measured operating points with their species and date, and never let one row imply a field-frequency pair serves two species at once.
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Dee voltage does not set the final energy (ideal on-crest model): the magnet and usable radius fix the ladder height, the voltage is the rung spacing - k = E_max/(q*U0) crossings, first-orbit radius r1 = sqrt(2*(q/m)*U0)/omega_cyc.
k = E_max/(q*U0) ; v1 = sqrt(2*(q/m)*U0) ; r1 = v1/omega_cycSource quote & editorial note
Die Endenergie der Ionen ist so etwas wie die Höhe einer Leiter und die Beschleunigungsspannung ist dann der Abstand der einzelnen Sprossen [tr.: final energy is the ladder height, voltage the rung spacing]
Editorial note, tabletop extrapolation: Recomputed for 1000 V protons at 185 mT: r1 = 24.7 mm, matching the book. A 150 keV machine at 1 kV needs 150 ideal crossings; at 5 kV only 30 - relaxing vacuum and field-error tolerance roughly in proportion. The idealization to keep visible: real voltage also moves capture, turn separation and whether the top rung is reachable at all (dg-1376's ceiling-vs-attainability).
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Expect possible extra peaks at B0/3, B0/5, ... below a species' main peak: the book notes ions that happen to carry 1/3, 1/5, ... of the maximum velocity are also resonantly accelerated - odd-harmonic operation, omega_RF = k*omega_cyc with k odd.
B = (v/v0)*B0 for v = v0/3, v0/5, ... ; omega_RF = k*omega_cyc, k oddSource quote & editorial note
Ionen, die zufällig 1/3; 1/5; ... der Maximalgeschwindigkeit haben, werden jedoch ebenfalls resonant beschleunigt [tr.: ions with 1/3, 1/5 ... of the maximum velocity are also resonantly accelerated]
Editorial note, tabletop extrapolation: Odd reciprocal-field peaks are CANDIDATES for harmonic operation - same species, same probe radius assumed - and whether they are detectable depends on capture and gap geometry; treat them as one hypothesis in the peak ledger (dg-1426), not something every machine must show.
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The COLUMBUS authors could draw only partly on earlier amateur and student cyclotrons (Niell, Dewan, Steiger, Baumgartner/Heuer, Koeth's Rutgers work) - 'the boundary conditions were too different'.
Source quote & editorial note
Trotzdem konnten wir nur bedingt auf bereits gemachte Erfahrungen zurückgreifen. Zu unterschiedlich waren die Voraussetzungen [tr.: prior experience was only partly usable; conditions were too different]
Editorial note, tabletop extrapolation: The transferable layer across amateur machines is the METHOD - dependency diagram, rigidity sizing, vacuum chain, species-by-q/m - not the numbers: copy the method, recompute every quantity for your own boundary conditions. (Which differences blocked reuse here isn't itemized in the quote; the lesson survives without the itemization.)
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Resonant acceleration requires omega_RF = k*omega_cyc with k odd (1, 3, 5, ...); the fixed-frequency property (period independent of radius and velocity) holds while the accumulated phase slip from gamma - 1 stays acceptable for the chosen turn count and phase window - at 0.1c the frequency is already ~0.5% low, which may or may not matter depending on turns.
T = 2*pi*m/(q*B) ; omega_RF = k*(q/m)*B, k = 1, 3, 5, ...Source quote & editorial note
ωHF = k · ωZyk = k · v/r = k · (q/m) B mit k = 1; 3; 5; ... [tr.: RF frequency equals an odd multiple of the cyclotron frequency]
Editorial note, tabletop extrapolation: Third-harmonic operation (k = 3) lets a 0.2 T magnet accelerate protons with a 9 MHz resonator, at the cost of a narrower phase window per crossing; it is the formal basis of the sub-harmonic peaks in I(B) spectra (dg-1424).
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Smallest-scale existence proof: the first operational cyclotron (1931) used a 0.55 T electromagnet with 10.18 cm pole faces and approximately 2,000 V of oscillating potential to produce hydrogen ions of about 80 keV.
