Proving the Beam

An accelerated beam exists only where the magnet’s field and the RF frequency satisfy the resonance condition for some charged particle (I keep seeing "cyclotron resonance", "RF resonance" and "impedance matching". Are these the same thing? What has to match what?). Wouters wrote the test down in 1949: check the sharpness of the resonance against RF tuning and magnet current, and its sensitivity to the hydrogen pressure (Wouters (1949), p. 11; beam-measurement chapter; #real-beam). The three controls are not three samples of one fixed background. The gas-off sweep shows what the RF and the collector produce without a discharge (with the feed closed the source has only residual gas to work on, so it makes far fewer ions, not none). The RF-off sweep shows what the source and the field produce without acceleration. The detuned sweep shows what survives when the resonance condition is broken and everything else runs. The Rutgers group ran the same controls on a neutron counter. They moved the target so it saw only low-energy ions, starved the source of gas, and detuned the field a little, and the signal followed the beam each time (Koeth (2017), p. 4). A control with the source off and everything else running, RF included, catches the machine’s own electrical noise (Koeth, p. 1).

The checks have to be combined because a collector signal has several other ways to arise, and each one passes some of the tests. Leakage across an insulator into the collector lead is steady and ignores the magnetic field. Rectified RF pickup, RF caught by the collector lead and read as a steady current, appears when the RF comes on. It can change with frequency because the dee voltage changes with tuning, so frequency dependence alone proves little. Secondary electrons, knocked out of the plate by arriving ions, read as positive charge arriving, so the bias plateau (the bias range over which the reading stops changing) comes before any number is quoted (How do I know my beam-current detector could detect the beam I'm looking for, before I use it to troubleshoot the cyclotron?). Electrons or slow ions from the source can reach the plate without any acceleration. They are charged particles, so they do respond to the magnetic field, just not sharply. Direct ions are source ions that fly one half-turn from the source into a nearby collector, at the field where their starting energy matches that radius. The magnetic field bends an ion on a circle whose radius is set by its energy, so at one field that half-circle ends on the collector. The COLUMBUS book computes the voltages at which that happens for its geometry (Prechtl & Wolf (2020), p. 74). Sub-harmonic beam is real accelerated beam at a third or a fifth of the predicted field, where the ion takes three or five RF cycles to go round once and still arrives at each gap crossing with the voltage pushing its way (Prechtl & Wolf (2020); Yuly (2013), p. 4-5; 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?). At a third of the field the ion takes three times as long to go round, so three RF cycles pass per turn and it still meets the gap in step. Tank modes: on the Rutgers 9-inch an unexpected peak at half the field was traced to a higher mode of the RF tank (the resonant circuit that drives the dee) rather than to a different ion; the particles were protons (Koeth, p. 8). A hot probe emits electrons thermally (Howard (ed.), p. 40), and one thesis labels one of its scan peaks “secondary collisions” (Cressman (2006), p. 12). The collector itself intercepts beam that would have gone farther, and its bias can pull in nearby low-energy particles. A signal that does not show the predicted field and frequency dependence needs investigation.

Keep three questions apart, because the same peak answers them to different degrees. Is something being accelerated? The resonance behaviour and the controls above answer that, and most finished amateur machines stand on that rung (What should count as a first success? Do I need to get the beam out of the chamber, or can I demonstrate acceleration with a detector inside?). What is it? The magnet field at the peak, at a known frequency, gives charge-to-mass ratio times harmonic number, not an identity, and hydrogen in does not mean protons out (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?). Charge-to-mass ratio is the ion’s charge divided by its mass, the only property of the ion the resonance condition contains; harmonic number is how many RF cycles pass per turn, one on the fundamental, three or five on a sub-harmonic. How much energy does it have? Almost always computed from field and radius, not measured. The site’s builds table marks every such energy “computed”, and professional practice found internal-target energies off by a tenth from that arithmetic (Cohen (1952), p. 5). The Mullins record keeps the three apart. Its hosted performance note lists what seven years of logging established. Resonance-locked, background-subtracted collector peaks appeared at the field predicted for hydrogen ions at the set frequency, on 42 dates across several rebuilds. The sub-harmonics sat in their predicted places, a third and a fifth of the main peak’s field, and the sweep went flat when the RF was detuned. It then lists what the record did not establish. The species, formally, because H₃⁺ on its third harmonic sits at the same field as H⁺ on the fundamental. H₃⁺ has three times the proton’s mass on the same charge, so its fundamental needs three times the proton’s field and its third harmonic a third of that. The energy, never measured. The dee voltage, nominal only. And controls taken on the same sweep. Its summary phrase is “hydrogen-ion cyclotron resonances consistent with acceleration” (hosted performance note, §5, §8; /library/amateur/#mullins). A machine can be convincingly working and still carry a list like that.

