Finding and Keeping a Beam

The setting you command and the quantity that changes, knob by knob:

Knob (what you set)	What actually changes	What to remember	On the documented machines
Magnet current	The magnetic field, and so where the resonance falls	The field differs from what the current implies: hysteresis, coil temperature, probe position. Read it with the RF off	Moved during every run; sweeping it at fixed RF is the standard way to find resonance (Livingston & Blewett (1962), p. 156)
RF frequency	Where the tank is driven	The dee voltage follows only if the tank is tuned there	Set before the run on a fixed-frequency machine; touched again when the tank drifts (My RF circuit tunes up nicely on the bench. Why does it change when I close the chamber, pump down, turn on the source, or raise the power?)
RF drive level	The amplifier’s input, and so the power delivered	Dee voltage rises as the square root of delivered power; the amplifier’s temperature rises too	Mullins: no beam below about 70 mV of drive, diminishing returns and hot transistors above 200 mV (§4.3)
Filament current	The heater’s temperature	Emission is extremely sensitive to it (Wolf (ed.), p. 38-39); approach the optimum from below while watching the meter	Mullins optimum between 2.35 and 2.7 A across three filaments, with a useful range a tenth of an ampere wide (§4.3)
Filament bias	The energy of the electrons that make the ions	Its effect varies by machine and was not modelled on either	Mullins: changed emission and the peak’s position in field; Houghton: no measurable difference over the range tested (§4.3; Fuller (2013), p. 48-49)
Gas flow	The chamber pressure and the source’s output	Low flow gives a clean narrow peak; ten times the flow gives more current and a wider, uglier one	Moved during runs (§4.3; What's the simplest practical way to control the gas flow and the chamber pressure? Needle valve, leak valve or mass-flow controller, and can I leave the setting alone once I find it?)
Collector bias and position	Which current the meter reads, and at which radius	A measurement adjustment first; a collector pushed inward intercepts the beam, and a bias can influence slow charged particles near the plate	Bias suppresses secondary electrons so the reading means ion current (How do I know my beam-current detector could detect the beam I'm looking for, before I use it to troubleshoot the cyclotron?)

Some of the knobs establish the basic operating conditions, some help you find resonance (the ions circling in step with the RF, so that each crossing of the accelerating gap speeds them up), and others affect how you measure the result. The setting you command and the quantity that changes are never the same thing (It worked yesterday. Why doesn't putting every knob back where it was bring the beam back?). Magnet current. The ions, the charged particles being accelerated, respond to the field, which differs from what the current implies by hysteresis (the iron’s field depends on whether the current was raised or lowered to reach it), coil temperature and the probe’s position. The resonance is found by moving this knob with the RF fixed, which Livingston and Blewett give as the standard technique (Livingston & Blewett (1962), p. 156). On the Mullins machine the field knob is a programming voltage into the supply, 6.1 to 6.7 V for 570 to 600 mT, swept (ramped slowly through a range) or set by hand. The field is read on a Hall meter with the RF off (hosted operators-manual note, §2, §4). RF frequency. It is a setup adjustment on a fixed-frequency machine and an operating control on a swept one (I keep seeing "cyclotron resonance", "RF resonance" and "impedance matching". Are these the same thing? What has to match what?). The Mullins log settled at 8.8 to 9.1 MHz from 2020 on, after earlier running at about 3.3, 6 and 11.5 MHz (hosted rf-dee-source note, §3.4; performance note, §5). RF drive level. Power rises as the square of voltage, and the amplifier’s temperature rises with the drive as well (How much RF power do I need, and how does that become voltage on the dee? Can I read the voltage off the power meter, or do I have to measure it?). The Mullins log ran 110 to 160 mV of generator drive, found no beam below about 70 mV, and found diminishing returns and hot transistors above 200 mV (§4.3). Filament current (the heater current, under the Mullins log’s column name) changes emission, which is extremely sensitive to the filament’s temperature (Wolf (ed.), p. 38-39; My filament is glowing. How do I know it's actually making ions? And what are the filament current, the bias voltage and the emission current each telling me?). The Mullins optimum moved from 2.7 A to 2.35 A across three filaments, all above the 1.8 to 2.0 A knee its bench test found, and the manual’s rule is to approach it from below while watching the electrometer (§4.3; rf-dee-source note §6.3). Filament bias. On the Mullins machine it changed emission, the peak’s position in field and the beam’s sensitivity to filament current, with no model made; on Houghton’s it made no measurable difference over the range tested (§4.3; Fuller (2013), p. 48-49). Gas flow. The shape of the beam peak (the rise in collector current as the magnetic field passes through resonance) follows the flow as well. The Mullins log’s trade-off is a clean narrow peak at low flow against more current and a wider, uglier one at ten times the flow (§4.3; What's the simplest practical way to control the gas flow and the chamber pressure? Needle valve, leak valve or mass-flow controller, and can I leave the setting alone once I find it?). Collector bias and position. The collector is the plate the beam lands on. Ions striking it knock low-energy electrons out of its surface, and each electron that leaves takes a negative charge away, which the meter counts as extra positive current. The bias is a voltage on the plate that pulls those electrons back; it suppresses secondary electrons so the reading means ion current, and the position sets which radius you are reading. Both can also affect the beam: a collector pushed inward intercepts it, and a bias can influence low-energy charged particles near the plate (How do I know my beam-current detector could detect the beam I'm looking for, before I use it to troubleshoot the cyclotron?).