Source quote & editorial note
This cyclotron utilized a 0.55 T electromagnet with pole faces 10.18 cm in diameter, and with an oscillating potential of approximately 2000 V, it produced hydrogen ions with kinetic energies of around 80 keV.
Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 11
Editorial note, tabletop extrapolation: A 10 cm, half-tesla, 2 kV machine made beam - these numbers CALIBRATE one demonstrated design point; they are not independent minima (resonant acceleration works at lower field or voltage with corresponding changes in frequency, radius and turn count), so use them as an anchor for expectations, not a floor for feasibility.
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2022 operating configuration per THPO001's Table 1 and text: 140 mm (5.5 in) dee diameter in a chamber 200 mm diameter x 75 mm high; flux density 185 mT (H+) / 370 mT (H2+); dee voltage 0.5-3.0 kV; final energy ~4.1 keV (H+) / ~7.5 keV (H2+).
Source quote & editorial note
[a] chamber with a diameter of 200 mm and a height of 75 mm. ... Diameter of the Dees 140 mm (5.5 in) Flux density 185 mT (H+) | 370 mT (H2+) ... Dee Voltage 0.5 - 3.0 kV Final Energy ~ 4,1 keV (H+) | 7,5 keV (H2+)
Editorial note, tabletop extrapolation: A long-serving teaching machine running protons at half its field capability eases magnet, RF and matching demands at the cost of energy. The quoted energies imply a ~48-50 mm detection radius (nonrelativistic equilibrium-orbit calculation at the stated fields - a derived number, not a printed one); treat the table as the published 2022 configuration without assuming every entry is a measured operating value.
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State a teaching cyclotron's requirements as two conditions before any dimensioning, per the 2013 design account: every operating parameter (vacuum, magnetic field, frequency) kept low enough that standard commercial components suffice, and the final energy kept small enough that no harmful radiation can arise, so that students can experiment at the running machine; the whole parameter table is then presented as the consequence of these two conditions.
Source quote & editorial note
In order to build such a small cyclotron one has to meet two conditions: Vacuum, magnetic field, frequency etc. must be so low that one can use standard components as far as possible, otherwise the costs will go to infinity; The final energy of the cyclotron must be small enough so that no harmful radiation can arise, so that the students can do experiments with the cyclotron. Table 1 shows the technical data of COLUMBUS. One can easily recognize that COLUMBUS meets all the conditions mentioned above.
Editorial note, tabletop extrapolation: A hobby-scale build benefits from the same requirements discipline; writing the cost condition and the radiation condition down first turns every later component choice into a check against them. The radiation condition itself needs its own verification, not just an energy number: whether 'no harmful radiation can arise' at a given operating point is the paper's claim for its machine, and X-rays begin when high voltage or RF is energized, before any beam.
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Preserve the pre-beam design snapshot as its own dated record. The 2013 conference table (design calculation, 2013) lists 140 mm dee diameter, 0.38 T flux density, 5.63 MHz, 2.0-3.0 kV between the dees, 6-8 revolutions, 24-48 keV expected final proton energy, and 1e-5 mbar chamber vacuum rising to 1e-4 mbar with hydrogen feed. Editorial observation: the 24-48 keV span tracks dee voltage times gap crossings under ideal synchronous gain (2-3 kV over 6-8 revolutions, two crossings each), the project's 2016 paper records that no beam operation was possible in 2013 and first beam came in April 2014 (so the table is pre-beam), and later published accounts of the same machine report operation well below these design values - the snapshot is the anchor for a documented design-versus-operating-point contrast.
Source quote & editorial note
Table 1: Technical Data — Diameter of the Dees 140 mm (5.5 in); Flux-density of the magnetic field 0.38 T; Vacuum in the chamber 10-5 mbar; dto with H2 10-4 mbar; Cyclotron frequency 5.63 MHz; Number of revolutions 6-8; Voltage between the dees 2.0 -3.0 kV; Final energy 24 - 48 keV … The expected final energies of the protons are 24 - 48 keV after 6 - 8 revolutions. These energies don't produce any radiation outside the chamber.
