Cyclotron Glossary

The vocabulary a newcomer meets in cyclotron literature and across this site — 92 terms, each defined in a sentence or three and linked onward to the page, calculator, or design rule that treats it in depth. Every entry has its own anchor, so any definition can be linked directly (for example /learn/glossary/#dee).

For the physics in narrative order, start with How a Cyclotron Works; for the hazard terms in context, read Safety.

A

accelerating gap: The space between the dees — or between the dee and the dummy dee — where the RF electric field acts on the beam. A particle gains up to qV of energy per crossing (V the dee voltage) and crosses twice per turn; inside the dees it coasts field-free. See How a Cyclotron Works.
activation: Radioactivity induced in material struck by the beam, created by nuclear reactions such as (p,n). Each reaction has a threshold energy, and below roughly 2 MeV proton activation of common materials is essentially impossible; the thresholds and their sources are on the safety page.
Agreement State: A US state to which the NRC has transferred its radioactive-materials licensing authority. It matters for a cyclotron only if the machine produces radioactive material above exempt quantities (see activation); the machine itself is regulated separately by the state as a radiation machine. See the legal survey.
ampere-turns: The product NI of coil turns and coil current, which drives magnetic flux around the magnet circuit. For an iron-dominated magnet below saturation, the gap field is approximately B = μ₀NI/g with g the pole gap; the magnet power calculator works this in both directions.
AVF: Azimuthally varying field — the pole geometry of hills and valleys that provides vertical focusing in an isochronous cyclotron. See also flutter and spiral sector.

B

beam current: The charge delivered per unit time, quoted as an electrical current; 1 μA of protons is 6.2 × 10¹² particles per second. Amateur machines typically circulate nanoamperes; commercial isotope-production cyclotrons run hundreds of microamperes. Measured directly with a Faraday cup.
betatron: An induction accelerator for electrons: a ramping magnetic flux through the orbit acts as a transformer with the beam as its secondary winding — no RF gap at all. Included here for contrast; see the accelerator comparison in How a Cyclotron Works.
betatron oscillation: The transverse oscillation of a particle about its equilibrium orbit, radial or axial, first analyzed for the betatron (hence the name). The number of oscillations per turn is the tune.
bremsstrahlung: "Braking radiation": X-rays emitted when fast electrons decelerate in matter. It is how dark-current electrons make an energized RF system an X-ray source even with no ion source running — see the X-ray hazard section.

C

CF (ConFlat) flange: An all-metal vacuum seal in which a knife-edge bites into a copper gasket; bakeable and suited to ultra-high vacuum. Most cyclotron chambers seal with O-rings instead and reserve CF hardware for gauges and small ports.
C-frame magnet: A magnet whose iron return yoke passes on one side only, like the letter C. It gives open access to the pole gap at the cost of an asymmetric flux path and a frame the magnetic load tries to spring open; compare H-frame magnet.
charge-exchange loss: Loss of beam when an ion collides with a residual-gas molecule and captures or loses an electron: its charge no longer matches the field steering it, and it leaves the orbit. Especially severe for H⁻, whose second electron is bound by only 0.75 eV. Together with scattering it sets the vacuum requirement — see the vacuum & beam-survival calculator.
chimney: The hollow anode tube of a PIG ion source, running between its two cathodes along the magnetic field. The arc burns inside it, and ions escape through a slit in its wall toward the puller electrode and the first orbit.
classical cyclotron: The original fixed-field, fixed-frequency machine: a near-uniform field falling slightly with radius for weak focusing, dees driven at constant RF. Its ceiling is the relativistic limit, roughly 10–25 MeV for protons — and it remains the realistic form for an amateur build.
coupling loop: A small conductor loop through which the transmitter feeds RF power into the dee resonator by magnetic induction. Rotating or resizing the loop adjusts how tightly it couples — part of the matching that presents 50 Ω to the transmitter.
cyclotron frequency: The orbital frequency of a charged particle in a magnetic field: f = qB/2πm, independent of speed and radius — 15.25 MHz per tesla for protons. This constancy is the fact the whole machine rests on; see How a Cyclotron Works.
cyclotron resonance condition: The requirement that the RF stay in step with the circulating ion: f_RF = h·qB/2πm, where h is the harmonic number (h = 1 in simple machines). Because the orbital period does not depend on energy, one fixed frequency serves from first lap to last — until the relativistic limit intrudes.

