Beam Measurement and Beam Quality

A working cyclotron announces itself during a magnet sweep, as a narrow current peak on a meter reading picoamperes — a peak that vanishes when the field is detuned by a fraction of a percent. This page covers the instruments and methods that make that reading trustworthy — the Faraday cup, the electrometer chain, the authentication tests, and the beam-quality measurements within reach of a small machine — drawing on the 1946–47 Berkeley commissioning memos where several of the techniques were invented, and on the student machines that still use them.

First beam is proof, not spectacle

Nothing visible happens when a small cyclotron starts working. The case against building one puts it bluntly: documented first beams run from picoamps to a few hundred nanoamps, at energies from tens of keV to 800 keV, and merely detecting them is a project in itself. That page treats the fact as a warning. This page treats it as the engineering problem it is: the machine's only witness is its instrumentation, so the instrumentation has to be designed and cross-examined like any other subsystem.

The problem is old and its solutions are documented. When the Berkeley 184-inch — the largest accelerator on Earth at the time — lost its beam at 82 inches radius in 1946, the crew found it again with copper targets, photographic film, and a second probe: the commissioning memos, hosted here as construction classics, read like a manual for interrogating an invisible beam with simple hardware. The same moves, scaled to a benchtop, are how the Rutgers and Houghton College machines proved their beams half a century later.

Scope: this page covers measurements an amateur can make with an internal probe, an electrometer, and film or a screen — plus the extracted-beam cross-checks (deflection channels, silicon detectors) that some student machines added. Nuclear-reaction proofs of beam — prompt gammas from a LiF probe tip, activation counting — belong with the experiments the beam can do, on Experiments by Energy Band; commercial diagnostics (beam-position monitors, wire scanners, current transformers) are out of scope entirely. Magnetic field mapping, which energy determination leans on, has its own literature in the magnet rules.

The minimum defensible first-beam claim runs through six steps, each covered below:

1. Measure the pickup background with RF on and no beam possible.
2. Suppress secondary electrons and confirm a bias plateau.
3. Sweep the field through resonance with the probe in close.
4. Kill the peak by detuning field or frequency, and by varying gas pressure — real beam dies, artifacts survive.
5. Identify the peak's species and harmonic before calling it fundamental.
6. Log current versus radius, and quote the number with its radius and energy.

How small the signal is

One microampere of protons is 6.2 × 10¹² particles per second — and a first beam is typically three to six orders of magnitude below that. The Houghton College cyclotron's first accelerated protons registered about 1.5 pA on the Faraday cup, at 9.2 keV and only 15.4 W of RF drive (Haas thesis, 2009); the same machine's highest-energy beam, 160 keV protons, peaked at 3 pA (Yuly et al., Cyclotrons 2013). The Rutgers 12-inch was stuck below 10 nA until ion-source work raised it (Koeth, ion source studies, 2006). At the friendlier end, the 6-inch machine in the Los Alamos small-cyclotron recommendations indicated 7 μA (Wouters), and a production machine like the Oak Ridge 86-inch circulated a milliampere at 23 MeV (ORNL-1196, p. 3) — a useful reminder that amateur beam measurement is a different discipline from operating a beam that melts targets.

Two consequences follow. The measurement chain must resolve picoamperes, because that may be all there is; and every nanoamp of spurious current — RF rectification, leakage across an insulator, secondary electrons — is large compared to the signal. Improvement, when it comes, tends to come from the ion source and gas handling rather than from RF power: Houghton raised 10 pA to 70 pA by lowering hydrogen pressure and filament bias at zero additional watts (Yuly, Small Cyclotron Conference 2010).

A Faraday cup that reads true

The Faraday cup is the primary instrument: an insulated conductor that stops the beam and passes the collected charge to a current meter. In principle it is an absolute measurement — no calibration factor, no gain — and with a low-noise current-to-voltage stage and careful mechanical design it reads down to ~10 pA even for a DC beam (Forck, JUAS lecture notes, §2.4). In practice it earns that status only after its error sources are checked: leakage and RF pickup (the next section), and above all secondary emission. Every ion that lands liberates low-energy electrons from the surface, with a mean energy below 10 eV (Forck). Each electron that escapes the cup counts as an extra positive charge collected, so an unsuppressed cup reads falsely high — flattering, and wrong.