Editorial note, tabletop extrapolation: A conference paper's date fixes the claim, not the beam; when reusing published small-cyclotron parameters, check whether the paper predates first beam and label such values as design predictions rather than demonstrated performance.
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At very low energy a deliberately flat (flutter-free) cyclotron field paired with electrostatic axial focusing from a high RF harmonic is a viable architecture; the LBNL cyclotron mass spectrometer chose it over an azimuthally varying field because it is a simpler magnet configuration when the harmonic provides adequate focusing.
Source quote & editorial note
A flat field without flutter was selected since it is a simpler configuration for this very low energy and the high harmonic provides adequate electrostatic axial focussing
Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: removing hills and valleys is viable at low energy only where the RF harmonic and dee geometry demonstrably supply the axial focusing the flutter no longer provides — the LBNL machine ran at harmonic 15 with electrostatic focusing doing that job. Verify axial stability by analysis or tracking before deleting flutter from a design; low energy alone does not guarantee it.
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Sizing a small cyclotron is a compromise between center-region clearance and transit time: better clearance requires either a larger (costlier) magnet or a smaller injection radius, and a smaller injection radius worsens the transit time at high harmonics — so the design seeks a magnet just large enough that the injection radius still gives a good transit-time factor with good center-region transmission.
Source quote & editorial note
The overall size of the machine is dictated by the mass resolution needed, the turn separation needed to clear the center region, and the injection energy. Better center region clearance requires a larger magnet, which is more expensive, or it requires a smaller injection radius, making the transit time worse for high harmonics. So a compromise has to be made giving good transmission in the center region and a large enough injection radius to give a good transit time factor
Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: on high-harmonic or low-voltage designs the center region can drive machine size alongside the final-orbit rigidity — check the transit-time factor at the first gap crossing before shrinking the injection radius to save magnet steel, and check that the extraction-radius rigidity still fits the pole.
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The whole-system payoff of a PM-energized cyclotron magnet is elimination of magnet coils, power supplies, and magnet cooling — reducing utility requirements enough that the LBNL team judged their 1 T, 30-cm-pole instrument portable for use in hospitals, trucks or airplanes. The accepted cost is loss of field-strength variability, tolerable for a single-ion-mass instrument; the source notes other ions could be reached by scaling injection energy, RF frequency and dee voltage to the fixed field.
Source quote & editorial note
The resulting loss in variability of the field strength is acceptable because the instrument is intended to be used for only one single ion mass with charge 1, although scaling of injection energy, rf frequency and dee voltage could be used to accelerate other ions ... No coils or power supplies and no cooling are required for the magnet. This reduces the utility requirements for the spectrometer system as a whole. This reduction and the small size and weight make the system "portable", conceivably permitting utilization in medical studies in hospitals, or for environmental monitoring in trucks or airplanes
Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: a fixed-field PM magnet trades away tuning range — B fixes the orbit and RF frequency scale, and the electrical settings (frequency, dee voltage, injection energy) must be matched to it; they are matching parameters for reaching a different ion, not substitutes for field adjustment. Best suited to machines committed to one species and one configuration at a time. The cooling eliminated is the magnet's own; RF and other systems keep theirs.
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Design the extraction radius with margin over the minimum that meets the physics requirement: the LBNL CMS could reach its turn count with 1500 V per turn at an extraction radius of 9 cm or less, but was conservatively laid out for 12 cm extraction (50 keV) on a 15 cm pole face.
Source quote & editorial note
With modest energy gain per turn, 1500 V, it is possible to achieve this figure with an extraction radius of ≤ 9 cm. We have conservatively designed the instrument for an extraction radius of 12 cm, corresponding to an energy of 50 keV ... [Table 1:] Pole face radius 15 cm
Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: radius margin keeps the working orbit away from the field-edge rolloff and leaves headroom in turn count and final energy above the bare requirement. It does not bend the rigidity relation — at fixed field the orbit radius for a given energy is fixed, so lower-than-planned dee voltage costs turns, not radius. Committing the magnet to the bare-minimum radius leaves no recovery path once it is built.
