Cyclotron Info

Builder FAQ · Part 1, Deciding and designing

Before You Build

Can an amateur actually build a cyclotron? Should I?

Yes, and the record says who did it and how long it took. The build census lists 27 amateur and school cyclotron projects since 1947. 8 of them demonstrated or routinely operated a beam; the rest stalled, are still in progress, or simply left no further record, which is not the same as failing. Most of the finished machines had an institution behind them, a college or a school. A few were built at home, and one of those logged first beam within about a year of its start (census). Should you? Probably not, for reasons that have nothing to do with physics. It is expensive. The work is mostly tedious and spans half a dozen trades, vacuum, RF and machining among them, across years with little visible progress. The result is a needle on a meter, and there is little to do with it afterward (should-you-build-one page). Before buying iron, decide the purpose, concretely enough to fail (see What should count as a first success? Do I need to get the beam out of the chamber, or can I demonstrate acceleration with a detector inside?), and whether you are building alone or with an institution behind you. Then pick a first milestone that pays off in months.

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An ion source emitting ions, a chamber pumped down to its base pressure, the lowest pressure it settles at, or the RF circuit’s resonance found with a signal generator all qualify as that first milestone (so-you-want-to-build-one page). If the real goal is hands-on physics rather than a cyclotron as such, there are routes that deliver more physics per dollar (should-you-build-one page).

Where projects stop. The documented stalls are rarely physics, and they are the minority of the non-finishers: most of the census’s open entries are projects whose outcome is simply unknown. One college honors project built around the chemistry department’s 2 T NMR magnet never reached beam. Two high-school students completed every subsystem of a 2 MeV machine at a national laboratory and were then barred by lab rules from powering it. A well-equipped home build went into storage still waiting for its 3 kW RF supply. A student team wound down when its members left for university (census: Knox, Cyclotron Kids, Kwolik, Dawson). The skills page’s list is the gate: vacuum, RF, magnetics, machining, high-voltage instrumentation, and patience across years of no visible progress. Nobody enjoys all of them, and the one you dislike is where projects tend to end. The census illustrates that observation about project risk; it does not prove it as a statistic.

To understand it. “Amateur” covers two kinds of project, and they finish at different rates. The institution-backed builds have a machine shop, a budget line and successors who inherit the work. Iowa State’s physics club ran 1.5 MeV protons in 1957. Houghton College’s program started in 2001, reached first beam in 2007 and is still running. The Rutgers 12-inch took eleven years from a 1995 start to reliable 800 keV beams (census entries). The independent builds that reached beam are rarer and smaller: a high-school student’s two machines at home in the mid-1990s, and a father-and-son basement build that logged first beam within about a year of its 2017 start (census). Builders at the 2010 amateur cyclotron conference estimated two to three years and roughly $125,000 in parts if everything were bought new. Every finished machine leans on surplus and donations (should-you-build-one page, citing Symmetry, 2010).

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What should count as a first success? Do I need to get the beam out of the chamber, or can I demonstrate acceleration with a detector inside?

A detector inside the chamber is the standard of success. None of the amateur or school machines in the census is documented to have run an external beam. The first success is a resonance peak on an internal collector that behaves like a beam. Sweep the magnetic field at a fixed RF frequency, and the collector current rises at the field where the ions cross the gap in step with the RF every turn. A stray current that reaches the plate by some other route does not depend on that match, and Wouters’ 1949 checks use the difference. The evidence becomes strong when the peak is sharp, responds to hydrogen pressure, and dies when field or frequency is moved a little off the match. Write two things into the plan as the definition of done: that peak passing those checks, and the species, which kind of ion it was. Name the species as candidates, or identify it as far as the evidence allows. Energy can stay computed, labeled as computed. Extraction belongs in a later plan, if ever, and only after the internal beam is understood.

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The best of the census machines, the Rutgers 12-inch, ran 800 keV protons for years with the beam ending inside the chamber (beam-extraction page). The builders of the COLUMBUS school cyclotron wrote the principle down: “the particle beam does not even need to be extracted” to meet the machine’s purpose (Prechtl & Wolf (2020), p. 27). The collector is a metal plate inside the chamber that the ions land on, read as a current. The test of a first success is that someone else could read your record and agree that a cyclotron resonance was accelerating ions (How should I document that my cyclotron is accelerating protons? What would someone else need to evaluate the claim?).