If it does not work. The checks fail in different ways, and each failure narrows the search without naming the cause by itself. The signal is flat across the whole sweep. No resonance was detected within the magnet’s field range and at the sensitivity you tested, which is all the observation says. If both were adequate for the beam you expect (How do I know my beam-current detector could detect the beam I'm looking for, before I use it to troubleshoot the cyclotron?), then leakage, pickup, thermal emission or a source current reaching the plate are the candidates for what the meter does show, and the RF-off and source-off controls split them. The signal appears whenever the RF is on, at any field. Pickup or an RF-driven discharge are the first things to test: move the choke (the coil that keeps RF out of the meter), change the lead, look at the pressure gauge (an RF-lit discharge needs gas). A broad bump at low field only. Direct or half-turn ions are a candidate. The COLUMBUS calculation gives the field at which they would arrive for your geometry (Prechtl & Wolf (2020), p. 74). Moving the collector changes what direct and accelerated particles both do, so compare what you see with that calculation rather than expecting one kind to vanish and the other to stay. A peak at exactly a third or a fifth of the predicted field. Beam on a sub-harmonic is consistent with it and is the first candidate to write down. Another species, an overlapping harmonic or an electrical signal remain possible until the peak passes the same checks as the main one. Label it with its candidates and keep going, since the fundamental, the full-field peak, may be above your magnet’s reach (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?). A peak at an unpredicted field. Compute the candidates before concluding anything: every plausible species times every odd harmonic (three, five, seven RF cycles per turn), the tank’s other modes (Koeth, p. 8), and the direct-ion field. A peak that survives gas-off or a detune. It may be unwanted current, a non-resonant particle, or a process that happens to depend on the field; some backgrounds do. That is a reason to investigate, not yet a verdict. A nuclear signature is radiation the beam makes when it strikes a target. If you add a nuclear signature, prompt gammas from a lithium target under proton bombardment for instance (Wouters (1949), p. 11), you are producing radiation on purpose. The survey instrument, the limits and the stop conditions of safety-before-beam come first, not after the count.

To understand it. The classical standard is two independent lines of evidence, ranked. The Iowa State machine read beam two ways, a microammeter from target to ground and a Geiger counter on the reaction rate from a lithium target. It judged the reaction rate the more reliable monitor, at about 1,500 counts a minute against 20 of background (Burns (1961)). The ORNL 63-inch supported its first beam with gammas at eight times background plus a physics argument about which charge state (how many electrons the ion is missing, which sets its energy gain per crossing) could carry enough energy to make them (Howard (ed.), p. 9). Wouters’ “final proof” was the lithium-fluoride probe tip (Wouters (1949), p. 11), a lithium target that gives the prompt gammas above. The Rutgers neutron work ran its three tests and its source-off control, and stated the inference chain from dose rate to yield in the paper (Koeth (2017), p. 4, Koeth, p. 1, Koeth (2017), p. 5). Cohen’s caveat applies to all of it: diagnostics taken with the machine detuned to a convenient intensity may not describe the operating beam, and the caveat is stated with the result (Cohen (1952), p. 9). None of the documented amateur machines needed a nuclear signature to claim first beam. COLUMBUS runs at tens of keV, where no usable nuclear signature is expected from its beam; nuclear reactions at those energies are far too rare to count with workshop instruments, not impossible. Houghton, the 9-inch and the Mullins machine claimed beam on resonance behaviour and controls. Rutgers and Iowa State added nuclear evidence later, when the energy allowed it and the experiment wanted it. The signature is a Level 2 or 3 step, and a radiological one.