The Rutgers 12-inch run-up has the shape of a run on the documented machines: pump, gauge off, magnet on, bias on, heater up until emission reaches its target, then gas until emission rises (Koeth (2006), p. 5). During commissioning the RF frequency and match (the adjustment that lets the amplifier’s power into the tank instead of reflecting back) are adjusted repeatedly, and on some machines the source or the collector is moved while running (Hausman (1954), p. 6; Howard (ed.), p. 10; Where exactly should the filament or the source opening go? Is "at the center" good enough, and how do the first orbits avoid hitting the source?). On a fixed-frequency machine the RF match and frequency are typically set before the run and touched again when the tank drifts (My RF circuit tunes up nicely on the bench. Why does it change when I close the chamber, pump down, turn on the source, or raise the power?). The dee’s clearance and the pressure gate are set less often still. Wouters’ 1949 design recommendation covers the whole class: choke and bypass every circuit connected to a tank element so that RF stays out of the meters and supplies, and make the controls and meters for the magnet, source and RF readable and adjustable from the operating position (Wouters (1949), p. 9). The Mullins rack is one implementation of it, with every supply switched from one panel behind a keyswitch and every gauge read as a voltage on a panel meter (§2).

If it does not work. Three questions apply to each knob. Accuracy: does the commanded value equal the physical one? Mostly not, and it mostly does not matter, because the operating point is found by watching the beam. It matters when a number is quoted. Log the quantity: the magnetic field with the RF off, the electrode voltage rather than the supply setpoint (Rovey (2007), p. 2), the chamber pressure rather than the valve turns. Stability: does the quantity hold while you look elsewhere? The magnetic field drifts with coil temperature and the tank’s resonant frequency with tank temperature. The Iowa State machine held its field to a few parts in ten thousand with a regulated supply, and found that study results taken before the field was regulated were only qualitative (McGuire (1961), p. 9, Burns (1961), p. 6). A small machine can live with drift if it re-finds the peak often and logs when it did. Range: can the knob reach where you need it? The Mullins drive could not go below 70 mV and make beam, nor usefully above 200 mV. The filament optimum sat just above the emission knee (the heater current at which emission turns on sharply), so the useful range of that knob was a tenth of an ampere wide (§4.3). A knob with a narrow useful range is one to set by watching the result, not by its dial. The knob that moves the beam and the knob that was moved last are the two first suspects when something changes (It worked yesterday. Why doesn't putting every knob back where it was bring the beam back?).

To understand it. The classical machines turned the live knobs into regulated loops and the setup adjustments into interlocks. Magnet current regulated to a part in a thousand or better (Livingston & Blewett (1962), p. 194, McGuire (1961), p. 9). Arc voltage and arc current held by two independent loops (Livingston & Boch (1952), p. 66). A filament-arc regulator that trims the heater to hold the arc, which one ORNL study found shortened filament life compared with running the heater at constant current (Yonts (1954), p. 12, Yonts (1954), p. 15). Dee voltage servoed; and the tune held by a phase comparison, which Houghton, a college machine, also built (Koeth et al. (2010), p. 21). The University of Washington’s control requirements: Everything interlocked so that no single fault can do serious damage, every major system startable from one position in a definite sequence, and pilot lights for every state (The University of Washington 60-Inch Cyclotron: Progress and Status…, p. 95). For a first beam the amateur equivalent is a written startup and shutdown order with its abort points. The Mullins note reproduces its 2021 checklist with the corrections five years of running made to it (hosted operators-manual note, §3, §5, §7). The checklist is part of the operating system, not a substitute for protective controls and interlocks (What safety checks, expert review and local permissions do I need before I start testing the subsystems?).

Each test below has a prerequisite, an observable, and a limit on what it proves, because a subsystem that powered on without an obvious failure has not been shown to do anything. The Rutgers group’s version of the distinction: beam that is low even close to the source points at the source, not the RF (Koeth (2006), p. 1).