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Reference operating point of the ISU undergraduate cyclotron (1961, the source's stated operating conditions): 17,000 gauss center field, 22.5 cm dee diameter, 10 kV peak dee-to-dee (V0 = 5 kV dee-to-ground used in the calculations, per the figure annotations), dee height 2.4 cm, dee gap 1.4 cm — the 1.5 MeV machine's working parameter set, with calculations run to 11 cm radius (the companion Burns paper reports about 2 uA maximum beam current, dg-1573).
Source quote & editorial note
carried out on the Iowa State University undergraduate cyclotron which operates under the following conditions: Magnetic field strength, B0 — 17,000 gauss; Diameter of dees — 22.5 cm; Peak dee-to-dee voltage, 2V0 — 10 kv; Dee height, 2k — 2.4 cm; Dee gap — 1.4 cm
Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: a fully documented parameter set for a very-high-field undergraduate build — 1.7 T on a small pole is what buys MeV-class energy in 11 cm with only 10 kV of RF. The rigidity relation sets the energy-radius product (a uniform 1.7 T at 11 cm would give somewhat more than the reported 1.5 MeV; the real radial profile droops); the RF voltage sets gain per turn and phase acceptance, not the final energy. It anchors the high-field corner of the small-machine design space.
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Design specification (no beam yet) for the IUAC table-top teaching-cyclotron magnet — an H-frame DC electromagnet producing 1.2 T in the median plane across a 51 mm (nominal, +/-0.05 mm) pole gap with 305 mm diameter poles; pole shoes are specified removable, and one set of spare pole shoes (02 nos, drawing IUAC/CYCLO/11) is a named procurement line item.
B = 1.2 T at median plane; pole gap g = 51 +/- 0.05 mm; pole diameter = 305 mmSource quote & editorial note
[Drawing IUAC/CYCLO/11, sheet 1 of 1:] POLE TIP-SPARE ... QTY: 02 NOS ... 310.00 ... 35.00 ... Magnet steel-AISI-1010 ... 15 Kg [cf. IUAC/CYCLO/10 POLE TIP-1: 305.0 +/-0.2, 30.00 +/-0.02, 17 Kg]
IUAC, e-Tender 09/GOR/2024–25 — H-Dipole Water-Cooled DC Electromagnet for the Table-Top Cyclotron: Engineering Specification and Acceptance Tests (2024) — p. PDF pp.18 and 29 for the text (printed 18, 29); drawing IUAC/CYCLO/11 is PDF p.57 (printed 57, Annexure-L)
Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: a professional lab building a teaching machine chose exactly the H-frame, ~1.2 T, ~30 cm pole class that amateur cyclotrons occupy — and made removable pole shoes plus a spare set a procurement line item, the natural hedge for the shimming and re-profiling iterations small magnets commonly need. Pricing spare pole stock alongside the main steel order is insurance worth evaluating on any build.
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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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Achieved result reported for the Rutgers 12-inch cyclotron deflector: a high-voltage electrostatic beam deflection channel was designed, constructed and commissioned, and a 500 keV proton beam was successfully intercepted at its nominal cyclotron radius of 4.0 inches and brought to a radius of 4.5 inches in 43 degrees of azimuth — the beam remaining internal, with the first image of 500 keV protons recorded on the phosphor screen at the channel exit.
Source quote & editorial note
A high-voltage electrostatic beam deflection channel has been designed, constructed, and commissioned in the Rutgers 12-Inch cyclotron. A 500 keV proton beam has successfully been intercepted at it's nominal cyclotron radius of 4.0 inches and brought a radius of 4.5 inches in 43° of azimuth. This project has provided the experience necessary to confidently design an extraction channel for the 19-Inch cyclotron project. … [Figure 10 caption:] First image of 500 keV protons on phosphor screen.