The ions are made in a discharge (the glow a current lights in low-pressure gas), and which one dominates depends on the source and how it is run. An ion is an atom or molecule that has lost or gained an electron and so carries a charge; H₂⁺ is a hydrogen molecule missing one electron. The physics was settled a century ago with magnetic analysis of discharge products. Electron impact on hydrogen makes H₂⁺ first, protons come from breaking it, and H₃⁺ forms when an H₂⁺ meets another molecule (Smyth (1925), p. 1). Hogness and Lunn summarised what their discharge tube showed: H₂⁺ dominated at low pressure, H₃⁺ at higher pressure and small drawing voltage, and H⁺ was favoured by a large voltage and an inert carrier gas (Hogness & Lunn (1925), p. 9). Those are tendencies observed in particular apparatus, and a source of another type can sit elsewhere. The documented cyclotron sources show the spread. The Rutgers 12-inch’s PIG source delivered protons and H₂⁺ together, about five to one (Koeth (2013), p. 2). A hooded cold-cathode source showed no H₂⁺ at its normal operating point and grew some when starved of gas (Forringer (2004), p. 89). Oliphant and Rutherford’s fresh discharge was mostly molecular ions and became “nearly all protons” only after running for some time (Oliphant & Rutherford (1933)). Residual gas, the air and water the pumps have not removed, adds N⁺, O⁺ and H₂O⁺ to the list, though their resonances fall far from hydrogen’s because they are far heavier. Choosing a different particle on purpose is a separate question (Could I accelerate electrons or other ions instead of protons? Would any of those be easier for an amateur?).

More than one peak is normal, and the extra peaks are information. Hold the RF fixed and sweep the magnet’s field, and each species resonates where B = 2πf·m/(q·k), with k the harmonic number, RF cycles per turn. At the same frequency H₂⁺ needs twice the proton field and H₃⁺ three times it, since they carry two and three times the proton’s mass on the same single charge. Each species then repeats at a third and a fifth of its own field. There the ion takes three or five RF cycles to go round once and still arrives at each gap crossing with the voltage pushing its way, so it gains energy (Prechtl & Wolf (2020); Yuly (2013), p. 4-5). Only odd multiples work. With one dee and grounded lids the ion crosses two accelerating gaps per turn, and an even multiple of its circling frequency gives no net energy gain over the two (hosted performance note, §5). Houghton labelled one scan’s peaks H⁺/3, H⁺/5, H⁺/7 and H₂⁺/9 (Yuly et al. (2010), p. 15-18), and the COLUMBUS workshop reads its one-third and one-fifth peaks on purpose (Wolf & Prechtl (2022), p. 2). The sweep is “a cheap first-pass mass spectrometer for the internal beam” (Yuly (2013), p. 4-5). COLUMBUS reads the field at each peak, computes q/m from it (the formula turned round, with f and k known), and compares with the table. Their proton peak came out within one percent of the tabulated value, and a second peak whose computed q/m was about half the proton’s (twice the mass per charge, so twice the field at the same frequency and harmonic) was assigned to H₂⁺ (Prechtl & Wolf (2020), p. 69-71, Prechtl & Wolf (2020), p. 71). A sweep can also carry peaks that are not accelerated beam: direct ions at low field (Prechtl & Wolf (2020), p. 74), a tank mode of the RF circuit (Koeth, p. 8) and collisions (Cressman (2006), p. 12) are the documented ones (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?).

A peak’s position leaves some things open. Coincidences. H₃⁺ has three times the proton’s mass on the same charge, so its fundamental needs three times the magnet field a proton needs, and its third harmonic a third of that. At every frequency, H₃⁺ on its third harmonic lands at the field of H⁺ on the fundamental, because three times one third is one, and changing the frequency moves the two together. That is mass-number arithmetic. H₃⁺ is three protons with two electrons, so its real resonance field sits about 0.04 percent from the proton’s, far less than a peak’s width on a small machine. On the Mullins machine at 9 MHz the main peak at 593 mT can be either or both; a filament discharge in hydrogen at 10⁻⁵ torr indicated makes H₃⁺ readily, and a fixed-frequency sweep cannot separate them. The defensible identification from the log alone is “hydrogen ions” (hosted performance note, §5, Table 3; /library/amateur/#mullins). Fully ionised deuterium and He²⁺ nearly share a charge-to-mass ratio too: the deuteron has about twice the proton’s mass on one charge, the helium nucleus about four times on two, and the two differ by about 0.6 percent in mass per charge. The Rutgers group showed that even an embedded velocity filter does not split that pair in practice, since the cyclotron is itself a velocity filter at each radius (Koeth, p. 2). A velocity filter passes one speed only, and two ions with nearly the same charge-to-mass ratio at the same field and radius move at nearly the same speed. Energy. The peak’s position fixes q/m times k. It does not measure the energy, which is computed from the field and the collector radius once a charge state is assumed. The computed figure also depends on which field you use, centre or orbit-averaged (weigh-the-ion exercise; Livingston & Blewett (1962), p. 287-288). The meter. A field read with the RF on can be wrong in either direction on a cheap Hall meter, because the RF interferes with the meter, as the Mullins log recorded in 2019 (hosted instrumentation note, §6). A field approached from above reads differently from one approached from below (Gonski (2013), p. 3). A peak shifted by the meter looks like a different ion.