D

dark current: Electron current drawn from electrode surfaces by strong RF fields (field emission), flowing with no ion source running. The electrons are accelerated across the gap and generate bremsstrahlung X-rays where they strike; amateur experience puts the practical onset at a few tens of kV of dee voltage. See Safety.
dee: One of the hollow, D-shaped copper electrodes inside the vacuum chamber. The ion coasts through its field-free interior for half a turn and is accelerated each time it crosses the accelerating gap; many small machines use a single dee facing a dummy dee. See How a Cyclotron Works.
dee stem: The conductor that supports the dee and carries RF to it. Its inductance resonates with the dee's capacitance to set the operating frequency — in larger machines the stem is a quarter-wave transmission line. The dee capacitance & matching calculator covers the arithmetic.
dee voltage: The peak RF potential of the dee, which sets the energy gained per gap crossing (up to qV). Higher dee voltage means fewer turns to final energy, which spends the phase budget more slowly and eases vacuum and turn-separation demands — one reason builders chase it. Small machines run from hundreds of volts to a few tens of kV.
deflector: The electrostatic element that peels the outermost orbit out of the machine: a curved channel between a grounded septum and a high-voltage electrode whose field nudges the final turn outward into the exit path. The classical means of extraction for positive ions.
diffusion pump: A high-vacuum pump with no moving parts: jets of heated oil vapor entrain gas molecules downward to a backing pump. Cheap and rugged — a surplus favorite — but it needs cooling water, a backing pump running at all times, and a baffle or cold trap to keep oil out of the chamber.
dummy dee: A grounded bar or frame standing in for the second dee in single-dee machines. It provides the far edge of the accelerating gap without needing RF drive of its own; the ion still gets two kicks per turn, at the dee's entrance and exit edges.

E

electron-volt (eV): The energy a particle of one elementary charge gains falling through one volt: 1 eV = 1.602 × 10⁻¹⁹ J. Accelerator energies are quoted in keV and MeV; a proton crossing a 10 kV gap gains 10 keV.
emittance: The area a beam occupies in transverse phase space (position vs. angle), commonly quoted in mm·mrad. It measures beam quality — smaller means better collimated — and focusing cannot shrink it (Liouville's theorem), only trade spot size against divergence.
equilibrium orbit: The closed orbit on which magnetic bending exactly matches a particle's momentum; a particle displaced from it executes betatron oscillations about it. In an AVF machine the equilibrium orbit scallops through the hills and valleys rather than being a circle.
external ion source: An ion source outside the machine, feeding beam to the center through a hole in the pole (axial injection) and bent onto the median plane by an inflector. Costlier than an internal source, but it keeps the source gas load out of the chamber and allows species an internal source cannot produce.
extraction: Getting the accelerated beam out of the machine at final radius — classically with a deflector and septum, or by stripping in H⁻ machines. Efficiency matters twice over, because lost beam also activates the machine; many amateur machines skip extraction and use the internal beam directly.

F

Faraday cup: A conducting cup that stops the beam and passes the collected charge to a current meter — the standard direct measurement of beam current. A suppressor electrode or a small magnetic field keeps secondary electrons from falsifying the reading.
FFA: Fixed-field alternating-gradient accelerator (historically FFAG): the magnetic field is constant in time like a cyclotron's, but focusing comes from strong alternating gradients — a concept from 1950s MURA work, revived since the 2000s. The fixed field permits rapid cycling and very large acceptance.
field index: n = −(r/B)(dB/dr), the dimensionless measure of how fast the field falls with radius. Stability of both oscillation planes in a weak-focusing machine requires 0 < n < 1, with vertical focusing demanding n > 0; classical machines run a few hundredths to about 0.2 near extraction. The design guide collects the field-shaping rules.
filament ion source: The simplest internal source: a hot tungsten filament near the machine center emits electrons that ionize hydrogen gas, and the gap field pulls the ions into orbit. Easy to build but modest in output, and filaments burn out; the step up is a PIG source.
flutter: The measure of azimuthal field variation in an AVF machine: F = ⟨(B − ⟨B⟩)²⟩/⟨B⟩², the mean-square relative ripple around one orbit. Together with the spiral angle, flutter sets the vertical focusing that lets an isochronous field rise with radius.