The vacuum system, with nothing inside. Blank off the pump with only a gauge on it and read its ultimate, the lowest pressure it reaches. Then add the plumbing, the empty chamber, and the chamber with its contents, reading each time. The Mullins note records exactly that: pumps alone 1.8 × 10⁻⁶ torr, empty chamber 3.4 × 10⁻⁶, working chamber near 10⁻⁵ (hosted chamber-vacuum note, §12). A rate-of-rise curve, the pressure’s climb over time with the pump valved off, hints at leak versus outgassing (gas leaving the inner surfaces) (My pump is rated to reach a much better vacuum than I need. Why can't my chamber get there? What are pumping speed and conductance?). What it proves: the pressure the beam will see, roughly, and whether the system is tight. What it does not: anything about the gas-on pressure, which the source sets.

The magnet, with a meter. Read the magnetic field at the centre against the coil current, going up and coming down. That measures the hysteresis loop (Zickler (2010), p. 26). A cheap Hall meter and a current reading are enough to put the field where the RF frequency says it should be (the field sets how fast an ion circles, so the RF frequency fixes the field that matches it). The Mullins calibration table is such a set of readings (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?). What it proves: that the expected resonance field is approximately within the supply’s range. What it does not: that the assembled machine will accelerate at that field, or the field’s shape with radius, which Level 2 of the magnet entries covers if it becomes necessary.

The ion source, on the bench and in the gap. The filament’s emission can be measured with the collector as an anode, a plate held positive to draw the emitted electrons, with no RF and no beam. The Mullins bench test found emission turning on sharply between 1.8 and 2.0 A of heater current at 101 V of bias, and the machine has always run just above that knee (hosted rf-dee-source note, §6.3). With the magnet on, the dee can be biased negative with DC, so that it draws the positive ions out of the source with no RF, and the ions collected. The Rutgers group characterized its source that way across pressures and arc currents before relying on the cyclotron for it (Koeth (2013), p. 2), and the 63-inch tested its source by collecting after a half-turn in the magnetic field (Howard (ed.), p. 24). It is an option, not a prerequisite; the Mullins machine never ran it. What those prove: that electrons are emitted, that ions can be drawn out, and roughly how many. What they do not: that ions are born where the RF can capture them, or which species they are (My filament is glowing. How do I know it's actually making ions? And what are the filament current, the bias voltage and the emission current each telling me?, Where exactly should the filament or the source opening go? Is "at the center" good enough, and how do the first orbits avoid hitting the source?).

The RF system, cold and then hot. On the bench the tank, the dee’s resonant circuit, can be resonated against a capacitor standing in for the dee, which the Mullins builder did against a plastic “simulated chamber” of 387 pF. The resonance then has to be found again installed, because the real dee and lids are a different capacitance (hosted rf-dee-source note; §4.1; My RF circuit tunes up nicely on the bench. Why does it change when I close the chamber, pump down, turn on the source, or raise the power?). With the chamber closed and pumped, the pickup (a small probe that samples the dee’s RF) shows the resonance and the reflected-power meter shows the match. The ring-down of a pulsed dee (the decay of its voltage after the drive is cut) is an optional check for whether a low-voltage discharge band, a range of dee voltages at which a discharge forms, sits in the way (Fulbright (1961), p. 4). What those prove: that RF is present and the circuit has a measurable resonant response at the chosen frequency. What they do not: the voltage at the accelerating gap, which stays an inference until it is independently established; the Mullins pickup never was calibrated, and the machine found beam without that (How much RF power do I need, and how does that become voltage on the dee? Can I read the voltage off the power meter, or do I have to measure it?).

The detector chain, with the beam suppressed. Run the RF at operating power with the gas off, which starves the source, or the magnetic field far from resonance, which leaves any ions out of step with the RF, and log what the electrometer reads. A beam reading must stand above that floor, read under conditions where accelerated beam should be absent (the beam-measurement chapter). Vary the collector bias and confirm the reading settles to a plateau, a range over which it stops changing. Inject a known current if you can. It is the test the record most often skipped (How do I know my beam-current detector could detect the beam I'm looking for, before I use it to troubleshoot the cyclotron?).

If it does not work. The tests sort the failure, and the order you run them is the order of cost rather than a prescription. No volts on the dee is found cold, with the pickup, before anything else is energized. No emission is found with the heater and bias alone. No ions drawn out is found with the DC-biased dee. Pressure that will not reach the gate is found with the gauges and the valve. Each of those is a subsystem that has not yet done its job, and none of them needs the others to be tested. A test can pass and still mislead. The Rutgers 12-inch’s first pole tips were ground parallel to a part in ten thousand and gave a magnetic field with no focusing at all, nothing to hold the ions near the midplane between the poles, which the report says lost nearly every ion to the dee lids (Koeth, p. 1). And a test done in a reduced configuration carries over only as far as the configuration does. The ISU group declared results taken before its field was regulated to be qualitative only (Burns (1961), p. 6). Log what configuration each test was run in.