Which rung the evidence reaches. The trap is claiming more than the evidence supports. A peak on the collector as the magnet sweeps is a hypothesis. The evidence for acceleration becomes strong when it passes the checks Wouters set out in 1949: the peak is sharp against RF tuning and magnet current, it responds to hydrogen pressure, and it dies on a small detune, the magnetic field or the RF frequency moved a little off the matching value, where leakage current, current that reaches the collector by some route other than the beam, does not (beam-measurement page). Those checks reinforce one another; they are not a proof, and the background, the collector’s own behavior and independent consistency checks still have to be in the record (beam-measurement page). Most finished amateur machines stop there. Next is identifying what was accelerated, because hydrogen in does not mean protons out. Sweeping the magnet at fixed frequency puts each species at its own field, since each charge-to-mass ratio keeps step with that frequency at a different magnetic field, and the same species appears again at a third and a fifth of that field, where it circles at a third or a fifth of the RF frequency, going round once every three or five RF cycles, and still arrives at each gap crossing with the voltage pushing its way. Comparing the observed peaks with the fields expected for each species and harmonic (a harmonic is one of those lower-field repeats) gives a way to identify candidate particles, strongest when other measurements support the assignments (Yuly (2013), p. 4-5; beam-which-ion covers the coincidences no sweep separates). Energy comes after that. It is usually computed from radius and field rather than measured, the census marks it that way, and professional practice warns that an internal-target energy inferred from the field alone can be off by a tenth (Cohen (1952), p. 5). Beyond those are a beam current worth quoting, an energy measured rather than inferred, and finally a beam brought outside. The amateur record barely reaches them.

To understand it. Extraction is a different engineering problem from acceleration. Each turn’s radius grows with the ion’s energy, so the energy gained per turn sets the radial step between one turn and the next. The final turns may be separated by only a fraction of a millimetre, depending on the energy gain per turn; even when they are farther apart, fitting a septum (the thin partition that separates the final turn from the one inside it) between the beam and the surrounding hardware is its own problem, and the deflector that peels the final turn, an electrode whose electric field pulls that turn outward, needs tens of kilovolts in vacuum beside the magnet (beam-extraction page). The Rutgers group built one and used it as an energy diagnostic rather than a beamline. Extraction also changes the safety and regulatory questions, and those have to be evaluated on their own: COLUMBUS’s builders chose no-extraction so that nothing leaves the apparatus, a rationale reported here as theirs (census entry), and the legal section explains why a closed beam does not by itself settle how a machine is regulated.

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How do the particle, the energy, the magnet size, the field and the RF frequency fit together? Which of them can I actually choose?

Start from the purpose, which sets the energy you need, tens to hundreds of keV for the machines this FAQ is about; then you choose about two more things, and physics constrains the rest. Choose the particle. Choose the magnetic field, or the pole size, the diameter of the iron faces the ions circle between, because with the energy fixed each sets the other. The highest energy is set by the field and the radius the last turn can use. Pick any two of energy, field and radius and the third follows (cyclotron-energy calculator). The RF frequency then follows from the field and the particle, to a first approximation with no freedom at all. An ion circles at a rate set by the field and its charge and mass, 15.2 MHz per tesla for protons, and the RF has to run at that rate. The dee voltage, the RF voltage across the gap, is a separate choice. Each crossing adds an energy set by that voltage, so it largely determines how many turns the ion takes to reach the final energy. Every turn is more distance travelled through the residual gas, the gas left in the chamber, so the turn count is what the vacuum requirement is estimated from (path-length calculator).