G

gauss (G, kG): The CGS unit of magnetic flux density: 1 tesla = 10,000 gauss = 10 kG. Cyclotron literature habitually quotes fields in kilogauss — an 18 kG magnet is 1.8 T — and this site gives tesla with kG in parentheses where its sources do.

H

harmonic number: The integer h relating RF frequency to orbital frequency: f_RF = h·f_orbit. Running h > 1 lets slow (heavy or low-charge-state) ions use a conveniently high RF frequency; simple proton machines run h = 1.
H-frame magnet: A magnet whose yoke returns flux symmetrically on both sides, the poles bridging the middle of the "H". Stiffer and magnetically cleaner than a C-frame, at the cost of weight and access to the gap.
H⁻ (H-minus) acceleration: Accelerating the negative hydrogen ion instead of the proton, so that a thin stripping foil at any radius converts it to H⁺ — the field then bends it out of the machine, giving near-total, clean extraction at a selectable energy. The costs: better vacuum, since the loosely bound second electron is easily stripped by residual gas, and moderate fields, since strong fields strip it electromagnetically. The dominant design for commercial isotope machines.
high vacuum: The pressure regime, roughly 10⁻¹ to 10⁻⁷ Pa (10⁻³ to 10⁻⁹ torr), in which molecules fly ballistically rather than behaving as a fluid. A cyclotron typically needs 10⁻³ to 10⁻⁴ Pa (10⁻⁵ to 10⁻⁶ torr) so the beam survives its hundreds of meters of spiral path; the vacuum calculator connects pressure to beam survival.
hill and valley: The alternating high-field ridges (hills) and low-field grooves (valleys) machined into the poles of an AVF cyclotron. The orbit scallops between strong and weak sectors, and the resulting forces focus the beam vertically — the escape from the weak-focusing bind worked out by L. H. Thomas in 1938.

I

internal ion source: An ion source (filament or PIG) mounted at the machine center, inside the main vacuum. Simple and compact — the near-universal amateur choice — but its gas feed loads the vacuum system and limits the species menu; compare external ion source.
isochronous (AVF) cyclotron: A cyclotron whose average field rises with radius to keep the orbital period exactly constant despite relativity, the vertical defocusing this causes being defeated by hills and valleys (often spiraled). It delivers continuous beam at high current and is essentially every cyclotron built since the 1960s; see How a Cyclotron Works.
isochronous field: A field profile whose azimuthal average rises with radius in proportion to the Lorentz factor, ⟨B⟩(r) = γ(r)·B₀, making the revolution time independent of energy. It is the opposite of what weak focusing wants — hence the AVF solution.

K

Kilpatrick limit: An empirical criterion (W. D. Kilpatrick, 1957) for the maximum RF surface electric field sustainable without vacuum sparking, as a function of frequency. Modern conditioned surfaces routinely exceed it by factors of about two, so it serves as a conservative design bound for gap and electrode spacing.
K-value: A cyclotron's bending limit, quoted in MeV: nonrelativistically T/A = K·(Q/A)² for an ion of charge Q and mass number A, so K equals the machine's approximate maximum proton energy. It is set by the maximum magnetic rigidity, and machine names like "K500" quote it; the world cyclotron map catalogs machines by energy.