To understand it. The large machines staged commissioning deliberately. Nevis debugged its source and central region with the beam stopped at small radius in graphite, where no neutrons were made, before surveying full radius at reduced duty (Rainwater et al. (1971), p. 5). Davis ran heavier, slower species until its shielding vault was finished (Jungerman (1966), p. 7). The 44-inch was rebuilt with a spacer that let it run at a third of its energy for test operation (Howard (ed.), p. 20). The University of Washington scheduled the machining of its deflector (the beam-extraction electrode) to begin only after an internal beam existed (The University of Washington 60-Inch Cyclotron: Progress and Status…, p. 116). Those are the professional versions of the amateur sequence: ion source glowing, chamber at pressure, resonance on a signal generator (the build-guide chapter). The scale-model habit, building the RF circuit at reduced size before building it full size, is documented at every large machine and is what the bench capacitor stands in for (Anderson (1947), p. 16).

The Mullins machine’s detector chain is one copper plate on a translator, one electrometer, and a scope. The note calls the plate a “pseudo-Faraday cup” (a Faraday cup is a metal cup that catches charged particles so their current can be read) and traces the order-of-unity limit to the alligator-clip lead and friction-fit ground between them (hosted instrumentation note, §3, §5).

The background, with the beam suppressed. Two things about the background matter: its size, which a peak has to stand above, and whether it is steady, fluctuating or drifting, which decides how much a peak of a given height means. It changes when a choke (the inductor that keeps RF out of the lead) degrades or a leak path appears, so it is logged every session (the beam-measurement chapter). The Mullins log carries a same-configuration background row beside every signal row from mid-2020. The best beam on record is quoted as 5.6 times its background for that reason, a ratio of signal to the background’s size, not to its fluctuation. The same note records a baseline that stepped and drifted, so the quotable evidence on that machine is the reproducible peak rather than the number (hosted performance note; instrumentation note §5, §9). The bias plateau. Ions landing on the plate knock out low-energy electrons, and each one that escapes counts as an extra positive charge, so an unsuppressed plate reads high. A bias voltage on the plate that pulls the escaping electrons back stops the loss. Bias the plate and vary the bias. When the reading stops depending on it over the range you can test, you have evidence that secondaries are no longer dominating the reading, though leakage, interception and other artifacts can remain (Fuller (2013), p. 55-56, Yuly (2013), p. 4-5). The Mullins record shows the cost of skipping this: its early positive currents were inflated by secondary emission, and the sign of the logged current flipped when the bias was applied correctly in mid-2020. The early absolute currents are not to be trusted, though the resonances were real throughout (instrumentation note §4). Leakage. Disconnect the plate at the feedthrough and read the meter; whatever remains is the cable and the insulators, not the beam. Response time. An electrometer on its low ranges settles in seconds, and a narrow peak swept past it too fast is not seen. The Mullins log found that a four-minute sweep showed pulses that faster sweeps hid (instrumentation note §7). A known signal. The electrometer’s own source, a resistor from a battery, or the filament’s emission current collected on the plate with no RF proves the meter reads and the lead conducts. The last is how the Mullins plate was first used (rf-dee-source note §6.3).

If it does not work. The null reading needs the most care, and its meaning depends on what the chain has been shown to do. Nothing on the meter means no current above the background at that radius with that bias, and that is all. It does not mean no accelerated ions exist. The plate may sit outside the radius the beam reaches, a shield in front of it may be intercepting the beam, the bias may be wrong, or the lead may be open. The 12-inch’s shielded cup had a lip thicker than the turn spacing, the radial step between one turn of the spiral and the next. The ions landed on the lip, which was grounded, and their current drained away unread before the sensitive surface saw them. The fix was a bare block and a choke in the lead outside the vacuum (Koeth (2006), p. 4, Koeth (2006), p. 1, Koeth (2006), p. 1). A reading that will not go away when the magnetic field is detuned (moved off the value that matches the RF), the gas is shut, or the RF is pulled off resonance needs another explanation before it is called beam. A real accelerated beam responds to field and frequency in the way cyclotron resonance predicts, dying on a small detune, a few gauss on the documented machines, a gauss being a ten-thousandth of a tesla, so a few gauss is about a part in a thousand of a 0.6 T field (beam-measurement chapter, #real-beam). A small move of the magnetic field leaves the ions arriving at the gap out of step with the RF, gaining nothing, and falling short of the collector. A signal that does not show those relationships may be stray current, non-resonant particles or another process, and some backgrounds depend on field or frequency too. No single test excludes every other explanation (the beam-measurement chapter, citing Wouters). A reading that steps or jumps with nothing changed points at the lead and its connections before the machine. The Mullins note names its clip-lead segment as a plausible contributor to its baseline steps, alongside gas-flow variation, and does not choose between them (instrumentation note §5). A current that rises as the collector moves inward past where the beam should be can be low-energy ions and electrons rather than beam. A positive bias reduces that contribution, as one classical machine found inside six inches (Heusinkveld et al. (1955), p. 12). A reading that changes sign is the bias case above. The order of these checks is whatever the symptom suggests; none of them requires beam.