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What sets what: the design dependencies What sets what: the beam-physics dependencies of a small cyclotron solid blue: you choose · black: follows from the choices · dashed orange: a constraint that pushes back · arrows show dependencies, not a build sequence Magnet constraints iron approaches saturation progressively, knee often 1.5 to 2 T in the iron; the gap field also depends on geometry, coil current and cooling Purpose what the beam is for Energy T tens to hundreds of keV, set by the purpose Field profile, focusing, alignment map the useful orbit region and check vertical clearance; a centre reading is not a field map Particle charge q and mass m (protons or H₂⁺ to start) Magnetic field B T = (qBR)² ÷ 2m: energy goes as the square of (field × radius), for a slow ion in a near-uniform field Usable radius R the largest orbit the field quality, focusing and clearances support, not simply the pole radius; pick two of T, B and R and the third follows RF frequency f f = qB ÷ 2πm for fundamental operation (k = 1); 15.2 MHz per tesla for protons; B and q/m set the nominal frequency Practical RF range 5 to 20 MHz is one common design range, not a limit; the whole RF system must tune to the chosen frequency Peak gap voltage Vg between the two sides of the accelerating gap; a coupled choice, not a free one Turns N ≈ (final energy − starting energy) ÷ average energy gain per turn; at unchanged phase and capture, lower gap voltage means more turns Path length the lengths of the growing orbits summed, from N and R; not the turn count alone Operating pressure target pick an acceptable surviving fraction; losses along the full orbit from ion–gas loss data for the species and energy Gap-voltage constraints the first orbit must clear the source and electrodes (depends on launch geometry and operating point); RF power and losses, capacitance, feedthrough ratings, cooling and vacuum voltage holdoff Phase slip more turns, less tolerance of field error and detuning, including the change of circling rate with radius and energy Pump, pipe, gas load check the pressure with the source gas flowing; effective speed includes the pipe; the gas load is the source, leaks and outgassing B and q/m pick two of T, B, R T R iterate: revisit the choices until magnet, RF, vacuum and clearance agree Read it from the purpose: with the particle chosen, picking two of energy, field and radius fixes the third, and for fundamental operation the field and the particle set the nominal RF frequency. The gap voltage is a coupled choice: it sets the turn count, turns and radius set the path through the residual gas, and the orbit length, gas composition, ion–gas loss data and the surviving fraction you accept set the pressure target. Constraints push back on every choice, so the work is a loop, not a sequence. Beam-physics dependencies only. Before buying or energising hardware, a separate safety review covers interlocked RF and high-voltage enclosures, protective earthing, stored-energy discharge and verified isolation, magnet protection and cooling, vacuum structural ratings, and a radiation assessment with shielding and survey instruments (the safety entries). A collector current also needs controls for pickup, leakage and non-beam current before it counts as a resonance, and it is not a radiation measurement.
What sets what in the beam physics of a small cyclotron; the arrows show dependencies, not a build sequence. The purpose sets the energy. With the particle chosen, picking two of energy, magnetic field and usable radius fixes the third, since for a fixed particle the energy is proportional to the square of the product of field and radius (Humphries (1986), p. 524), and for fundamental operation the field and the particle set the nominal RF frequency, 15.2 MHz per tesla for protons (Humphries (1986), p. 524). Magnet constraints push back on the field, the field profile and focusing on the usable radius, and the RF you can build on the frequency. The peak gap voltage is a coupled choice: with the energy it sets the turn count, turns and radius set the path through the residual gas, and the orbit length, the gas, the ion–gas loss data and the surviving fraction you accept set the operating pressure target (Prechtl & Wolf (2020), p. 41-42, Prechtl & Wolf (2020), p. 54). Gap-voltage constraints, source clearance among them, push up on the voltage (Prechtl & Wolf (2020), p. 42-43); phase slip pushes back on the turn count; the pump, the pipe and the gas load push back on the pressure. The COLUMBUS authors present a dependency diagram linking these choices (Prechtl & Wolf (2020), p. 27-29); drawing one for your own machine is a loop, revisited until magnet, RF, vacuum and clearance agree. It covers beam physics only: a separate safety review comes before buying or energising hardware.

The frequency has no freedom when the machine runs on the fundamental, with the RF at the same frequency as the ion’s circling. A real machine must still tolerate field variation and phase slip, the ion arriving at the gap a little earlier or later each turn than the RF peak, a drift that adds up over the turns; and some run on an odd harmonic, the RF at three or five times the circling frequency.

The decisions go in this order. Particle and purpose first, which sets an energy band (choosing-your-machine). A magnetic field the iron can hold. A pole large enough that the final orbit sits inside the usable field. The frequency then reads off the field. Last, a dee voltage the RF system and the gaps can hold, which sets turns and therefore the pressure estimate. The COLUMBUS authors draw the dependency diagram before dimensioning anything, separating the inputs they choose from the quantities that follow (Prechtl & Wolf (2020), p. 27-29). Draw it for your own machine before the first purchase.

If it does not work. If the numbers will not close, the pair to revisit is magnetic field and radius: a field the iron can hold whose frequency the RF you can build reaches, and a radius whose energy you actually need. The dee voltage then sets turns and the pressure estimate. If the estimated vacuum requirement looks impractical, reconsider the dee voltage, the pumping arrangement, the gas load and the intended operating point together (What pressure should I aim for when the cyclotron is running? Don't I need more gas to make ions, but less gas to let them spiral around?; Can I copy a successful amateur cyclotron but change it to suit the parts I already have? Can I combine parts of different designs, or just scale one down?).

To understand it. Two relations carry the chain. The orbital frequency of an ion of charge q and mass m in a magnetic field B is f = qB/2πm, which for protons is 15.2 MHz per tesla. It does not depend on energy or radius, which is the principle the machine rests on (how-a-cyclotron-works page; Humphries (1986), p. 524). The energy at radius r is T = (qBr)²/2m, or about 48 (ZRB)²/A MeV with Z the ion’s charge and A its mass, both in proton units, R in metres and B in tesla (Humphries (1986), p. 524). In a conventional iron-dominated magnet, ordinary iron becomes increasingly difficult and expensive to use above roughly 1.5 T, where the poles saturate and stop adding much field for more coil current; higher fields are possible, and one student machine ran 1.7 T, but they are usually a poor bargain for a small machine (choosing-your-machine and magnet-design pages). So a small iron magnet’s frequency lands in the 5 to 20 MHz shortwave range and the energy ceiling is set by radius once the field is chosen. The usable radius is smaller than the pole radius: the field falls away toward the edge of the poles, and the usable field ends about half a gap-length inside the pole edge, so a 30 cm pole with a 10 cm gap offers roughly 9 to 10 cm of orbit (magnet-design page, after Livingston and Blewett).