L

linac: A linear accelerator: many gaps in a straight line, each timed to push the passing bunch. It trades the cyclotron's compact reuse of one gap for unlimited energy reach; see the accelerator comparison in How a Cyclotron Works.
liner: The grounded metal surface lining the vacuum chamber around the dees, forming the RF return path and the ground half of the dee-to-ground capacitance. In larger machines it is a distinct water-cooled copper shell; in small ones the chamber wall itself serves.
Lorentz factor: γ = 1/√(1 − v²/c²) = 1 + T/mc², the relativistic energy factor. It is the villain of the classical cyclotron: the orbital frequency falls as f/γ, breaking resonance — see relativistic limit.
Lorentz force: F = qE + qv × B, the force on a charged particle. The magnetic part, always perpendicular to the velocity, bends the orbit without changing speed — the magnet only steers; all acceleration happens in the electric field of the gap.

M

magnetic rigidity: Bρ = p/q, the product of field and bending radius, equal to momentum per unit charge; units tesla·meters. It measures how hard a beam is to bend, and particles of equal rigidity follow identical paths in the same field — the working currency of beam transport.
matching network: The circuit that transforms the dee resonator's drive-point impedance to the transmitter's (usually 50 Ω) so power flows in rather than reflecting back. Implemented with a coupling loop, a capacitive tap, or an L-network, and judged by SWR; see the matching calculator.
mean free path: The average distance a molecule travels between collisions: for air at room temperature λ ≈ 6.6 mm / p, with p in pascals — about 6.6 m at 10⁻³ Pa (7.5 × 10⁻⁶ torr). The beam's full path length must fit within a modest number of scattering lengths; the vacuum calculator does the trade.
median plane: The symmetry plane midway between the pole faces, where the beam circulates. Focusing forces vanish on it by symmetry and push displaced particles back toward it; the source slit, dees, and probes are all aligned to it.
multipactoring: A resonant avalanche of secondary electrons bouncing between RF surfaces in vacuum, absorbing drive power at low field levels so the dee voltage refuses to rise. Cured by surface conditioning, a DC bias on the dee, or ramping through the susceptible voltage band quickly.

O

O-ring seal: An elastomer ring (usually Viton) compressed in a groove — the demountable vacuum seal of practically every amateur chamber, workable into the 10⁻⁵ Pa range. Elastomer permeation and outgassing set its limit; compare the all-metal CF flange.
outgassing: The slow release of gas adsorbed on and dissolved in surfaces under vacuum — water films, fingerprints, plastics. Once real and virtual leaks are fixed, outgassing sets a chamber's ultimate pressure; clean handling and pumping time (or bakeout) are the cures.

P

particle accelerator (legal definition): In most US state codes, a device that imparts kinetic energy to charged particles by electromagnetic means — but thresholds and wording vary by state, and some states capture small machines through generic radiation-machine language instead. Whether a state's definition reaches a given machine decides its registration duty; see the jurisdiction-by-jurisdiction survey.
phase slip: The accumulated drift of an ion's gap-arrival time relative to the RF. A fixed-frequency machine has a phase budget of roughly ±90° over the whole acceleration, and frequency or field errors of order 1–2% exhaust it — which is why fewer turns at higher dee voltage help. See How a Cyclotron Works.
phase stability: The 1945 discovery of Veksler and McMillan: with a suitable synchronous phase, an ion arriving early receives a kick that makes it later, and vice versa, so phase errors oscillate gently instead of accumulating. It is what makes the synchrocyclotron and every synchrotron work.
PIG (Penning) ion source: The classic internal cyclotron source, named for the Penning (Philips) ionization gauge geometry it borrows: two cathodes face each other along the magnetic field with a hollow anode chimney between them, and the field traps electrons oscillating between the cathodes so they ionize the feed gas efficiently. Built cold-cathode (high voltage) or hot-cathode (high current).
(p,n) threshold: The minimum proton kinetic energy at which a (p,n) reaction — proton in, neutron out — becomes energetically possible. For materials common in a machine: ⁷Li 1.88 MeV, ⁹Be 2.06, ⁶⁵Cu 2.17, ⁵⁶Fe 5.44, ²⁷Al 5.80 MeV; below threshold that route produces no neutrons and no activation. Full table and sources on the safety page.
pole: The iron column and face that deliver the magnet's flux to the gap; the pole face (or pole tip) is the machined surface bounding the pole gap. Pole diameters are customarily quoted in inches — Lawrence's machines were the 27-inch, 37-inch, 60-inch, 184-inch — and the usable uniform-field radius ends roughly half a gap length inside the pole edge.
pole gap: The axial distance between pole faces. A smaller gap gives more field per ampere-turn — below saturation B ≈ μ₀NI/g — but must still house the dees, the chamber, and the beam's vertical excursions; the magnet power calculator quantifies the trade.
precession: Slow rotation of the orbit center about the machine center that occurs when the radial tune differs slightly from 1. Extraction systems exploit it: a deliberate orbit off-centering precesses around the machine, and the deflector is placed where the precession adds to turn separation.