If your RF system can operate over a wide enough frequency range, lowering the RF frequency brings the fundamental resonances of several hydrogen ions within your magnet’s range. In the formula above every ion’s field scales with the frequency, so lowering the frequency lowers them all together. This can reveal additional peaks and help identify which ions are present. But some species-and-harmonic combinations overlap at every frequency, so even this scan may not uniquely identify the particles responsible for a particular peak. The H⁺ fundamental and the H₃⁺ third harmonic are the standing example. Lowering the frequency moves both together, and the peak at the proton field can carry either or both at every setting. The scan adds the H₃⁺ fundamental as a separate peak, three times higher in field. Its presence and size say whether H₃⁺ is in the source’s output at all, which is supporting information about the shared peak, not a separation of it. For the Mullins magnet, at or below about 4.3 MHz the H⁺, H₂⁺ and H₃⁺ fundamentals sit at 282, 564 and 846 mT, and a 2018 run at 3.26 MHz showed H⁺ and H₂⁺ as separate peaks at 214 and 427 mT (hosted performance note, §5, §12). COLUMBUS designed for the same kind of scan. At a fixed 2.82 MHz, protons resonate near 185 mT and H₂⁺ near 370 mT, and doubling the field was judged easier than doubling the frequency (Prechtl & Wolf (2020), p. 37-39). A tank (the dee’s resonant circuit) tuned near 9 MHz may not deliver useful dee voltage at 3 or 4 MHz without retuning or new parts (I keep seeing "cyclotron resonance", "RF resonance" and "impedance matching". Are these the same thing? What has to match what?; 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 energies at those settings are low, since energy at a given radius falls with the field; the scan is for identification.

If it does not work. A peak where none is predicted. Compute the candidates before concluding. Take every plausible species, including the residual-gas ions, times every odd harmonic up to seven or so. Add the tank’s other modes and the direct-ion field for your source-to-collector geometry. The Mullins note’s Table 3 is a model of the layout, one row per ion, one column per harmonic, with the magnet’s maximum marked. A strong peak at a third of the expected field and nothing at the field itself. Check whether the fundamental is inside your magnet’s range at all. On the Mullins machine the H₂⁺ fundamental at 9 MHz would need 1,185 mT against a maximum of 851. Peaks that move between runs. Hysteresis (the iron’s magnetisation lags the coil current, so the same current gives a slightly different field) and the meter are suspects before the species is (Gonski (2013), p. 3; 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 whose height changes with gas flow or arc current (the source’s discharge current) while another does not. The difference is an observation about the source’s chemistry, consistent with the century-old recipe (Hogness & Lunn (1925), p. 9, Forringer (2004), p. 89). It suggests which peak is which; it does not establish it. A pronounced peak at a field that matches a simulated low-harmonic molecular ion. COLUMBUS saw that, H₂⁺ at a fifth of maximum speed, and the simulation and the measurement agreed (Wolf (2016), p. 3): genuine beam, of an unintended species.

To understand it. Species matters beyond the label. Molecular ions are destroyed more readily in residual gas than protons are. A proton is lost when it captures an electron from a gas molecule and becomes a neutral atom, which the magnetic field no longer steers; an H₂⁺ can also be broken apart. A cross-section is the likelihood of that per molecule passed. The compiled total destruction cross-section for H₂⁺ in hydrogen exceeds the proton’s electron-capture cross-section over the same energies, so at the same pressure the molecular beam survives fewer turns (Barnett et al. (1990), p. 629; Barnett et al. (1990), p. 44; 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?). Once the machine is capable of a nuclear reaction the species sets the hazard. The Davis group deliberately ran H₂⁺ and alphas before protons until their shielding was complete (Jungerman (1966), p. 7; Can the machine make radiation, or hurt me some other way, before I've even detected a beam?). On the measurement side, the Rutgers 12-inch made its deflector (the extraction electrode at the edge) a q/m spectrometer by halving the field at fixed frequency and stepping the deflector voltage (Koeth, p. 6). COLUMBUS plans a Wien filter (a velocity filter) behind an extraction system to measure the ions’ speed directly (Wolf & Prechtl (2022), p. 3). A nuclear signature identifies by physics: the 63-inch concluded N³⁺ (nitrogen missing three electrons) from the energy a gamma burst implied (Howard (ed.), p. 9), and activation decay curves name the product and so the projectile (Howard (ed.)): the half-life of a target made radioactive names the nucleus formed, and so what formed it. Those are Level 3 instruments. The low-frequency scan is Level 1 where the RF allows it, and it informs the identification rather than settling it.