Dee voltage enters differently. In the COLUMBUS book’s picture, the magnet and the usable radius fix the height of the ladder and the dee voltage the spacing of the rungs (Prechtl & Wolf (2020), p. 41-42). Halve the voltage and the ion takes twice as many turns to reach the same energy. More turns means a longer spiral through the residual gas, so the pressure target can be estimated from the voltage once the path length and the gas are known. COLUMBUS states its vacuum criterion as a mean free path, the average distance an ion travels before it meets a gas molecule, at least as long as the whole spiral (Prechtl & Wolf (2020), p. 54). The voltage also has a floor. The ion starts beside the source at the centre, and its first gap crossing sets the radius of its first half-turn. The first half-turn has to clear the ion source, which on COLUMBUS meant at least 200 V for protons and 400 V for H₂⁺ (Prechtl & Wolf (2020), p. 42-43).

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Could I accelerate electrons or other ions instead of protons? Would any of those be easier for an amateur?

A cyclotron will accelerate anything charged, and changing the particle does not make the machine much easier. The frequency, the energy and the source change. The magnetic force that turns an ion grows with its charge, and the turning it produces shrinks with its mass. At the same magnetic field the circling rate, and so the RF frequency, scales with charge over mass. The same force fixes the momentum an ion carries at a given radius, so momentum grows with charge, and energy is momentum squared over twice the mass. Energy at the same field and radius therefore scales with charge squared over mass (Humphries (1986), p. 524; see the table). The lower frequency of a heavier ion is a different RF design, not automatically an easier one. For a first machine: protons or H₂⁺, a hydrogen molecule with one electron removed, from hydrogen, because the sources, the RF frequency range and the published record all assume them. Expect a species mix, more than one kind of ion, and plan to identify it. Helium if hydrogen handling is the obstacle. Deuterium only inside a radiation plan. Electrons only if the goal is to watch a few-keV orbit rather than to build an accelerator.

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ParticleFrequency, relative to protonsEnergy at the same field and radius
Proton, H⁺1 (15.2 MHz per tesla)1
H₂⁺1/21/2
Deuteron, D⁺1/21/2
He⁺1/41/4
He²⁺1/21

In the table, H₂⁺ is a hydrogen molecule with one electron removed, a deuteron is the nucleus of heavy hydrogen, one proton bound to one neutron, and He²⁺ is a helium atom with both electrons removed. Whether the lower frequency helps depends on the amplifier and resonator you have. Electrons are a different machine class. One choice, deuterium, belongs in a safety discussion rather than a convenience comparison. The census has machines that ran protons, H₂⁺, helium ions, deuterons and, in one case, the ions of residual air.

To understand it. In symbols, f = 15.2 MHz per tesla × Z/A and T ∝ Z²/A; the doubly charged helium ion, with twice the proton’s charge and four times its mass, therefore keeps the lower frequency and recovers the proton’s energy. The Rutgers group retuned its 12-inch from protons to deuterons by dropping the RF to 7.15 MHz and winding, for the dee’s 78 pF, a new tank coil, the coil that resonates with the dee’s capacitance (Koeth (2017), p. 1); the magnet, chamber and source stayed. The source is the real variable. Hydrogen sources make a mix of H⁺, H₂⁺ and H₃⁺ whose proportions change with the operating point and even with running time (I'm feeding hydrogen into the chamber. Does that mean the accelerated particles must be protons? Why might I see more than one resonance peak?).

The first Niell cyclotron ran on residual air, with no gas system at all, and showed a clear resonance consistent with nitrogen ions and their harmonics. No gas system makes it the cheapest demonstration that cyclotron resonance is real, and the hardest to interpret, because the chamber supplies whatever it contains; the census lists the machine as beam-demonstrated and states the evidence so a reader can weigh it. Helium is clean and inert and needs no hydrogen handling. Several machines ran it (Houghton, Niell II), and one plan staged commissioning on helium first (Cressman (2006), p. 2).

Deuterium is the exception, and it is a safety question rather than a convenience one. The D–D reaction has no energy threshold, so a deuteron beam on any surface that has absorbed deuterium can produce neutrons at energies where a proton beam produces none (safety page). The D–D reaction is two deuterium nuclei fusing, one from the beam and one held in the surface; no threshold means it can occur at any beam energy. Having no threshold is not the same as having a large yield: the rate at tens of keV is small, and natural hydrogen’s trace of deuterium does not make every hydrogen cyclotron a consequential neutron source. It does mean that a deliberate deuterium run is a radiation decision to be assessed before the gas is bought. Professional commissioning has run the other way for the same reason, holding off protons until the shielding was finished and doing early beam work with slower species. An H₂⁺ is two protons travelling together and an alpha is four particles together, so at the same magnetic field and radius each particle in them arrives with less energy than a lone proton would, and the nuclear reactions that make radiation become far less likely as that energy falls. The report’s own words are “lower velocity and yield” (Jungerman (1966), p. 7; the experiments-by-energy page).