Q

Q factor: The quality factor of the dee resonator: 2π times the energy stored over the energy lost per RF cycle. Higher Q yields more dee voltage per watt of drive but sharper, more drift-sensitive tuning; clean copper resonators reach Q in the thousands. See the dee capacitance & matching calculator.

R

radiation machine: In state regulation, a device that produces ionizing radiation when energized — X-ray sets, and accelerators however small. A machine can fall outside a state's accelerator definition and still be a registrable radiation machine once it emits above exempt levels; see the legal survey.
registration (vs. licensing): The two regulatory postures for radiation machines. Registration means notifying the state — a form, a fee, and conditions such as a responsible individual, postings, and surveys; licensing means obtaining approval before operating. For small accelerators most US states require registration and a minority license; details in the legal section.
relativistic limit: The classical cyclotron's energy ceiling: as γ grows the orbital frequency falls to f/γ, the ion slips out of phase with the fixed RF, and the two fixes — a rising field vs. weak focusing — conflict, as Bethe and Rose showed in 1937. In practice 10–25 MeV for protons, the exact figure set by dee voltage. The escapes: the synchrocyclotron and the isochronous cyclotron.
resonance crossing: Passage of the tune through a low-order rational value during acceleration, where field imperfections drive betatron amplitudes to grow — the classic case is Q_r = 1 driven by a first-harmonic field error. Machines survive by keeping errors small and crossing fast.
roughing pump (backing pump): A mechanical pump — rotary vane or scroll — working from atmosphere down to around 1 Pa. It plays two roles: roughing the chamber down before the high-vacuum pump takes over, and continuously backing a diffusion or turbo pump, which cannot exhaust to atmosphere.
RSO (radiation safety officer): The named individual responsible for an institution's radiation-safety program — surveys, records, training, postings. State registration forms for a radiation machine generally require one; for a private build that person is, in practice, the builder.