All the suppression methods date to the field's first decade. Oliphant and Rutherford, measuring 100 μA proton beams in 1933, insulated their target and let the magnet's stray field trap the secondaries: “The stray magnetic field over T effectively prevents the escape of secondary electrons, so that the current measured is the true ion current” (Proc. R. Soc. A 141, 259, p. 262). An internal probe in a cyclotron sits in exactly such a field, and a 10 eV electron in even a 10 mT fringe field spirals with a radius near 1 mm (r_c = 3.37 √E[eV] / B[mT] mm; Forck) — though it still travels freely along field lines. The cyclotron's own field therefore does most of the suppressing for an internal probe, while an external cup, in a beamline outside the poles, needs the ring or grid; either way, the plateau check below is what proves the reading.

The electrostatic versions are equally simple. A retarding grid a short distance in front of the cup, held at an adjustable negative potential, drives escaping electrons back in (Houghton permanent-magnet cyclotron design study). Biasing the collector itself positive does the same job from the other side: Houghton found that adding a +9 V battery measurably lowered the reading — “the bias reduces the emission of secondary electrons, resulting in a more accurate measurement” (Fuller thesis, 2013, pp. 55–56). A lower number that is real beats a higher one that is secondaries. Whichever method is used, the acceptance test is the same: vary the suppression (bias on/off, grid voltage swept) and confirm the reading settles to a plateau that no longer depends on it.

Reading picoamps next to kilowatts of RF

A picoammeter or electrometer — the Keithley 617 class is the workhorse of the documented student machines, and its instruction manual is a free education in low-current practice — will resolve the beam. The difficulty is everything between the cup and the meter: the collector lead originates centimetres from a dee carrying kilovolts of RF at MHz, and any rectified pickup arrives as a DC offset indistinguishable from beam.

Three habits carry most of the burden. Put a large series inductance in the collector lead rather than a thick RF shield around the tip — a choke kills the MHz pickup without blocking the DC beam current, and a thick shield has costs covered below (Koeth, ion source studies, 2006). Give the probe circuit a high resistance to ground and protect the meter with chokes and bypass capacitors (Wouters, LASL recommendations). Keep the meter itself at ground potential, in the return leg, never floating at the hot side of anything — a rule the amateur-HV literature states as bluntly as any accelerator text (Farnsworth-fusor construction guides). To those, add the electrometer maker's own discipline of short cables and clean insulators — and patience, because low-current ranges need seconds to settle (Keithley 617 manual).

The pickup floor is measurable, and should be measured: run the RF at operating power with the ion source gas shut off, or the magnet detuned well off resonance, and log what the meter reads. The result is a background check rather than a full noise floor — a running discharge loads the RF differently — but it approximates what the beam must exceed, and logging it each session catches degraded chokes and new leak paths early.

Resonance signatures: beam or artifact

The standard first-beam procedure is a resonance sweep: fix the RF frequency, push the probe in close to the center where the resonance tolerance is loose, and slowly sweep magnet current while watching the collector — “either one rocked back and forth until a current peak is indicated on the target probe” (Wouters, LASL recommendations, p. 11). The Rutgers 9-inch prototype found its first beam exactly this way on September 16, 1999. A peak on the sweep, though, is a hypothesis, and Wouters supplies the cross-examination in the same passage: check “the sharpness of resonance as a function of r.f. tuning and magnet current, as well as . . . its sensitivity to hydrogen gas pressure.” Orbiting beam exists only where f = qB/2πm holds, so it dies on a few-gauss detune; stray ion leakage to the probe is broad and barely cares. A “beam” that survives detuning is an artifact.

A genuine sweep also shows more peaks than naively expected, and the extra peaks carry information. An ion kicked on every nth RF cycle still accelerates, so each species resonates at B/3, B/5, and so on down the field axis — Houghton logged H⁺/7, H⁺/5, H⁺/3 and H₂⁺ harmonics in one scan, a cheap mass spectrometer for the internal beam (Yuly, Small Cyclotron Conference 2010; Fuller thesis). Label every peak with species and harmonic number before claiming fundamental proton beam. The species question is real: Oliphant and Rutherford's fresh hydrogen discharge delivered mostly H₂⁺, and “after running for some time it changes over and becomes nearly all protons” (1933). The mix depends on the source and its operating point, so verify the species rather than assume it — the harmonic scan above is the tool.