For electrons the cyclotron stops being the right machine. An electron has the proton’s charge and is 1,836 times lighter, so its cyclotron frequency at an iron magnet’s field is in the microwave range, 28 GHz per tesla. A few-MHz electron cyclotron needs a field of a fraction of a millitesla, which is a pair of coils, not a magnet. The more decisive limit is relativity, which arrives almost at once. A particle’s mass grows as its energy becomes a noticeable fraction of its rest energy, and a heavier particle circles more slowly, so it reaches the gap later and later against a fixed RF. An electron’s mass has grown by 2 % at about 10 keV, the same fraction as a 20 MeV proton, and in a fixed-frequency machine with a uniform field and the usual quarter-cycle phase budget (how far the ion may lag before the gap voltage it meets has fallen to zero) that mismatch spends the budget within a dozen or so turns (how-a-cyclotron-works page, applied to the electron rest energy of 511 keV). Under those classical assumptions an electron cyclotron tops out in the few-keV range; more dee voltage per turn or a shaped field moves the limit, as they do for protons, but not by orders of magnitude. Electrons historically went to betatrons and linacs. The census holds one documented electron cyclotron, a 1958 science-fair machine with no surviving technical record. Electrons also bring the X-ray question forward: tens of keV of electrons striking metal is an X-ray tube by definition (see Can the machine make radiation, or hurt me some other way, before I've even detected a beam?).

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How do I know which requirements in a book or paper apply to my cyclotron? One says the magnetic field should be uniform, another says it should decrease with radius, and another says it should increase. Who is right?

All three can be right, because they describe different requirements; reading the literature means working out which requirement a sentence serves before deciding whether it binds you. A uniform magnetic field is the ideal for keeping the circling rate constant, since that rate depends on the field. A field weaker at the outer turns than at the centre, decreasing slightly with radius, pushes an ion that strays up or down back toward the middle of the gap. That is vertical focusing, and its cost is a small timing drift called phase slip. In the weaker outer field the ion circles a little more slowly, reaches the gap a little later each turn, and the lag adds up. A field that increases with radius belongs to machines whose revolution time stays the same at every energy even as the ion grows heavier at tens of MeV: isochronous cyclotrons. A first amateur machine is the classical kind. It accepts the few-percent radial decrease because the focusing matters more than the slip at sub-MeV energies, while holding the field nearly constant around each circle. Before adopting or skipping a requirement, ask what machine class, energy, current and purpose it was written for.

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The focusing comes from the field’s shape: where the field weakens with radius its lines bow outward, and the sideways part of the field pushes a stray ion back (The drawings show a flat spiral. What keeps the particles from wandering up or down and hitting the dee? Do I need "focusing"?). The increasing field compensates for relativistic mass gain: the ion grows heavier as it speeds up and would circle more slowly, and a stronger field at larger radius restores the pace, with a different focusing arrangement built into sector-shaped poles. The second and third are different compromises, not the same rule at different sizes.

Four questions sort almost any requirement. Which machine class? Classical fixed-frequency, synchrocyclotron, or isochronous; the how-a-cyclotron-works page’s last sections tell them apart, and the census machines are all classical. What energy? Below about 1 MeV a proton’s relativistic slip is a small per-turn effect, and the COLUMBUS book treats machines below a rigidity (magnetic rigidity, the field times the orbit radius, a measure of the ion’s momentum) of about 0.3 tesla-metre as non-relativistic. The requirements that exist to fight relativity do not bind there (King (2002), Prechtl & Wolf (2020), p. 32-33). What current? For the accelerated beam, Smirnov’s review places space-charge effects, the beam’s own charge pushing it apart, at a scale of a few hundred microamperes and above, far above an amateur internal beam (modeling-tools page); that is a scale, not a threshold, and rules about it describe a different regime, though the plasma inside the source is a separate question with its own charge densities. What purpose? Extraction efficiency, beam quality, energy resolution and duty cycle are the subjects of most professional papers. A machine whose success is an internal resonance peak can defer them (What should count as a first success? Do I need to get the beam out of the chamber, or can I demonstrate acceleration with a detector inside?).

Before you skip one. The Design Guide carries an applicability level on every rule, from 1, governing the feasibility of any cyclotron, to 5, professional machines only. The level is breadth, never weight, and never permission to skip (design-guide page). The easiest professional specification to dismiss is often one a small machine still needs in a weaker form. ORNL’s instrument builders relaxed an “extremely high” uniformity requirement to what their measurement actually needed and got a simpler magnet, but they relaxed it to a number, not to nothing (Alford (1961), p. 7). When a source and your machine disagree, name the difference in class, energy, current or purpose that explains it. If you cannot name one, the requirement probably applies.