Editorial note, tabletop extrapolation: Read the achievement precisely: internal deflection onto a screen 0.5 inch further out in radius — not extraction from the chamber. For a small-machine builder that is the right first milestone: it proves the channel geometry, the HV system and the diagnostic before any attempt on the fringe field (the 19-inch extraction intent, dg-1676, is the stated next step).
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The Rutgers 12-inch geometry landmarks used throughout its field analysis are r = 0 (centre), r = 5 inches (maximum ion radius), r = 6 inches (pole tip edge) and r = 8 inches (reference point), with nominal magnet operation at about 32 amperes.
Source quote & editorial note
Fig.2 Simultaneous normalized field plot of the three current values: 20, 30, and 40 Amperes. The vertical dashed lines indicate, r = 0 – the center, r = 5 – the maximum ion radius, r = 6 – the pole tip edge, and r = 8 – the reference point. … Nominal magnet operation is about 32 amperes.
Editorial note, tabletop extrapolation: A concrete radius budget from one as-built machine: the beam uses 5 of the 6 inches of pole radius — the outer inch is where this pole's field rolls off — with nominal operation about 32 A. How much pole another machine must reserve depends on its gap-to-pole ratio, shaping and uniformity requirement: derive it from a field model or map rather than transplanting the 5/6 fraction.
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On the Rutgers 12-inch, a 1.2 MeV proton machine with no appreciable relativistic mass increase, weak focusing is stronger than pure Thomas (unspiralled AVF) focusing — from the study's own tune comparison, near the 12.7 cm maximum ion radius the weak-focusing nu_z is about 0.7 while pure Thomas focusing gives only about 0.07 — because a non-relativistic machine can use a falling field and does not need the rising field that makes AVF necessary in larger cyclotrons.
Source quote & editorial note
The pink trace (lowest) in Figure 15 displays the sole effect of Thomas focusing, - AVF focusing without a spiral edge. It is interesting to note that in our case, weak focusing is in fact stronger than the colloquially termed AVF “strong focusing.” This peculiararity arises from the fact that our small (1.2MeV) cyclotron does not noticeably suffer from relativistic effects. If it did, the magnetic field would need to increase with radius, as opposed to our decreasing field, in order to keep the more “massive” ions in step with the RF.
Editorial note, tabletop extrapolation: The qualitative result matters for a 100 keV-1 MeV machine and cuts against the modern instinct: with no relativistic detuning to fight, a non-relativistic machine may use a FALLING field, and this study found its tapered weak focusing stronger than its unspiralled Thomas alternative. No numeric ratio should be carried: Fig. 15's ordinate is printed 'field index - n' while text and caption call it νz, and its weak-focusing trace disagrees with the p.6 νz ≈ 0.7 value — if the plotted quantity were νz² the tunes would be its square roots — an internal inconsistency of the source, flagged. AVF earns its complexity when a rising (isochronous) field is needed, and can still be chosen at low energy for acceptance or tune control; this machine's own later spiral tips (dg-1745) are that choice made deliberately.
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Scaling the Rutgers machine from the 9-inch prototype to the 12-inch magnet did NOT carry the beam performance over: only fractions of a nA were achieved in the larger magnet despite the 9-inch having produced ~10 nA. The diagnosis chain ran pole tips first (radially tapered tips designed, installed, characterized — only a slight current increase), then the ion source, where analysis SUGGESTED the dee's high voltage was suppressing filament electron emission and hence ion generation during the correct RF phase.
Source quote & editorial note
The experimenters were quickly disappointed when only fractions of a nAmp beam were achieved in the larger magnet. Much effort was put into understanding the problem. First, pole tips with a slight radial taper to promote focusing were designed, installed and characterized [2,3]. Still with only a slight increase in beam current with the installation of the new pole tips, the ion source came under suspicion. An analysis of the simple ion source suggested that the DEE's high voltage was suppressing electron emission and thus suppressing ion generation during the appropriate RF phase.