Seeing the beam: film in 1947, phosphors now

Current tells how much; film tells where — though at picoamp levels only the electrometer speaks, and imaging joins once current and energy rise. The origin story is worth knowing anyway. Soon after its November 1946 first beam, the 184-inch was found to stop accelerating at 82 inches radius instead of the designed 85, and the theory group blamed vertical oscillations pumped where the field index n reaches 0.2. James Vale's crew settled it with hardware any amateur could make: U-shaped targets of 1/16-inch copper sheet, slots 2½ to 4½ inches wide, “run into the tank, one at a time, on the regular probe mechanism, . . . bombarded with a large deuteron beam for about 1 to 3 minutes, removed from the tank” — then laid on photographic film so the activation exposed it. The radioautographs showed “a rapid spreading vertically of the beam at about 81 ½ inches. This agrees quite closely with the point at which n = 0.2 from magnetic measurements” (MDDC-984, 1947, with the film prints reproduced). One experiment, six photographs, mystery closed: the beam's vertical envelope, imaged with no electronics at all.

The method generalized: measuring “the width of the region of induced radioactivity on the leading edge of probes inserted to different radial locations” became a standard vertical-envelope diagnostic (Livingston & Blewett, Particle Accelerators, p. 174). The trick is closed to most amateurs, though: exposing film through activation takes beam energetic and plentiful enough to activate the target strongly — for the 184-inch, deuterons at tens of MeV and large currents. That is a statement about what darkens film, not a safety boundary: activation and, with deuterons, neutron production begin at far lower energy and current, which is why Safety treats any beam on any target as a radiological question. The amateur-accessible descendants are the phosphor screen and the witness plate. A scintillating screen watched by a camera is the standard beam-spot viewer in professional machines (Forck, JUAS notes, §3.1), and it works at student-machine intensities: Rutgers put a phosphor screen behind an electrostatic deflection channel and measured not just the extracted spot but its energy spread from the spot geometry (Ponter et al., Small Cyclotron Conference 2010). At picoamp first-beam levels a screen is unlikely to show anything to the unaided eye — there the electrometer remains the only witness, which is why the previous two sections exist.

Probes and shadows: profile, extent, turn structure

A radial probe — the Faraday collector on a sliding seal or linear feedthrough — is the workhorse diagnostic, and beam current versus probe radius is the single most informative curve a small machine produces (Livingston & Blewett, p. 174). Each shape names a first suspect — not a verdict, since apertures, mis-steering, vacuum, and probe geometry can mimic any of them:

• Gradual fall with radius — magnetic focusing weakening; the Houghton fix was ferromagnetic shims between chamber and pole faces to recover current at large radius (Fuller thesis, pp. 52–53).
• Abrupt cutoff at one radius — phase slip: once the accumulated phase error passes π/2 the ion gains nothing at the gap and then loses energy, so “the beam current will drop suddenly to near zero beyond whatever radius the ions tend to reach” (Morrow thesis, 2015). That points at field shape or dee voltage, not at focusing.
• Low current even at small radius — where turn spacing is large and masking is impossible, the ion source itself is underperforming; more RF power will not fix it (Koeth, ion source studies, 2006).

Anything inert ahead of the collecting surface — a shield lip, a grounded face — must be thinner than the local turn spacing, or it intercepts beam the collector never sees. At 10 kV peak-to-peak and 1.0 T, turn spacing near 4 inches radius is only 0.04 inch — which is how a 0.06-inch RF shield on the Rutgers collector tip masked real beam (Koeth, ion source studies, 2006). At lower dee voltages the spacing is smaller still. This is the quantitative reason the sanctioned pickup fix is the RF choke rather than a thick shield.