To understand it. The Faraday cup is in principle an absolute instrument, with no gain and no calibration (every charge that lands is counted once), but only when each error source is dealt with. Secondary emission is suppressed by bias, by a retarding grid, or by the machine’s own magnetic field, which traps a 10 eV electron in a millimetre-scale spiral, so it stays at the plate (the beam-measurement chapter, citing Forck and Oliphant and Rutherford). RF is kept out by a series choke in the lead rather than a thick shield around the tip (Koeth (2006), p. 1). Leakage is held down by high resistance to ground and chokes and bypasses at the meter (Wouters (1949)). The meter sits at ground potential in the return leg, never floating on the hot side (What should be grounded and what needs to float? I have a filament heater supply, a filament bias supply, RF drive, a biased collector plate going to an electrometer, a magnet supply, vacuum-gauge supplies, and exposed metal everywhere. Which parts can be tied together, which must be isolated, and what does "floating" actually mean?). An open plate in the fringe field (the weaker magnetic field at the edge of the poles), as on the Mullins machine, has only the field doing part of the suppression, so its reading was always relative (instrumentation note §3). The classical cross-checks, a nuclear signature from a LiF tip (radiation from a nuclear reaction, which no stray current can produce) or a second probe at another azimuth, turn a peak into a proof (Wouters (1949), p. 11; How do I know my cyclotron is actually working? If I measure a current, how do I know it's accelerated particles rather than something else in the chamber?). The Keithley 617 manual, which the documented student machines used, covers the low-current practice: short cables, clean insulators, zero-check, and patience on the low ranges.

The Rutgers 9-inch found its first beam on 16 September 1999 by slowly sweeping the magnet with the RF fixed (Koeth et al. (2010), p. 8). The Mullins machine found its 2018 resonances the same way: a 600-second triangle ramp on the magnet supply and the collector current drawn against it on a persistence display (a scope that keeps the trace on screen). Houghton’s first protons were 1.5 pA at 15 W of RF (Haas (2009), p. 69). Wouters’ 1949 instruction to the six-inch builder is still the method. Push the collector, on its movable arm, in toward the centre, where the resonance tolerance is loosest (an ion that has made few turns has had little time to fall out of step), and rock either the magnet current or the RF frequency back and forth until a current peak appears (Wouters (1949), p. 11). The pattern in each case is the same. Establish approximate conditions for each subsystem; then vary one main parameter, usually the magnetic field, while watching for a reproducible signal.

Before any of it, the safety checks and stop conditions of the earlier group are done and written down, the survey instrument is on, and the amplifier’s protection is in place (What safety checks, expert review and local permissions do I need before I start testing the subsystems?, Can the machine make radiation, or hurt me some other way, before I've even detected a beam?, People talk about RF "conditioning". What does that mean, and how do I tell conditioning from a fault that means I should stop?). Then the sequence the physics suggests, and the documented machines followed: Settle what does not need beam (What can I test before the whole cyclotron works? How do I check each subsystem without already having a beam?): the chamber at its pressure gate, the RF tank resonant at the chosen frequency with the match made, the detector’s background logged. Set the magnetic field where the frequency says the proton resonance should be, using the cheap meter, read with the RF off. The field sets how fast a proton circles, so the RF frequency fixes the field that matches it. The relation is 65.6 mT per megahertz for protons, and the Mullins log precomputes that field, and its third and fifth, for every run; at a third of the field a proton circles at a third of the RF frequency and still meets the RF in step on every third cycle, and likewise at a fifth (hosted operators-manual note, §3, §4.2). Bring the source up until emission is at its usual value and gas until the pressure is in the window (My filament is glowing. How do I know it's actually making ions? And what are the filament current, the bias voltage and the emission current each telling me?; 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?). Then sweep the magnetic field slowly across the expected value and watch the collector. The Mullins log found that a four-minute sweep showed peaks that faster sweeps hid, because the electrometer takes seconds to settle on its low ranges (instrumentation note §7). A peak that re-draws in the same place on every pass is a candidate; random noise and baseline steps seldom repeat, though an artifact tied to the sweep itself can, which is what the controls are for. Wouters supplies the checks in the same paragraph as the method. The peak should sharpen and die on a small detune of field or frequency, and it should respond to the gas (the beam-measurement chapter; How do I know my cyclotron is actually working? If I measure a current, how do I know it's accelerated particles rather than something else in the chamber?). The gas check rests on the ions being made from the gas. The Mullins practice when the sweep shows nothing is to set the field near the expected value, tune the RF frequency for maximum collector current, and only then sweep. Its log reads “found RF freq by peaking DC current after close resonance” (instrumentation note §7).