Now, for a first beam. Cyclotron resonance condition: the magnetic field and the RF frequency match for one charge-to-mass ratio, so the ion arrives at the gap in step turn after turn. It is the setting you search for (I keep seeing "cyclotron resonance", "RF resonance" and "impedance matching". Are these the same thing? What has to match what?; glossary #resonance-condition). Species and harmonic number: which ion is resonating, and how many RF cycles pass per turn, one on the fundamental, three or five on a sub-harmonic. Together they are why one gas makes several peaks and why a peak’s field names candidates rather than a particle (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?; glossary #harmonic-number). Beam current: the charge per second the collector catches, as the meter indicates it. It is the number you log with its bias, and it stays an instrument-indicated figure until the collector’s behaviour is understood (How do I know my beam-current detector could detect the beam I'm looking for, before I use it to troubleshoot the cyclotron?; glossary #beam-current). Background: the same reading with the beam suppressed by one control or another. It is what the peak must stand above, in size and in steadiness (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?). One more term will be asked of you even though it is not needed to find the beam: energy, as computed, (qBr)²/2m at the collector radius (q the ion’s charge, B the magnetic field, r the radius, m the mass) with the field convention named, which is the number almost nobody has measured (How should I document that my cyclotron is accelerating protons? What would someone else need to evaluate the claim?; the cyclotron-energy calculator).

Soon, when you interpret losses or characterise the beam. Phase slip and the phase budget: the ion’s arrival drifts against the RF as the magnetic field changes with radius, because the time per turn is set by the field; past about a quarter cycle it stops gaining useful energy and can eventually be decelerated and lost, one reason beam can end at a radius (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?; glossary #phase-slip). Turn separation: the radial step between one turn and the next, shrinking with radius because the same energy gain per turn buys less radius as the orbit grows; whether a collector lip masks beam (I can detect acceleration near the centre, but not farther out. Is that a partly working cyclotron? How do I find where the particles are being lost?; glossary #turn-separation; the path-length calculator). Radial profile and vertical extent: current against collector radius, and how tall the beam is at the aperture (beam-measurement chapter, #probes-shadows). Energy spread: the width of the energy distribution at one radius; where several turns overlap at the collector its scale is of order the per-turn energy gain (neighbouring turns differ by one turn’s gain, and both land on the collector), a configuration-dependent estimate and a few keV at amateur dee voltages (Baartman (2023), p. 10; beam-quality chapter; #energy-spread). Time structure: the beam arrives in bunches at the RF frequency, since only ions crossing the gap near the right part of the cycle are carried, so peak current exceeds the average; one machine’s frames put the bunch at about 40° of the cycle (Koeth (2015), p. 9). It matters when you count pulses or read a fast scope. Tune, betatron oscillation, field index: the vocabulary of focusing, the small wobbles about the orbit and the field slope that sets them (The drawings show a flat spiral. What keeps the particles from wandering up or down and hitting the dee? Do I need "focusing"?; the beam-dynamics laboratory; glossary #tune; #field-index). Phase stability belongs to synchrotrons and synchrocyclotrons; in a classical cyclotron the window is a budget, not a restoring force (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?).