S

sector-focused cyclotron: Umbrella term for cyclotrons focused by azimuthal field structure — that is, isochronous/AVF machines. In separated-sector (ring) variants the hills become individual magnets with open valleys for RF and injection, as at PSI and TRIUMF.
self-excited oscillator: An RF system in which the dee resonator itself is the frequency-determining element of the oscillator, so drift in dee tuning is tracked automatically — the traditional and simplest cyclotron arrangement. The alternative, a driven (master-oscillator / power-amplifier) system, imposes a stable external frequency but must keep the resonator tuned to follow it.
septum: The thin grounded electrode separating the last circulating turn from the deflector's field region. It must be thin — beam inevitably strikes it — yet survive the heating; septum burn-up is a classic extraction failure, and septum losses drive local activation.
shim: Iron added to the magnet — edge rings, discs, wedges — to shape the field: flattening it, setting the field index, or extending the usable radius (the Rose shim ring). Classical machines were commissioned by cut-and-try shimming; the design guide collects the rules with their sources.
sievert (Sv): The SI unit of dose equivalent — absorbed dose weighted for biological effect. 1 Sv = 100 rem, so 1 mrem = 10 μSv; US regulations still speak in rem, and a common exemption threshold of 0.5 mrem/h is 5 μSv/h. See Safety and the legal survey.
space charge: The mutual electrostatic repulsion of the beam's own particles, which defocuses and dilutes it; strongest at low energy, so the machine center and first turns set a cyclotron's current limit. Negligible at amateur nanoampere currents, central at commercial hundreds of microamperes.
spiral sector: A hill whose boundary spirals outward rather than running straight along a radius. The slanted edge crossings alternate focusing and defocusing, which nets extra vertical focusing (suggested by Kerst in 1955) — the reason high-energy AVF poles look like pinwheels.
stripping foil: A thin foil, typically carbon a few μg/cm² thick, that strips electrons from ions passing through it. In H⁻ machines it converts H⁻ to H⁺ mid-orbit, reversing the bending direction and sending the beam cleanly out of the field; the foil's radius selects the extraction energy.
superconducting cyclotron: A compact cyclotron whose main coils are superconducting, reaching average fields of 3–5 T — several times the ~2 T that iron allows — so the same energy fits in a fraction of the size and weight (energy scales as B²R²). First realized as the K500 at Michigan State (1982); now common in proton-therapy machines.
survey meter: A portable dose-rate instrument, Geiger–Müller or ion chamber. This site's standing rule: own a calibrated one before first pump-down, and let the survey — not calculation — decide where shielding goes; see Safety.
SWR (standing-wave ratio): The ratio describing how much RF power reflects from an imperfectly matched load; 1:1 is a perfect match. Between the transmitter and the dee resonator it is the practical gauge of the matching network's adjustment.
synchrocyclotron: A cyclotron that sweeps its RF frequency downward during each acceleration cycle to follow γ, escaping the relativistic limit; phase stability holds the bunch together during the sweep. The price is pulsed beam at low duty cycle and far lower average current. The Berkeley 184-inch and its siblings reached hundreds of MeV this way; the form is revived in some compact therapy machines.
synchrotron: A ring accelerator that ramps its magnetic field to hold the orbit radius constant while sweeping the RF upward — the configuration of every GeV-and-beyond machine. Contrast the cyclotron, which fixes both field and frequency and lets the radius grow; see the comparison table in How a Cyclotron Works.

T

transit-time factor: The factor (≤ 1) by which the actual energy gain in a gap falls short of qV₀, because the RF field changes while the particle is crossing. It stays near unity when the gap is short compared with the distance traveled per RF cycle — one reason gap geometry matters more as frequency rises.
trim coil: A flat coil, usually one of a concentric set on the pole faces, whose current fine-tunes the radial field profile — in isochronous machines, dialing in the rising average field exactly. Azimuthal siblings (harmonic coils) cancel first-harmonic field errors that would drive resonances.
tune: The number of betatron oscillations per turn, radial Q_r and vertical Q_z (also written ν_r, ν_z). In a weak-focusing field Q_r = √(1 − n) and Q_z = √n, with n the field index; simple rational values are danger spots — see resonance crossing.
turbomolecular pump: A high-vacuum pump whose bladed rotor, spinning at tens of thousands of rpm, knocks molecules toward the exhaust; it needs a backing pump. Clean (no oil near the chamber) and push-button to run, but mechanically delicate — ingesting debris or venting hard at full speed can destroy it.
turn separation: The radial spacing between successive turns: Δr ≈ r·ΔE/2E nonrelativistically, with ΔE the energy gain per turn — millimeters on early turns, often under a millimeter at extraction. It must exceed the septum thickness for clean extraction; raising dee voltage or exploiting precession widens it.

V

virtual leak: Gas trapped in an internal void — a blind tapped hole, an unvented O-ring groove — bleeding out so slowly that the system behaves as if it leaked, though no leak detector finds one. Prevented with vented screws and relief passages in every trapped volume.

W

weak focusing: The gentle restoring forces of a field with 0 < n < 1: the radially falling field's outward-bowing lines push off-plane ions back toward the median plane, and radial displacements are likewise restored. It holds the classical cyclotron's beam together for its hundreds of turns; see How a Cyclotron Works.

Y

yoke: The iron frame that closes the magnetic circuit between the poles. It must carry the full flux without saturating — cross-section comparable to the pole's — and its geometry, H-frame or C-frame, is usually a build's single heaviest procurement decision.

Missing a term you hit elsewhere? The library indexes the primary literature these definitions rest on, and the theory page develops the core ideas from first principles.