Editorial note, tabletop extrapolation: The most transferable failure story in this memo: a working small machine did not automatically scale to a bigger magnet, and the leading suspect was not focusing but a source-to-dee electrostatic interaction — the dee's field suppressing filament emission at the useful RF phase, per the authors' analysis (a suggested mechanism, which their chimney redesign then acted on). Worth testing on any open-filament source sitting in the dee's fringe field.
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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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The Rutgers 12-inch cyclotron's magnet is a 12-inch-diameter H-frame iron-core magnet giving a nominally 1 Tesla vertical field across a 2-inch magnet gap, with interchangeable iron pole tips; the machine is rated 1.2 MeV protons.
Source quote & editorial note
The 12-inch diameter H-frame iron core magnet provides a nominally 1 Tesla vertical field in the 2-inch magnetic gap. … Interchangeable iron pole tips allow for application of various focusing schemes. … The Rutgers 12” Cyclotron (Fig. 1) is a 1.2 MeV particle accelerator dedicated to student education and exploration.
Editorial note, tabletop extrapolation: PDF p.1 = printed p.291. The closest published match to the 8–12 inch class: same pole-diameter band, H-frame topology, a NOMINAL 1 T across a 2-inch gap, interchangeable tips, and a 1.2 MeV rating. Read the parameter set as an existence proof for the class, with one conversion warning: 1 T is roughly double a 0.5–0.6 T amateur magnet, so this machine's energies do not transfer to a weaker field at the same radius (E ∝ B²r²).
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On the Rutgers 12-inch cyclotron the vacuum chamber runs at 10E-5 Torr and holds a 5-inch radius DEE plus dummy DEE, driven at up to 10 kV peak RF over a tunable 2-30 MHz range; protons and 2H+ come from an internal cold-cathode Penning Ion Gauge (PIG) source, and diagnostics are a radial probe and a deflector each carrying a phosphor screen / current collector.
Source quote & editorial note
holds a 5-inch radius DEE and dummy DEE with a peak applied RF voltage of 10 kV and tunable frequency 2 - 30 MHz.
Editorial note, tabletop extrapolation: PDF p.1 = printed p.291. A self-consistent parameter list for a machine at exactly this scale: 5-inch dee radius inside 12-inch poles, "10E-5 Torr" as printed — read as 1×10⁻⁵ Torr, the operating pressure the companion paper WEPPT025 states unambiguously — and a reported 10 kV peak applied dee voltage over a tunable 2–30 MHz range. The single-dee-plus-dummy-dee topology and the every-diagnostic-is-also-a-current-collector pattern are the parts worth copying; the numbers are reference-machine parameters, not targets.
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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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As a stated future plan (not an achievement) at the time of the 2013 conference, the Rutgers program had secured an H-frame 19-inch magnet — a General Electric magnet delivered to Rutgers in 1947 and run for 35 years for NMR research before storage — for a second-generation educational cyclotron; its coils were awaiting new copper windings.
Source quote & editorial note
The cyclotron facility has already secured an H-frame 19-inch magnet, a special General Electric magnet delivered to Rutgers in 1947 … and operated for 35 years for NMR research before retirement to storage.[13] Upon acquisition, the venerable magnet coils were in need of refurbishing and are currently awaiting new copper windings. … Future plans include the assembly of a second generation 19-inch educational cyclotron.
Editorial note, tabletop extrapolation: PDF p.5 = printed p.295. One documented acquisition route: a decommissioned 1947 GE NMR electromagnet, secured for a planned second-generation educational machine — with the coils needing refurbishment as part of the price. It also records the scale step this program judged worth taking from a proven 12-inch: 19 inches, not 30. Before buying any surplus magnet of that vintage, inspect winding insulation, cooling passages, resistance and field quality; rewinding is a real possibility, not a certainty. This was a plan in 2013; the paper reports no beam from the 19-inch machine.
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The Rutgers group state that, reaching a maximum energy of 1.2 MeV protons, their 12-inch cyclotron is not a radiological hazard and is easily approachable while operating; a companion paper adds that because of its low energy the machine does not activate during operation and is incorporated into lab coursework in a laboratory classroom. These are the source's own characterizations of their machine.