Two probes see what one cannot. The synchroscope traces of the 184-inch beam showed recurring “pips” whose interpretation needed proof, so Yeater's crew added an auxiliary copper probe through a Wilson seal 155° around from the regular one and walked it inward in fractions of an inch. As the auxiliary probe reached beam radius, current transferred from one probe to the other, photograph by photograph, with the phase relation of the pips visible on both — proving the fine structure was the beam bundle precessing past the probes rather than any RF artifact (MDDC-987, 1947). The shadow logic — one intercepting element upstream, one detector downstream, geometry does the rest — needs no synchroscope: a fixed shadow bar ahead of a movable collector resolves where beam circulates. Its refined descendant, a differential probe with fingers a couple of millimetres apart, resolves individual turn structure and the radial oscillation near extraction (Botman & Hagedoorn, CERN Accelerator School on cyclotrons); vertical extent, likewise, comes from a slotted target in the MDDC-984 pattern, sized to the chamber at hand.

Energy: one formula and several cross-checks

Beam energy in a cyclotron is set by geometry and field: T = (qBr)²/2m, the non-relativistic form (ample at amateur energies), evaluated with the field at the radius r where the collector sits and a centered orbit assumed — the relation behind the energy, field & radius calculator. Its accuracy is inherited entirely from how well B and r are known. The probe radius is a caliper problem. The field deserves more care: a Hall gaussmeter is a percent-class instrument unless carefully calibrated, while proton NMR gives B(gauss) = (234.82 ± 0.13) × f(MHz), an absolute method (Livingston & Blewett, pp. 286–287). The running machine is itself a field meter: at resonance, the RF frequency and q/m hand back the field — but only its average from center to the orbit radius, good to perhaps 0.5% if assigned to a specific radius (Livingston & Blewett, pp. 287–288).

One formula invites circular self-congratulation, so the documented machines supply independent checks that use the beam against itself:

• First-turn radius. The radius of the first half revolution satisfies E(r) = ½eV_p-p for an ion starting at rest near the gap at peak phase, so the landing point of the first half-turn measures the effective dee voltage — Rutgers plotted this “beam-inferred dee voltage” alongside its pickup and rectifier readings (Koeth, Small Cyclotron Conference 2010).
• Beam-cutoff threshold. Rutgers calculated that first ions clear the source structure at 165 W of RF drive; ramping power down, the beam vanished at 170 W. A 3% end-to-end validation of the voltage chain, for free (Koeth, Small Cyclotron Conference 2010).
• Deflected-spot geometry. With an electrostatic channel and a phosphor screen, spot position and width give energy and energy spread: Rutgers predicted 12.7 keV spread on a ~0.5 MeV beam and measured 13.3 keV (Ponter et al., 2010).
• Silicon detector. A PIPS diode, energy-calibrated against a known alpha source (Spraker et al. practice), reads the energy of beam particles scattered from a thin foil — after correcting for scattering kinematics and energy lost in the foil. Certificate-grade detectors resolve 11 keV FWHM for alphas at their recommended +130 V bias (Canberra BKPD 50-11-500 certificates, 2012), comparable to or finer than an amateur beam's spread. The design problem is count rate rather than resolution: the detector wants thousands of particles per second, while even a nanoamp carries billions, so the foil-and-angle geometry does the attenuating.

The classical final proof — a nuclear reaction with a known threshold, like prompt gammas from LiF on the probe tip (Wouters) — doubles as an energy bound. It also means deliberately making radiation, with the shielding, monitoring, and survey obligations of Safety; it belongs with the experiments a small beam can actually run, and stays outside this page's scope.

Beam quality within amateur reach

Professional beam quality is emittance: the phase-space area, in mm·mrad, that focusing can reshape but — in ideal transport — never shrink (glossary; what these parameters mean and what degrades them is its own page). Measuring it takes slits or grids and a drift space — done exactly once among the documented student machines, with dedicated beamline hardware, yielding ~25 mm·mrad radial from a PIG source slit (Forringer thesis). For a first machine, four humbler numbers describe the beam honestly:

• Radial profile — the current-vs-radius curve of the previous section, plus where it ends.
• Vertical extent — a slotted target or witness plate in the MDDC-984 pattern; the beam should fit well inside the dee aperture.
• Energy spread — for multi-turn extraction, of order 2qV_dee from turn overlap, with V_dee the peak gap voltage (Baartman): a ~20 keV scale at a 10 kV dee. Turn structure visible on a differential probe means the spread can be narrower at a well-chosen radius.
• Time structure — the “continuous” beam is bunched: on the Rutgers machine, into roughly 40° of each RF cycle, so average current there understates peak by about 9× (Koeth, CAARI 2014); the width varies with machine and tuning, and it matters for any counting or pulsed diagnostic downstream.