To understand it. The word “critical” needs the same treatment. Ask what the requirement protects: does violating it prevent acceleration, reduce how many ions survive, make the result harder to measure, or limit a later goal? The field index is a worked example. It is a single number, written n, that measures how fast the magnetic field falls with radius: zero for a perfectly flat field, larger as the fall steepens. “Keep n between 0 and 1 everywhere ions circulate” is the usual weak-focusing stability condition in the linear approximation; outside that band the restoring force vanishes and the beam is lost, axially (up and down) at one end and radially (in and out) at the other (Livingston & Blewett (1962), p. 161). It is a feasibility rule for the main acceleration region, with the central turns, where electric focusing, by the electric field at the dee gap, dominates, treated separately. “Taper the field so n = 0.2 arrives only at the final radius” protects against something more specific. At n = 0.2 the ion’s radial and vertical oscillations, its small in-and-out and up-and-down swings about the ideal orbit, fall into a special frequency relationship, the radial one exactly twice the vertical, and small field imperfections can then transfer motion from the radial direction into the vertical, until particles strike the dee. How serious that becomes depends on how strong the imperfections are and how many turns the particles spend near the condition. A machine with low dee voltage takes many turns to cross it and is most exposed; one that accelerates hard crosses it in a few turns and may survive (beam-dynamics page). “Hold azimuthal variation under 0.1 to 0.2 percent”, the variation being the change in field around one circle at a fixed radius, is the bound classical operators converged on for machines that extracted (magnet-design page), and the Rutgers 9-inch prototype made ten nanoamperes on flat poles with no field shaping at all (Koeth (2006), p. 1).

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Can I copy a successful amateur cyclotron but change it to suit the parts I already have? Can I combine parts of different designs, or just scale one down?

Copy a proven machine if you can. It is the cheapest design decision available, and professional laboratories did it too. Swap parts with care, because a cyclotron’s subsystems are tied together by a few hard relations, and a change in one usually forces changes in two others. The magnetic field sets the RF frequency and, with the radius, the energy. The dee and the chamber around it form a capacitor, and the RF circuit is built around its value. The dee voltage sets how many turns the ions make, and more turns means more path through the leftover gas, so the turn count sets the pressure estimate. Scaling down is possible, but it is not the same machine made smaller. The magnetic field distribution, the pattern of field across the gap, scales cleanly; the RF and the energy requirements change with the geometry and have to be redesigned. When one experienced group moved its working design to a larger magnet, most of the beam did not come with it, an illustration of recommissioning, not a controlled experiment. Whatever you change, redo the design point, the pair of field and radius, from the new part’s measured properties.

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What has to be redone for any change is the design-point pair of magnetic field and radius, the first-orbit clearance, the tank (coil plus dee capacitance), and the vacuum budget (the pressure the spiral needs, set against the gas the source admits and the pumps remove). What has to be measured again is the magnetic field at the centre against coil current and the dee capacitance, the capacitance between the dee and the grounded chamber around it; a field map is for when the beam’s behaviour calls for one (Do I really need to map my magnet's field accurately? Is one reading in the middle enough, and which value goes into the frequency and energy calculations?).

If it does not work. Change the magnet and you change the field, which moves the RF frequency and the energy ceiling together; the Rutgers 12-inch needed a new tank coil just to run at half frequency for deuterons (Koeth (2017), p. 1). Change the magnet gap and you change the focusing profile (the field’s fall-off with radius), the voltage the gap can hold, and the clearance the first turn needs around the source. Change the chamber or the dee and you change the capacitance the tank resonates against. One college build skipped measuring it and tuned by trial and error; Houghton measured 79 pF and designed from it (Cressman (2006), p. 18). Change the dee voltage and you change the turn count, which changes the vacuum the spiral needs and whether the first orbit clears the source (Prechtl & Wolf (2020), p. 54, Prechtl & Wolf (2020), p. 42-43). Change the ion source and you change the gas load the pumps must carry (vacuum page). Almost nothing is a free substitution. ORNL’s verdict on a machine built fast from adapted parts: it ended up unshieldable, with a marginal field, a capped dee voltage and a gap half of what was needed, and none of it could readily be corrected (Howard (ed.), p. 20).

Many projects start with a surplus magnet, and it can work. The Rutgers 9-inch ran on a Varian NMR magnet turned on its side, Houghton on a commercial laboratory electromagnet, COLUMBUS on a donated Bruker magnet (census). It is no guarantee of success: the Knox College build was designed around the chemistry department’s 2 T NMR magnet and never documented a beam, though the record does not say why (census). The record supports the method: design from the magnet’s measured field-versus-gap curve and usable radius (Dewan (2007), p. 7-8), and check that the frequency and RF that fall out of that field are ones the builder can actually produce. A 2 T field, with the proton frequency rising in step with the field, means a 30 MHz proton RF system holding kilovolts, on a small usable radius.

