Choosing Your Machine

Two pages come before this one. Should You Build a Cyclotron? argues no; So You Want to Build a Cyclotron covers the skills and costs if you proceed anyway. This page is the third question: which machine? Two early choices — what you want the machine to do, and what beam energy that requires — set the size of the iron, the reach of the RF, the radiation footprint, and the rules that apply. (On rules: in the US, most states regulate particle accelerators at any energy — the 51-jurisdiction survey; outside the US, identify the responsible regulator before purchase.) Each energy band below ends in a project brief: the design point, the closest documented builds, and what to read before spending money.

Purpose picks the band

Machines get chosen backwards. The documented pattern in the build census is a target energy picked first — often "1 MeV," round and impressive — and a purpose discovered later, when the builder learns what a nanoampere at that energy can actually show. One census project, The Cyclotron Project, revised its target from 1.1 MeV down to 60 keV after confronting the incidental-radiation consequences of the bigger number. The order that works is the reverse: name the thing the machine must demonstrate, and let that set the energy.

Three purposes cover nearly every amateur machine on record:

• See cyclotron resonance work. A resonance curve mapped by hand; an internal beam arriving at a collector. Any energy does this; 5–100 keV does it with the smallest iron, the gentlest RF, and the lightest radiation footprint. This is the purpose the machines that finished mostly served.
• Count nuclear events you caused. Alpha particles from ⁷Li(p,α) or ¹¹B(p,α) arriving in a silicon detector at rates worth logging. Honest counting starts near 100 keV and becomes routine in the 100–500 keV band — the experiments page works the rates.
• Measure nuclear physics. Excitation curves with real statistics, the 675 keV ¹¹B(p,α) resonance, gamma spectroscopy. That is 500–1000 keV territory, and exactly one amateur machine on record has demonstrated a beam there.

If your purpose is beyond that menu — neutron production, isotope chemistry, anything requiring megaelectronvolts — read Beyond 1 MeV, the question changes before anything else on this page.

Pick two numbers; physics picks the rest

A classical cyclotron's design point is fixed by two choices: final energy T and magnetic field B. For a proton machine running on the fundamental RF harmonic — the configuration of every machine in the census — the final orbit radius and the RF frequency then follow directly:

r = √(2mT) / qB      f = qB / 2πm

Here T is the ion's kinetic energy, B the magnetic field, m and q its mass and charge — SI units throughout (T the symbol is energy; T the unit in the table below is tesla). The two relations set the machine's first-order scale, not its whole design.

The energy calculator carries the derivation and handles any particle; the table below is the proton case at three representative fields, computed from CODATA constants (classical mechanics is good to about 0.1% at 1 MeV). Radius is the number that buys iron: the pole must extend beyond the final orbit, and field quality collapses near the pole edge, so a machine needs poles comfortably larger than the r in this table. The frequency column is what your RF chain must deliver at kilovolts, into a sparking load, in vacuum — it depends only on field, not on energy.

The high-field column looks like a bargain — 1 MeV on a 10 cm orbit — and the record shows why it is not. Pole iron begins saturating near 1.5 T (magnet design covers that wall), so the last column is bought with disproportionate excitation, and the frequency that rides along, 23 MHz at kilovolt amplitude, is a harder RF problem than 8 MHz. One census machine, the Central High School cyclotron, reported 2 T on 7-inch poles and a theoretical 1 MeV; no measured beam was ever documented. Berkeley's magnet volume states the underlying trade plainly: there is an optimum field for a given energy, balancing the cost of scale against the cost of excitation, and it cannot be pinned down without a model magnet (TID-5215, pp. 33–38; dg-835). Magnet cost itself grows only about linearly with radius at fixed rigidity — Powell's argument for choosing radius on beam physics rather than on iron savings (TID-5215, p. 24; dg-1298). And before optimizing any of it, note that the cheapest design decision is somebody else's design: pick the documented build nearest your band and model only what you change.

5–25 keV: the machine is the experiment

In this band the cyclotron itself is the physics: ions spiral, the resonance condition holds or it does not, and the resonance curve you trace — beam current against RF frequency at fixed field — is the same measurement Lawrence's students made. The COLUMBUS school cyclotron is the modern proof that the band is a destination in its own right: 24–48 keV protons on a 150 mm laboratory magnet — 0.38 T in routine operation, 0.7 T available, and the top of the energy range needs the stronger field — designed without extraction, the builders' stated rationale being that the beam never leaves the chamber. The first Niell cyclotron demonstrated resonance with nothing but residual air as the ion supply. What the band withholds is nuclear: reaction products exist here only in immeasurably small numbers — the experiments page prices it out.

25–100 keV: the proven first-machine band

This band keeps getting chosen on purpose. COLUMBUS designed into the bottom of it, The Cyclotron Project retreated into it from a megavolt ambition, and Niell II finished in it: protons at about 70 keV on a 0.67 T field with a final orbit of 5.7 cm — numbers the relation above reproduces exactly, which is the kind of check worth running on any build log you read. Near the top of the band the first transmutation comes into reach, barely: thick-target ⁷Li(p,α) at 100 keV yields on the order of a hundred alphas per hour into a close silicon detector at a nanoampere (worked arithmetic). That is a countable signal, and it is also a lesson in what "barely" means: at 48 keV the same setup yields about two per hour.