If it does not work. The sweep shows a flat line. A flat line is what four different absences look like. The Mullins log’s own words: “easy to miss resonance; if no RF or resonance, flat output from sweep on electrometer, tough to distinguish” (instrumentation note §7). The four are no dee voltage, the wrong frequency for the magnetic field range swept, no ions reaching the gap (the space between the dee’s edge and the facing electrode), and a detector that cannot see them. Each has a check that does not need beam (What can I test before the whole cyclotron works? How do I check each subsystem without already having a beam?, How do I know my beam-current detector could detect the beam I'm looking for, before I use it to troubleshoot the cyclotron?). Which to run first depends on what was last changed and what the pickup and the emission meter already say. Widen before you narrow: if the expected magnetic field is uncertain by a few percent, sweep wider and slower. Look for the sub-harmonic peaks at a third and a fifth of that field as a check on the main one; a family in those ratios is consistent with one species on odd harmonics, and what it does and does not identify is beam-which-ion’s subject. The Mullins 2018 scan of the low-field region showed a whole family of them, each within a few millitesla of an odd fraction of a hydrogen fundamental, the field at which one hydrogen species circles once per RF cycle (instrumentation note §7; Table 5; Yuly (2013), p. 4-5; Fuller (2013), p. 46-47). Change one thing per sweep and write down the three readings that matter, magnetic field with RF off, pickup, pressure, beside the collector reading (It worked yesterday. Why doesn't putting every knob back where it was bring the beam back?). Give the magnet its settling time. A supply that has just been stepped takes seconds, a coil that has been running takes longer to stop drifting, and the magnetic field read during a fast ramp lags the current, because the changing field induces eddy currents in the solid iron that oppose the change (Zickler (2010), p. 23; Zickler (2010), p. 26; 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?). A peak that is broad, double or ugly makes gas and filament reasonable things to investigate, both quick to try; the Mullins log found them behind its own ugly peaks. The shape alone does not identify the cause (operators-manual note §4.2; §8; 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?). A peak at the wrong field may be a different ion (another mass or charge matches another field) or a harmonic (the ion going round once every three or five RF cycles, as above). The Mullins log also records its proton peak moving by a few percent with filament bias, mechanism not established (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?; My ion source is on all the time, but the RF keeps reversing. How do the ions start at the right moment? Do I have to synchronize the source with the RF?).

To understand it. The two knobs explored together, magnetic field and source, are the two whose right values cannot be computed well enough in advance. The magnetic field, because the meter at one point and the field averaged around the orbit disagree by percent; the source, because emission and gas interact in ways the log calls “somewhat dependent”. The rest can be set from a measurement without beam, so a first beam is usually a search along the field axis with the source re-examined between passes rather than over seven knobs at once. The classical resonance-curve procedure is the same search done carefully. Hold the frequency and dee voltage fixed, fix the target radius, and sweep the centre field through the beam’s tuning range, recording the current. The curve’s width and position then become the machine’s most reproducible measurement (Burns (1961), p. 3, Burns (1961), p. 6). The Rutgers 12-inch’s published run-up is the ordered checklist version for its configuration (Koeth (2006), p. 5). The Rutgers 9-inch made ten nanoamperes on flat poles, and the Mullins machine made its peaks within a fraction of a percent of the predicted field with a $111 meter (The books make the magnet requirements sound beyond amateur reach: field uniformity, steel homogeneity, and so on. Some amateur builds look much simpler. How good does my magnet really need to be?, 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?).

The resonance itself sets the narrowness. An ion in a magnetic field circles at a rate set by that field and by its charge and mass, and it gains energy only if the RF reverses in step with each gap crossing; that match is the resonance.

What to do: keep a log whose columns are measured quantities, attach the sweep trace (collector reading against the magnetic field as it is swept), and log the measured dee voltage if you have one; otherwise record the RF pickup reading (a probe near the dee whose signal follows the dee voltage), the drive power and the tuning conditions, marking which quantities are relative or estimated (dg-408 for logging the electrode voltage wherever it is measurable). The Rutgers 12-inch published its run-up for its own configuration, and the shape of it transfers even where the numbers do not: pump down, magnet to its standing current, bias on, heater up until emission reaches its mark, gas until emission rises, RF tuned to the tank’s resonance and brought up to power, then sweep the magnetic field watching the electrometer, the meter on the collector (Koeth (2006), p. 5). Let the magnet and the tank, the RF resonant circuit, settle. Sweep slowly enough that a narrow peak cannot slip between readings.

If it does not work. The hidden state is in four places.