To understand it. The precedent for copying is institutional. When the University of Washington built its 60-inch, it obtained the complete Berkeley drawings, followed them closely on the magnet, reserved original effort for the places the plans were silent, and had the machine assembled and ready to test in three years (The University of Washington 60-Inch Cyclotron: Progress and Status…, p. 6). At amateur scale the finished census machines are documented in build logs and theses. A design point taken from COLUMBUS or Rutgers is one known to work (choosing-your-machine page). The COLUMBUS authors, though, could draw only partly on the amateur machines before them because “the boundary conditions were too different” (Prechtl & Wolf (2020), p. 8). A copy is a copy of a configuration, not of a parts list.

On scaling: magnetostatics, the physics of steady magnetic fields, has no intrinsic length scale, so a geometrically scaled magnet, every dimension multiplied by the same factor, run at the same field reproduces the same field distribution, the same pattern of field across the gap (Wakerling & Guthrie (eds.), p. 25). The field distribution is the one thing that scales cleanly, and it sets a trap. The cyclotron frequency depends on the field, not on the size of the machine, so a half-size machine at the same field still needs the same RF frequency. A geometrically scaled resonator, though, has a natural frequency that doubles when its size halves, because the inductance and the capacitance that set it both shrink with its dimensions (MacKenzie (1947), p. 6). The RF circuit therefore has to be redesigned to the field, not shrunk with the iron. The energy, meanwhile, scales as (Br)², so the half-size machine reaches a quarter of the energy at the same field. When the Rutgers group moved from its working 9-inch prototype to the 12-inch magnet, the beam did not come with it: fractions of a nanoampere against the prototype’s ten, and a diagnosis that ran through the pole tips to the ion source before the machine recovered (Koeth (2006), p. 1). It is an illustration of redesign and recommissioning, not a controlled experiment that isolates scale as the cause; nothing carried over automatically.

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Do I need to simulate the cyclotron before building it? If a simulation shows one proton spiraling outward, how much does that prove?

No, not in the sense of mastering a beam-dynamics package, a program that follows many ions through the machine. Most documented amateur builds do not report running one. The ones that finished mostly describe closed-form arithmetic, formulas worked by hand or on the site’s calculators, plus one free magnet solver (modeling-tools page). A magnet solver is a program that computes the field a given arrangement of iron and coil produces. Modeling the magnet pays before iron is cut. Copper and steel are the expensive mistake, and the field’s shape across the gap depends on the whole iron geometry, so it cannot be discovered by trial winding. The spiraling proton shows that, within that model’s assumptions and numerical setup, the field and frequency you typed in are consistent, which the resonance relation already told you. It says nothing about whether a real population of ions, born at every point in the RF cycle and at scattered positions, survives to the collector. For a first machine, copy a proven design and model only what you change. Measure what can be measured: the capacitance between the dee and the chamber, and the field at the centre against coil current.

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If it does not work. Where measurement beats modeling: dee capacitance, which should be measured before the tank is designed rather than computed (Cressman (2006), p. 18); the magnetic field, which for a first beam is read at the centre against current and, if the beam asks for shaping, mapped and shimmed, a process one 1949 team concluded was iterative cut-and-try after their theory-guided scheme failed validation (Wakerling & Guthrie (eds.), p. 181); and the resonance itself, which a bench sweep finds in an afternoon. For a first machine, copy a proven design and model only what you change (choosing-your-machine page). In practice that means a FEMM cross-section of the magnet for the ampere-turn budget (coil current times turns, which sets the field the magnet can reach) and the field profile, the site’s calculators for energy, turns, vacuum and RF, and, if you want to understand the spiral, a few hundred lines of your own orbit integrator, a program that steps an ion through the field in small time steps. Treat its output as a picture of the physics, not a prediction of the beam.

To understand it. A single-particle picture leaves out most of the physics that loses beam. A real source emits continuously, so ions are born at every phase of the RF cycle, and only those born in a window around the right phase are captured into continued acceleration. Ions are born off the midplane and off the orbit center. Whether they are focused back or hit the dee depends on the magnetic field’s radial profile (field versus radius), not on an orbit drawn in a uniform field. The first half-turn has to clear the source hardware (Prechtl & Wolf (2020), p. 42-43). And every turn crosses residual gas, so survival falls exponentially with pressure times path length, since a collision with a gas molecule can remove an ion from the beam (Prechtl & Wolf (2020), p. 54). A simulation that answers a real question has to represent the mechanism that question depends on: a field map with its gradient for focusing, a spread of starting phases and positions for capture, a gas model for survival.

Houghton’s 2015 focusing thesis modeled magnet and chamber in Poisson Superfish, a field solver, and tracked ions in SIMION, an ion-tracking program, to justify one design change, magnetic chamber lids (modeling-tools page). The Rutgers group built a full 3-D SIMION model of its 12-inch and verified it against every configuration of the machine (Koeth (2013), p. 1). The model predicted that a set of radial-sector pole tips would fail at the normal dee voltage, and they did (Ruisard (2013), p. 2). The Cyclotron Kids designed a magnet yoke from scrapyard steel in Poisson Superfish. In each case the model answered a specific uncertainty on an existing or planned machine. The professional version of the same discipline is to validate the integrator against cases with known answers before trusting it (Moses (1963), p. 10), and to let the computation overrule folklore only once it has been checked (Blosser & Gordon (1961), p. 45).