Source quote & editorial note
reaching a maximum energy of 1.2 MeV protons, the Rutgers Cyclotron is not a radiological hazard and is easily approachable while operating.
Editorial note, tabletop extrapolation: PDF p.1 = printed p.369; the companion non-activation statement is we1pb02 PDF p.1 / printed p.291. Reported strictly as the authors' assessment of their own machine and setting — neither paper reports survey data, shielding or a licensing basis. Two physics limits on transferring it: a 1.2 MeV proton ceiling is not a universal no-activation threshold (thresholdless capture reactions such as 12C(p,γ)13N and light-element targets produce prompt gammas and activation below it), and the assessment assumes proton beams — deuteron contamination opens neutron channels. A builder in this class should read it as evidence such machines are operated in classrooms, and still do their own commissioning survey, species verification and regulatory review.
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Nine-inch cyclotron beam run of record 91699C, achieved values - resonant frequency 13.590 MHz, forward RF power 16 Watts, theoretical B-field 0.889 Tesla, H2 pressure in tank 5.1E-5 Torr, filament current 5.75 Amps at 5.0 Volts, filament bias -320 Volts, filament emission 21.0 microamps, maximum ion radius 7.0 cm, maximum ion energy 184 keV.
Source quote & editorial note
In run 91699C the resonant frequency was tuned to 13.590 MHz. Other parameters for run 91699C are listed below: fr 13.590 MHz / Forward RF Power 16 Watts / Theoretical B-field 0.889 Tesla / H2 Pressure in tank 5.1E-5 Torr / Filament Current 5.75 Amps / Filament Voltage 5.0 Volts / Filament Bias -320 Volts / Filament Emission 21.0 microAmps / Max. Ion Radius 7.0 cm / Max. Ion Energy 184 keV
Editorial note, tabletop extrapolation: The single most valuable calibration point in the wave for a 100 keV-1 MeV tabletop design - a complete achieved operating point, not a design target. The energy is internally consistent: with B = 0.885 T (the measured peak) and r = 0.070 m, E = (qBr)^2/(2m) computes to 184 keV, matching the printed value. Note the whole machine ran on 16 W of RF and 21 microamps of filament emission. The forward slashes in the quote separate table rows; the microamp symbol is printed as a Greek mu.
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The nine-inch cyclotron was explicitly a feasibility study for a twelve-inch successor - the author's stated plan at the time of writing was a twelve-inch magnet at 1.2 Tesla with an fr of 18 MHz to reach one million volt protons, with a capillary discharge ion source, and a tangential accessory vacuum port added after the twelve-inch system proved operable in order to extract the proton beam; he also states that a solid state amplifier is precluded once power requirements exceed 500 Watts, pointing instead to a tunable metal-ceramic sealed vacuum tube power amplifier driven by the ENI 350L.
Source quote & editorial note
Sufficient data has been taken with this feasibility-study cyclotron to warrant progression to a twelve inch magnet. It is reasonable to expect one million volt protons with a magnetic field of 1.2 Tesla, and an fr of 18 MHz. Such a magnet system is currently being obtained. ... The use of a solid state amplifier is precluded once power requirements exceed 500 Watts. ... Finally, after the twelve inch system has proved operable, a tangential accessory vacuum port will be added with the intention to extract the proton beam.
Editorial note, tabletop extrapolation: Design intent, not achievement — every number is a plan as of September 1999. What transfers is the staging philosophy: prove the concept on a small borrowed magnet (~184 keV, 9 inches) before committing to the larger machine. The "solid state precluded above 500 W" line is the author's 1999 equipment landscape, not a law — modern LDMOS amplifiers run solid-state into the kilowatts (the same lineage's later 1.5 kW AL-82 tube chain and pulsed operation, dg-1756/dg-1804, show the options both ways). The 1 µA figure on the same page is what "could have been achieved" with more source work — expectation, not measurement. Ellipses mark omitted text. (The first two quoted sentences begin on p.8.)