Hysteresis and coil temperature. Iron has hysteresis: the same magnet current gives a different magnetic field depending on whether you came up to it or down to it. Cycle the magnet through the same loop to the same maximum every time and approach the operating point along the same branch, rising or falling (Zickler (2010), p. 26). Then the coils warm. On the Rutgers 9-inch the field-setting resolution was limited by cooling-water temperature, not electronics: warm copper has more resistance, a voltage-regulated supply then delivers less current, and the field walks (Koeth, p. 2). Large coils take hours to settle; the 86-inch’s needed one to three (Livingston & Boch (1952), p. 33). The cure is to read the field with a probe every run and log it, as COLUMBUS does with a fixed Hall probe, a sensor that reads the field (Prechtl & Wolf (2020)).

Resonance drift with temperature. Heat expands the RF tank’s coil and the dee and the resonance moves. Houghton automated retuning for this (Koeth et al. (2010), p. 21); the 9-inch pumped transformer oil through its coil to hold frequency (Koeth, p. 4). Even a probe clipped on to check things adds picofarads of capacitance, which with the coil sets the resonance, and shifts the resonance (Koeth (2005), p. 4). Record the dee pickup reading and the forward and reflected power, not the amplifier’s dial.

Filament age, gas and surface conditioning. A filament ages as it runs: its geometry, resistance and temperature distribution all change, so the same heater current need not give the same emission from one day to the next; one ORNL study tracked erosion, the thinning of the wire, from the drift of the heater current alone (Yonts (1954), p. 29). A hydrogen discharge changes its ion mix with running time: Oliphant and Rutherford’s source started mostly H₂⁺ and “after running for some time … becomes nearly all protons” (beam-measurement page). H₂⁺ is a hydrogen molecule missing one electron and a proton is a hydrogen atom missing its electron; their masses differ, so each matches the RF at a different magnetic field. After a vent, letting air into the chamber, surfaces outgas for hours and the same valve setting gives a different pressure (Bertolini (2004), p. 49). Dark current is the electron current the voltage alone pulls off electrode surfaces with no beam present. Electrodes condition: dark current drops as they run and jumps after every air exposure (safety page).

Collector artifacts. An unbiased collector reads secondary electrons along with beam; one 1954 program treated its target reading as a relative indication for that reason (Hausman (1954), p. 8). Ions striking the collector knock electrons out of it, and an electron leaving reads as one more positive charge arriving. RF picked up by the collector wiring raises the electrometer background, and the Rutgers collector lead carries a large choke, a coil that blocks RF while passing the steady beam current, against it (Koeth (2006), p. 1).

One machine’s list. The Mullins log’s own hidden-state entries, from its hosted instrumentation note: the Hall meter reads wrong with the RF on, high one day and low another, so the magnetic field is read with the RF off (§6); the Hall probe is pushed into the magnet gap blind and sits differently each time (§6); a sweep of 240 to 600 s is needed or the peak slips between readings (§7); the electrometer baseline stepped with gas-flow variation or a clip-lead ground (§5); and the collector ran unbiased, its readings inflated by secondary electrons, until mid-2020 (§4; hosted instrumentation note, /library/amateur/#mullins).

To understand it. The classical machines turned the hidden state into regulated loops and logged quantities: magnet current held to a part in a thousand (Livingston & Blewett (1962), p. 194), dee voltage servoed, arc current (the ion source’s discharge current) on its own loop (What are all the knobs, and what does each one actually change? Which are operating controls, which are setup adjustments, and which can I leave alone?). The amateur version is the log with measured columns, which is also what makes the result reportable (How should I document that my cyclotron is accelerating protons? What would someone else need to evaluate the claim?).

Houghton’s record describes beam current falling as the collector was moved outward and attributes it to loss before full radius (Fuller (2013), p. 52-53). Even the Mullins machine’s radius scans, taken with an open plate, show little change in peak current over an inch or two inward of its standard setting. One day showed more current at one inner setting (hosted instrumentation note, §3). A beam that exists near the centre is the starting point of every commissioning in the record.

Production is the source making ions, and a verified peak at small radius has shown that it does. Capture is the first turns clearing the source and staying near the midplane, the plane halfway between the pole faces where the orbits should lie, and the same verified peak has shown that too, for the ions that made it. The Rutgers group’s rule: low current close to the source, where the turn separation (the radial step per turn) is widest and nothing can mask the turns, points at the source, while current that appears close in and dies farther out points at what happens next (Koeth (2006), p. 1; the ion-sources chapter). Survival is the long part. Staying in step with the RF, staying off the dee lips (the dee’s upper and lower edges, the nearest metal above and below the orbit), and not being lost to the gas (a collision with a gas molecule can take an ion out of the beam), over the many turns from the centre to the collector. Collection is whether the plate at the larger radius is actually reading what arrives.