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What should I read? The current literature seems hopelessly complicated and theoretical, and the old literature must be way out of date.

Start with the construction reports of the 1940s to 1970s, and leave the modern professional literature for later. The reports were written by people building machines close to your size who had to explain to a machinist what to cut next, and what has aged in them is the equipment and the vocabulary. The physics, the design decisions and the failure modes read as current. Most modern professional papers are about machines unlike yours: isochronous (the ions take the same time per turn at every energy), often superconducting (magnet coils cooled until they carry current without resistance), delivering milliamperes of beam. Their open questions are ones a first-beam builder can defer; the documented amateur first beams were built from the old reports, the amateur record and the builders’ own notes. The exception is the modern amateur and teaching record (Rutgers, Houghton, COLUMBUS), which is small and hands-on. Read the classics for the engineering, the amateur record for what it is like at your scale, and this site’s safety and legal pages for the part the classics get wrong, their era’s safety practice.

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Where to start. Wouters’ 1949 Berkeley Radiation Laboratory report UCRL-476 is the one document written for someone about to build a small machine: a filament recipe, arc values (the discharge’s voltage and current), and a commissioning procedure, the steps from a finished machine to a working beam, that still reads as a checklist (Wouters (1949), Wouters (1949), Wouters (1949)). Livingston and Blewett’s Particle Accelerators (1962), chapters 5 and 6, is the textbook the field learned from and is far more mechanical than modern texts; it is reading for understanding, not a prerequisite for a first beam. The Oak Ridge 86-inch report (ORNL-1196) shows how a crew commissions a machine and how long it takes: eight months from first beam to reliable performance (beam-measurement page). Then Koeth’s Rutgers papers on Q (how little energy the RF resonator loses per cycle), dee-voltage measurement and the ion source, the Houghton College thesis chain, and the COLUMBUS book and papers.

When the machine is stuck, read by failure rather than by subject: the construction reports’ commissioning chapters (ORNL-1196’s eight months), Koeth’s ion-source studies for a beam that is weak close to the source, the Houghton theses for focusing, what holds the circling ions near the midplane, and for the harmonic census, beams found with the RF at three or five times the orbit frequency, the ion going round once every three or five RF cycles, and the hosted Mullins notes for what seven years of a small machine’s log look like, failures included (/library/amateur/#mullins).

To understand it. What is out of date, so you can translate on the fly:

  • Units and words. Kilogauss for tesla (10 kG = 1 T), megacycles for megahertz, millimetres of mercury for torr. A 1949 arc “at 10⁻⁴ mm” is 10⁻⁴ torr (Wouters (1949)). A condenser is a capacitor.
  • Tubes. The classics build a self-excited oscillator around the dee itself (Livingston & Blewett (1962), p. 190-193): no separate frequency source, the tube feeding energy back into the dee’s resonant circuit, which sets the frequency itself. Koeth’s assessment, choosing the other path for the 9-inch, is that the self-excited oscillator is more efficient but “very complicated and demands an experienced radio engineer”, while a signal generator driving a solid-state amplifier at a fixed frequency is “the most stable and simplest to invoke” (Koeth, p. 3).
  • Instruments. The classics map magnetic fields with flip coils and fluxmeters (Livingston & Blewett (1962), p. 283-285), a coil turned over in the field giving a voltage pulse that the fluxmeter sums into a field reading, and read beam on galvanometers, sensitive current meters; a modern builder usually reaches for a Hall probe, a sensor that reads the field directly (Koeth, p. 2), and an electrometer, a meter for very small currents. These are not drop-in equivalents: ask what physical quantity the old instrument measured, then measure that with whatever is easiest now.
  • Materials and trade names. Glass dee insulators that cracked in a discharge (Wouters (1949)), square rubber gaskets (Livingston & Boch (1952), p. 41), “Lapp” water-line insulators (Livingston & Boch (1952)), and alloy and insulator trade names on the source drawings (Hausman (1954), p. 14). Carry over the function each part served, not the part.
  • Safety practice. The one place the old reports are dangerous to copy. Their exposure norms and weighting factors are of their era (Martin (ed.), p. 111), and their high-voltage and interlock habits predate modern rules. Exposure norms are the doses a worker was allowed; weighting factors are the numbers by which different radiations’ harm was weighed.

The judgment has not dated. ORNL’s own verdict on its 63-inch, built fast from adapted parts (unshieldable; a marginal magnetic field hard to keep shimmed, corrected with small pieces of iron; dee voltage capped by its bushings, the insulators that carry the dee stems through the chamber wall; a magnet gap half of what was needed; a single-species RF system, able to run one ion only), with none of it readily correctable (Howard (ed.), p. 20), is a warning for any surplus-driven build.

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