Later, for extraction, transport and experiments. Emittance: how spread out the particles are in position and direction. It matters when you transport or focus a beam efficiently; it usually need not be measured to demonstrate a first internal beam (beam-quality chapter, #phase-space; glossary #emittance). Brightness: how concentrated the beam is in that position-and-direction space, with conventions that vary by application; a source-comparison figure. Luminosity: a beam-target or colliding-beam figure that sets interaction rate per unit cross-section; it is not a property of the beam alone and rarely arises here. Precession: the slow rotation of an off-centre orbit’s displacement, used to open turn spacing before a septum, the thin wall at the entrance of an extraction channel (glossary #precession; beam-extraction page). Dispersion: in a bending magnetic field, where a particle lands depends on its momentum, which is what makes a bend a spectrometer (Ponter (2010), p. 35-40). Chromaticity: how a focusing system’s tune changes with momentum; usually unnecessary for understanding a modest first-beam demonstration. Fluence: particles per unit area delivered to a target over a run. It is not needed to prove first beam, but it enters radiation and target-exposure estimates even without extraction (Koeth (2017), p. 5; Can the machine make radiation, or hurt me some other way, before I've even detected a beam?).

If it does not work. A builder who cannot find a peak does not need an emittance; the flat sweep has its own checks (How do I find a first beam when all these settings affect one another? Does everything have to be perfect at once before anything happens?). A builder whose beam dies at a radius needs the second tier, in whichever order the last change suggests (I can detect acceleration near the centre, but not farther out. Is that a partly working cyclotron? How do I find where the particles are being lost?). A builder who wants to state a result needs the first tier, the controls and the conventions (How should I document that my cyclotron is accelerating protons? What would someone else need to evaluate the claim?). The test for any term: did a documented amateur machine get a convincing result without it? For the third tier, and most of the second, the answer is yes.

To understand it. The three tiers are one subject at different scales. Professional machines quote emittance and energy spread to several figures because at a milliampere and tens of MeV those numbers decide whether the beam lands on the target or on the beamline, whether turns separate at the septum, and whether the shielding holds (beam-quality chapter, #good-beam). The same quantities exist in a picoampere beam at 100 keV; they are not what limits it.

A useful first-beam record has six things: the machine’s configuration; the RF frequency; the approximate field and how it was read; the recorded collector-current behaviour, the trace itself if you have it; whatever background or detuning checks you could do; and a note on how reproducible the result was. A single well-documented resonance trace with that around it is meaningful evidence even when the controls are incomplete. It supports “a resonance on this machine consistent with acceleration”; it does not yet support a species or an energy. The Mullins record is one, kept for seven years with most of the next level added over time, and it supports the claim its note makes and no more (hosted performance note, §8).

A stronger, independently reviewable record adds the seven parts below. Every documented machine that is still cited kept most of them, and none kept all.

1. The machine, dated. Pole diameter and gap, dee arrangement and voltage convention (peak or peak-to-peak), source type. Collector type and position, with its radius convention stated (which point of the collector the radius is measured to). The instruments, with their ranges and calibration state. COLUMBUS published its design table before first beam, and the pre-beam snapshot is now the baseline every later number is compared with (Wolf (2013), p. 1). Keep the design values and the as-built values in separate columns.
2. The operating point at the peak. Frequency. Field, with how and when it was read (the Mullins rule is RF off, Hall probe at the centre; hosted instrumentation note, §6). Pressure with and without gas, and from which gauge. Filament or arc settings as measured quantities rather than supply setpoints, the numbers dialled on the supplies (Rovey (2007), p. 2). Collector bias. RF drive, and what the number is.
3. The sweep as data, not a spot reading. A current-against-field trace, saved as a time series or at worst a photograph of the screen with its axes. In the Mullins log one session holds seven current rows and no field, while a video of the same session shows a clean peak with its field axis. “Where a trace exists it holds information the columns do not” (hosted instrumentation note, §9).
4. The backgrounds. The same sweep with the beam suppressed: RF off, gas off, field detuned well away, each saved the same way. The Mullins note lists this as the first item of its own future campaign, “the standard the historical record defines but does not meet” (hosted performance note, §12). Record the background’s steadiness as well as its size (How do I know my beam-current detector could detect the beam I'm looking for, before I use it to troubleshoot the cyclotron?).
5. The checks. The bias plateau, the range of collector bias over which the reading stops changing. The peak’s width in field and in frequency. Its response to gas. The sub-harmonic family at a third and a fifth of the field. Whatever else you did to make the signal go away (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?).
6. The uncertainties. Which meter, whether it was ever checked against a reference, where the probe sat, which way the field was approached (Gonski (2013), p. 3). The Iowa State report ranked its own measurements: resonance-curve widths reproducible to a few percent, but the location of a broad peak uncertain by several gauss (Burns (1961), p. 6). Rank the measurements that way rather than adding decimal places.
7. Repeatability. How many dates, across which rebuilds, and the artifacts left in the record and flagged rather than deleted. The Mullins log kept a “not repeatable” microampere reading and a “probably bogus” frequency row in place, with their notes. Their presence is part of what makes the rest of the log believable (hosted instrumentation note, §5, §9).