One expectation-setting ratio belongs in this list: with a classical electrostatic deflector, the era's best was ~25% of the circulating beam extracted under optimum tuning, and routine operation got less (Livingston & Blewett, p. 182, on the MIT machine; H⁻ stripping machines extract nearly everything, but no amateur machine is one). A machine should be judged first on its internal-probe current at full radius; a 4:1 internal-to-extracted ratio is historically normal, not a defect.

First beams, then and now

In every case on this page, first beam was followed by months of measurement before the machine was believed. The 184-inch made first beam in November 1946; the commissioning memos above, dated February through June 1947, are its crew still proving what the pips meant. The Oak Ridge 86-inch made first beam in November 1950, and “a period of eight months elapsed . . . before reliable performance at high beam currents was achieved” (ORNL-1196, p. 97) — after which it ran production with the target shaft itself insulated as the metering lead and a modified watt-hour meter integrating the beam charge (ORNL-1196, pp. 72, 82). The student machines above went through the same arc at a millionth the current. The builds census records first-beam currents where builders published them; a reported current means more once the reader knows what a defensible one costs to obtain.

Go deeper

• The design guide's beam-measurement rules and detector rules — the builder's reference behind this page: each rule with its formula, source, and page citation.
• Energy, field & radius calculator — the energy determination, interactive; path length & turns for turn-spacing arithmetic.
• Hosted classics: the 184-inch commissioning papers (radioautographs, two-probe method) and ORNL-1196 (a production machine's metering, and its eight humbling months).
• Faraday cup, beam current, emittance, and equilibrium orbit in the glossary.
• Should you build one? — the page whose “underwhelming results” section this one answers.

Sources

• J. Vale, “184-inch Cyclotron Vertical Beam Oscillations in the Region of 82-inch Radius,” MDDC-984 (1947); F. W. Yeater, “Synchroscope Beam Pictures on Two Probes,” MDDC-987 (1947) — both hosted here.
• M. S. Livingston et al., The Oak Ridge 86-Inch Cyclotron, ORNL-1196 (1952) — hosted here; commissioning narrative pp. 97–98, current metering pp. 72–82 (PDF pages).
• M. L. E. Oliphant & E. Rutherford, “Experiments on the Transmutation of Elements by Protons,” Proc. R. Soc. A 141, 259 (1933), doi:10.1098/rspa.1933.0117 — magnetic secondary-electron suppression, H₂⁺ conditioning.
• M. S. Livingston & J. P. Blewett, Particle Accelerators, McGraw-Hill, 1962 — probe diagnostics (p. 174), extraction efficiency (p. 182), field measurement (pp. 283–288).
• L. F. Wouters, General Recommendations for the Design of Small Cyclotrons, LASL — first-beam procedure and beam authentication (p. 11).
• P. Forck, Lecture Notes on Beam Instrumentation and Diagnostics, Joint University Accelerator School, GSI (PDF) — Faraday cups §2.4, scintillation screens §3.1.
• Keithley Instruments, Model 617 Programmable Electrometer Instruction Manual, free from Tektronix.
• Rutgers 12-inch cyclotron documents: T. W. Koeth, Ion Source Studies Part I (2006); T. Ponter et al. and T. W. Koeth, Small Cyclotron Conference 2010 presentations — see the library (search “Rutgers”).
• Houghton College theses (Loucks 2007, Haas 2009, Fuller 2013, Morrow 2015) and Cyclotrons 2010/2013 papers — see the library (search “Houghton”) for links to the college archive.
• Canberra Industries, PIPS detector instruction sheet and BKPD 50-11-500 AM certificates (2012) — bias and resolution figures verified against the certificates; J. M. Spraker et al. on solid-angle calibration practice.
• R. Baartman, cyclotron beam dynamics (JINST 2023) — multi-turn extraction energy spread; J. I. M. Botman & H. L. Hagedoorn, CERN Accelerator School — differential probe technique.