The Dee and Its RF

The energy swings from the electric field of the charged dee into the magnetic field of the coil and back. The losses to resistance can be a few watts or a couple of kilowatts depending on how clean the current path is. A transformer can be part of that circuit, and in the usual small-machine design it is; the transformer’s inductance, how much magnetic energy its winding stores for a given current, and the dee’s capacitance, how much charge it holds per volt, are then the pair that must resonate at the cyclotron frequency. Matching means making the amplifier see the 50 Ω load it was built for, 50 volts for each ampere at its output. The whole arrangement, coil and dee together, is the tank, and it works at one frequency.

For a first beam: a tank that resonates at the cyclotron frequency with the dee you built; a return path (the metal the circulating current runs through from the chamber wall back to the coil) good enough that the amplifier you have reaches the volts you need; a match the amplifier tolerates; and some way to see RF on the dee and to peak it. An uncalibrated pickup, one whose reading follows the dee voltage without saying how many volts, does that job, and the documented first beams were found with one. A calibrated reading lets you quote a voltage later (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?). Some coupling method, how the amplifier feeds the tank, has to be chosen to get the RF running at all; optimizing that choice, and automating the tuning, can wait.

If it does not work. No RF on the dee at all usually means the tank is not resonant where you are driving it, and the pickup with a frequency sweep finds where it is (I keep seeing "cyclotron resonance", "RF resonance" and "impedance matching". Are these the same thing? What has to match what?). The warning sign once it runs is dee voltage that stops following the square root of power as drive rises, the law given below. That suggests a pickup saturating, the tune walking, or a discharge loading the tank, and more power fixes none of them (rf-conditioning-or-fault for the discharge case). A walking tune is the resonance drifting off the drive frequency.

To understand it. The Rutgers 12-inch dee measured 78 pF (Koeth (2005)). The charge on a capacitor is its capacitance times its voltage, and current is charge moved per second. To swing 78 pF to 8 kV peak at 15 MHz, about 60 A peak has to flow into the dee during one half-cycle and back out during the next (arithmetic from those values). The current is reactive: it does no work, it just moves charge. A 2 kW amplifier into 50 Ω supplies about 9 A peak. With a coil across the dee that current circulates between the two instead of through the amplifier, and the Oak Ridge designers’ summary applies: “The high dee voltage required in cyclotrons can be achieved for practical driving power only by using a high-Q resonant circuit” (Livingston & Howard (eds.), p. 17). Q measures the energy the tank stores against the energy it loses each cycle; the higher it is, the fewer watts a given dee voltage costs. Once the tank carries the current, dee voltage rises as the square root of drive power, a law Koeth measured from 5 W to 1,300 W on that machine; at 2 kW forward, the power sent from the amplifier toward the tank, it gave 8.4 kV peak (Koeth (2005), p. 2-3, Koeth et al. (2010), p. 19).

A transformer in this role is the Rutgers 9-inch “transmatch”: an 8-turn copper-tube coil chosen so that, with the dee’s own 70 pF, it resonates at the machine’s 13.6 MHz, and a 3-turn primary wound around it with taps to find the point that looks like 50 Ω to the amplifier (Koeth, p. 3). The secondary, the 8-turn coil, and the dee are the resonator; the primary, the 3-turn winding, is the match.

Losses decide how many volts each watt gives, and they range widely between machines. The resistance that matters is the whole RF path, the loop the current closes through coil, dee, chamber wall and supports, not the coil: the Rutgers coil computed 50 mΩ and the assembled system measured 800 mΩ, because the return current ran through a stainless chamber wall and stem support (Koeth (2005)), stainless steel being a far poorer conductor than copper, so the same machine needed 2 kW forward for its 8.4 kV. A chain built around a ham antenna tuner reached a Q of 16 at Houghton, against 920 for a bare copper tank (Haas (2009), p. 64, Koeth (2005), p. 6-8). At the other extreme, COLUMBUS measured about 330 kΩ across its dee at resonance, which puts the RF dissipated in its resonator near 6 W at 2 kV peak (Prechtl & Wolf (2020)). In every case the figure is power lost in the metal, and the power that goes into the beam is a separate, smaller quantity.

An ion in the magnet’s field circles at a frequency set only by that field and its charge-to-mass ratio, the charge it carries divided by its mass. The voltage across the gap between the dee, the hollow electrode the ions circle through, and the electrode facing it, which the ion crosses twice each turn, has to reverse in step with that circling so that each crossing pushes it forward, or the ion stops gaining energy (the how-it-works chapter; the guided exercise “Find the resonance”). The cyclotron resonance is set by the magnet current and the kind of ion. The RF resonance is set by the coil, the dee and everything near them. The match is made through the coupling (the dee-coupling chapter, practice section); an imperfect match can still put enough volts on the dee to find a beam, and “the amplifier has to see exactly 50 Ω” is a misconception.