Then sort every number into one of three columns, and never let them read alike. Measured: the magnet field at the centre with the RF off, the frequency, the collector current as the instrument indicated it and its background (instrument-indicated until collection efficiency and artifacts are understood; 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 pressure, the collector radius. Inferred: the species, as candidates with the coincidences named (I'm feeding hydrogen into the chamber. Does that mean the accelerated particles must be protons? Why might I see more than one resonance peak?). The energy, computed from field and radius with its convention. The dee voltage, where a method gives a number, the beam’s first-turn radius for instance (Koeth et al. (2010), p. 33; Koeth (2007), p. 5; that radius is set by the energy gained at the first gap crossings; hence by the voltage); an uncalibrated pickup (a small loop or plate near the dee whose signal rises with the dee voltage) gives a relative indication or a rough estimate, and it goes in the record as that, not as a voltage. The turn count. Designed or expected: the field the formula predicts for a proton at your frequency, the design energy, the design dee voltage. The Rutgers neutron paper is a model of the second column. It gives a measured dose rate, a stated RF duty factor, a stated conversion standard, and a yield marked “inferred”, with every link shown (Koeth (2017), p. 5). The site’s builds table does the same sorting for the census. It marks every amateur energy “computed”, because every amateur source states it as (qBr)²/2m at the radius where beam was detected. In the Mullins note the log’s keV figure uses the centre field. The field at the collector is about a tenth lower, since the field falls toward the pole edge, and the energy goes as the square, so the same run is 159 keV in one convention and about 130 in the other. The note’s canonical phrasing carries both (hosted performance note, §9).

The strongest supported conclusion is the one the record supports after its gaps are listed. For most first beams it reads like the Mullins note’s summary. Resonance-locked, background-subtracted collector peaks at the fields predicted for hydrogen ions, recurrent over so many dates, with the sub-harmonics in place. Species not formally established, energy computed and not measured, dee voltage nominal (hosted performance note, §8). “Accelerating protons” specifically needs the species step: evidence that separates the candidates. A low-frequency sweep narrows them, an independent line such as a nuclear signature can settle them (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?), and until that evidence is in the record the phrase is “hydrogen ions”. A reviewer trusts a claim with a limitations list more than a trace with none. The list also says what to measure next.

If it does not work. The flattering trace. One peak, saved, with no background on the same axes; a reader cannot tell signal from floor. The trace is still evidence of something. The controls beside it decide how much it can claim, so save them together whenever you can. Numbers without conventions. A dee voltage with no peak or peak-to-peak stated, an energy with no radius or field convention, a current with no bias. Each is unusable by a stranger and will be misquoted (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?; 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?). Setpoints logged as measurements. The Mullins dee-voltage column reads 801, 802, 803 and on to 809 V across rows, the signature of a spreadsheet fill on a nominal 800. The note had to retract “809 V” as a number (hosted performance note, §6). A placeholder belongs in the expected column, labelled. Deleted outliers. A cleaned record is less credible than a flagged one. A species claimed from the gas (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?).

To understand it. The classical reports model both habits, the ranking and the inference chain. Cohen’s energy measurements at the 86-inch state the accuracy floor of the method, a few hundred keV. They add the caveat that a detuned machine may not give the operating distribution (Cohen (1952), p. 5, Cohen (1952), p. 9). Miller and Kashy calibrated dee voltage by the X-ray endpoint (electrons crossing the gap make X-rays whose highest energy equals the peak voltage) and cross-checked it against turn counts (the number of turns to a given radius depends on the energy gained per turn), reporting the discrepancies table rather than the best case (Miller & Kashy (Michigan State University Cyclotron Laboratory), p. 1, Miller & Kashy (Michigan State University Cyclotron Laboratory), p. 4). The Rutgers group inferred dee voltage from the beam’s first-turn radius and plotted it beside the pickup and rectifier readings, three methods on one graph (Koeth (2007), p. 5, Koeth et al. (2010), p. 33). In each, more than one route leads to the number, the disagreement is shown, and the method’s floor is stated with the result. An amateur record with one route to each number is acceptable if it says so, and says which route.