If it does not work. Three plain questions, in the order of cost, and each is a suspect to test rather than a verdict. Is the collector really seeing what reaches that position? A collector has a finite size and position. It reads what strikes its surface, plus whatever secondary and stray currents it picks up, and a particle can reach that distance from the centre without landing on the plate. So the curve of current against radius reflects the beam and the collector’s ability to intercept and measure it, together, and the measurement side is settled first. Anything in front of the collecting surface thicker than the local turn spacing intercepts beam the plate never sees: the ions step outward by less than the lip’s thickness on each turn, so they land on the lip first. The spacing shrinks with radius, since each turn adds about the same energy and the same energy step moves the orbit outward by less the farther out it is. It was 0.04 inch at four inches on the 12-inch at its voltage, so a 0.06-inch shield lip hid real beam there (Koeth (2006), p. 1, Koeth (2006), p. 4). Probe-edge scattering and electrons emitted from a hot probe can also distort a radial curve, in either direction (Oak Ridge National Laboratory (1963), p. 278, Howard (ed.), p. 40). Repeat the inner reading after the outer one to be sure the machine has not drifted between them. Could the particles be striking something before they get there? Clearance, orbit position and vertical confinement are the candidates. A dee lip, the source structure, a lid too close, an orbit centred off the machine’s axis, or focusing too weak to hold the ions near the midplane over the extra turns (Where exactly should the filament or the source opening go? Is "at the center" good enough, and how do the first orbits avoid hitting the source?, How accurately do I need to line up the magnet, chamber, dee, ion source and collector? Which dimensions are really critical, and what should be adjustable?, The drawings show a flat spiral. What keeps the particles from wandering up or down and hitting the dee? Do I need "focusing"?). Could they be running out of acceleration, or be lost to gas? More turns means more accumulated phase slip (the drift of the ions’ arrival time at the gap away from the peak of the RF voltage, growing a little each turn when magnetic field and RF frequency do not quite match) and more path through the gas, and both grow with radius on a low-voltage machine (My ion source is on all the time, but the RF keeps reversing. How do the ions start at the right moment? Do I have to synchronize the source with the RF?, How many turns should a proton make before it reaches my target energy? Fewer turns sounds easier, but isn't the whole point of a cyclotron to accelerate over lots of turns?, 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?). The shape of the curve suggests which of these to look at first, and the beam-measurement chapter is explicit that it suggests rather than proves. A gradual fall with radius is consistent with weakening vertical focusing, which is the Houghton reading of its own curve (Fuller (2013), p. 52-53), and with other causes. An abrupt cutoff at one radius is consistent with phase slip: past a quarter cycle of accumulated slip the ion gains nothing at the gap and then loses (it arrives when the gap voltage has fallen to zero, and after that when it has reversed), so current drops suddenly beyond the radius the ions reach (Morrow (2015)). It is also consistent with an obstruction, with weak focusing, with a source effect or with collection geometry. A fall that recovers when the gas flow is reduced points at the vacuum budget. The lever common to the turn-count causes is more volts per turn (the same radius reached in fewer turns), which does not fix a wrong frequency, an unsuitable field shape or an obstruction (The literature says tens of kilovolts on the dee. Some amateur machines ran under a kilovolt. How is that possible, and what did it cost them?). What the classical machines looked at when the beam died at a radius is still the cheapest physical evidence: where it struck. Burn marks or heat tint on a dee lip at one radius, or on one side, say where and on which side the ions left the midplane. The 184-inch confirmed its loss radius from a sharp activation peak (metal made radioactive where the beam struck) on a dee lip (Sewell (1947), p. 3; magnet-dc-harmonics for the one-sided case). A five-segment probe on one ORNL machine showed most of the loss to the dees happening in the early turns, with little lost beyond half the maximum radius (Howard (ed.), p. 16). An early fall is therefore a reason to look at the central region before the outer field.

To understand it. The current-against-radius curve is highly informative when a movable collector exists, which is not a prerequisite for a convincing first beam, and should be taken carefully once the machine is stable. The same magnetic field, frequency, gas and emission at every radius, the background at every radius too, and the inner point repeated at the end (the beam-measurement chapter, citing Livingston and Blewett). The ways a curve can mislead are documented one by one: masking by a thick lip (Koeth (2006), p. 1), scattering from the probe edge (Oak Ridge National Laboratory (1963), p. 278), thermal emission from a hot probe (Howard (ed.), p. 40). The collector’s own radius may be known only to a convention, as on the Mullins machine, where two offsets differ by half an inch and the computed energy by a quarter, the energy being computed from the radius and growing as its square (instrumentation note §3). The classical diagnostics that resolve where the beam goes are two probes at different azimuths (angular positions around the machine), a shadow bar ahead of a movable collector, a slotted target that images the vertical extent, and a differential probe that resolves turns (the beam-measurement chapter, #probes-shadows). A threshold scan, the lowest dee voltage that still gives beam at several radii, distinguishes a limit at the centre from field errors spread over the machine (Oak Ridge National Laboratory (1963), p. 285). None of these is needed to call the machine partly working; they are the diagnostics the documented machines used to finish commissioning.