100–500 keV: counting nuclear events on purpose

This is the band where nuclear counting stops being a stunt. ¹¹B(p,α) on a thin target runs from roughly sixteen counts per hour at 150 keV to a few per second at 300 keV at a nanoampere of beam, geometry-dependent — assumptions, rates, and the detection stack are worked on the experiments page — and coincidence detection of the paired alphas crushes background. The price is paid in craft rather than iron: thin targets — the targets domain — a silicon spectroscopy chain, and honest beam-current measurement. Expectations should be calibrated by the record: the Mullins Cyclotron demonstrated about 164 keV at nanoampere scale, and the Houghton program's peak proton energy of 160 keV arrived at three picoamperes — its own paper states that a small machine's honest headline number is small (dg-525).

500–1000 keV: the top of the documented record

One amateur machine has a demonstrated beam in this band. The Rutgers 12-inch reached 800 keV at 200 nA — on 12-inch poles at 1.2 T, eleven years after the project began. The physics on offer is genuinely richer: the 675 keV ¹¹B(p,α) resonance, ⁷Li(p,α) at full rate, excitation curves with statistics that mean something (band four's menu carries the numbers). If those names mean nothing yet, that is itself information: this is a measurement-program band, not a first machine. The record is sparse because the engineering burden rises sharply — kilovolt-class RF into a 20 MHz-class resonator, field flatness held across a large pole, X-ray output that scales with dee voltage. Radiation protection planned from conception costs a fraction of protection retrofitted — the professional literature's blunt finding (AD-755510, p. 17; dg-1082) — and in this band that planning belongs inside the design work itself.

Beyond 1 MeV, the question changes

Above 1 MeV the census holds only intentions: two 2 MeV designs (one stalled, one of unknown fate), a period press claim never verified, and Central High's theoretical megavolt without a measured beam. Physics is not the reason the record stops — the Berkeley 27-inch was delivering 6.3 MeV deuterons by 1936. The regime is. Light-target (p,n) thresholds open from 1.881 MeV, neutron production brings bulk activation, and the safety and legal framework changes character (the experiments page's closing section). A machine there is a small facility: professional design-study discipline — energy set as an explicit compromise, every rejected alternative's defects enumerated in writing (ORNL-3540, pp. 20, 149; dg-890, dg-893) — plus shielding engineering and a relationship with a regulator. If that is the ambition, the honest path is the one the first page in this sequence points to: get near real machines — tours, builder communities, outreach programs short of volunteers — and read this site's library as preparation rather than as a build manual.

Copy a proven machine, or model your way to a new one

The cheapest design decision on this page is somebody else's design. When the University of Washington built its 60-inch, it obtained the complete Berkeley Crocker drawings and followed them — closely on the magnet, with original effort reserved for the places the plans were silent — and stood the machine up, assembled and ready for test, in three years (AECU-1951; dg-1327). A university physics department copying another laboratory's machine, in writing, without embarrassment. At amateur scale the equivalent move is open: the census's finished machines are documented in build logs and theses, and a design point taken from COLUMBUS or Rutgers is a design point that is known to work.

Departing from the record costs models. The professional sequence is consistent across the literature: fix gap, field, and uniformity from beam requirements first and settle details on a scale model last (TID-5215, p. 25; dg-1301); build a cheap scaled analogue whose stated purpose is to expose the riskiest subsystem before the full machine (ORNL-3540, p. 263; dg-892); retire RF risk on a scaled electrical model before cutting full-size metal, as Berkeley did for the 184-inch (UCRL-31, p. 16; dg-999). An amateur machine is small enough that a "model" approaches the machine itself — which is the strongest argument for copying the proven design outright and modeling only what you change. When the model question is the magnet, TID-5215's chapter on model magnets is the method, with the rare published check that full-scale performance landed slightly better than the models predicted.

The brief you can now write

A machine chosen on purpose fits on one page. Before buying iron, you should be able to write down:

1. Purpose — the single demonstration or measurement that will count as success, named concretely enough to fail.
2. Energy band — and the sentence explaining why the purpose requires it, with the rate arithmetic to back it.
3. Design point — field, final radius, and frequency from the calculator, with pole size chosen beyond the final orbit.
4. Analogue build — the census machine closest to the design point, and what its log says went wrong.
5. Radiation plan — the X-ray survey habit from day one, and the band's specific onsets from this page, per safety.
6. Jurisdiction status — what your state requires and when: usually registration, sometimes before operation.
7. Reading list — the per-band list above, plus the starter path's reading order.
8. First milestone — something that pays off in months, not years: source glowing, chamber at pressure, resonance found.

That document is a plan for study and for review by people qualified to check it — a radiation safety officer, or a builder who has finished one. It is not a build print, and this site does not publish build prints. What it is, is the pattern the census's finished machines share and its abandoned ones mostly lack: a purpose the builder could state, at an energy the purpose justified, on a machine sized to reach it.

Sources

• Design-point arithmetic: classical cyclotron relations with CODATA constants, cross-checked against the energy calculator's published example; census cross-checks in the text.
• Band physics, count rates, and safety onsets: Experiments by Energy Band (NNDC/NIST data retrieved live, August 2026).
• Machine histories and specifications: the build census and its cited build logs, theses, and papers.
• Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques, TID-5215, 1949 — hosted; field-choice and model-magnet doctrine.
• The University of Washington 60-Inch Cyclotron, AECU-1951, c. 1950 — hosted; the copy-a-proven-design record.
• A Proposal for the Mc² Isochronous Cyclotron, ORNL-3540, 1964 — hosted; design-study and modeling doctrine via the rules cited inline.
• Individual design rules as linked inline; each carries its verbatim source quote in the Design Guide.