The documented amateur machines settled them separately. On the Mullins machine the RF resonance is found by peaking the DC supply current drawn by the final amplifier, the last stage, and the voltage on the pickup, a small plate or loop near the dee whose signal follows the dee voltage, then fine-tuned on beam. The magnet is then swept, its current varied slowly while the collector is watched, to find the cyclotron resonance at that frequency (hosted rf-dee-source note, §4.2; the public build log’s first-beam method). Houghton found its RF resonance by a coarse-to-fine frequency sweep, half-megahertz steps, then tenths, then hundredths, plotting the dee voltage gain, which peaks at resonance (Haas (2009), p. 63-64). The 9-inch set its RF to the industrial 13.56 MHz and chose the magnetic field to suit (census). COLUMBUS tunes its matchbox, its matching network, until the directional coupler, the meter that separates power going toward the tank from power coming back, shows zero reflected power (Prechtl & Wolf (2020), p. 44-45).

You can satisfy any one without the others, and each failure has its own look. A perfect match with no beam is the common one. A reflected-power meter reading zero says the amplifier is matched, not that the dee has volts. A lossy tuner can absorb the power and still match, which is how Houghton’s antenna-tuner chain reached a Q of 16, Q being the measure of how little of its stored energy a tank loses each cycle (What is this "Q" people talk about? How do I measure it, how good does it need to be, and is higher always better?), and low kilovolts from tens of watts (Haas (2009), p. 64). A tank ringing at the wrong frequency gives high pickup voltage and no beam, because the ions are circling at a different rate. The cure is moving the magnetic field or the tank frequency. An amplifier driving an untuned tank gives low voltage at any power and a hot amplifier, because the power the tank does not accept is dissipated in the amplifier. The Mullins machine lost transistor pairs to mismatched loads in that state (hosted note §3.2). With the RF frequency fixed, collector peaks also appear at a third and a fifth of the proton’s resonant magnetic field, because an ion circling at a third or a fifth of the RF frequency still arrives at the gap when the voltage is pushing its way, after three or five RF half-cycles instead of one (Prechtl & Wolf (2020); Fuller (2013), p. 46-47; 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?).

If it does not work. Three readings, one for each of the three, tell you which is missing. The reflected-power meter reads the match. If it will not null, will not come down to zero, the coupling may be wrong or the tank may have drifted away from the frequency you are driving. The two adjustments do different jobs, and the reading alone does not say which is needed, so move each a little and watch what the null does. The pickup reads the RF resonance. If the pickup peaks at a frequency away from the cyclotron frequency the magnet’s field implies, retune the tank or move the magnetic field. Either works, as long as the two frequencies coincide (How do the particle, the energy, the magnet size, the field and the RF frequency fit together? Which of them can I actually choose?). The collector during a magnetic-field sweep, the electrode that catches the beam as a current, reads the cyclotron resonance. If the first two look right and the sweep shows nothing, the RF is still a candidate, because a strong pickup reading and a good match do not establish how many volts are across the gap (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 magnet, the source and the collector are the other candidates (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?). The three interact. Changing the coupling shifts the tank frequency a little, a probe added to measure the dee shifts it too by adding capacitance (Haas (2009), p. 64-65), and the match made cold moves when the chamber warms (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?). Readjust the same way each time and log the three readings together.

To understand it. At critical coupling, the best setting of the match, the dee voltage for a given forward power, the power the amplifier sends toward the tank, is maximum and the loaded Q, the Q with the amplifier connected, is exactly half the unloaded Q, the tank’s own (Koeth (2005), p. 6-7). Any coupling that presents 50 Ω at resonance gives the same dee voltage for the same forward power on a given tank. The method of coupling can therefore be chosen for convenience (Koeth (2005), p. 7; Should I use inductive or capacitive coupling to drive the dee? Which is easier to build, adjust and troubleshoot?). The cyclotron resonance is wider than a single frequency because a small difference between the ions’ circling frequency and the RF is tolerated, the ion arriving a little early or late at each crossing, until the accumulated phase slip spends its budget (Gonski (2013), p. 1; 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?). The RF resonance is wider when the Q is lower (What is this "Q" people talk about? How do I measure it, how good does it need to be, and is higher always better?). Whether the tank sets the frequency or an external source does is the dee-coupling chapter’s architecture question, with both answers documented.

Wouters recommended the single dee in 1949, with the symmetric grounded dummy-dee edge called “a refinement” to add after the machine works (Wouters (1949), p. 8). The dummy dee shapes the gap. A gap between a dee edge and a flat lid has an electric field that spreads and leans, and a leaning field pushes an ion up or down as well as forward. A gap between a dee edge and a matching grounded edge has an electric field that is more nearly uniform across the aperture, the opening the ions pass through, and symmetric above and below the midplane, the plane halfway between the pole faces where the ions circle, which is the field the first turns cross (dg-278’s “better ion focussing”; the source entry on vertical kicks; 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?). It also removes free space around the dee in which low-voltage electron discharges can form (MacKenzie et al. (1948), p. 23; People talk about RF "conditioning". What does that mean, and how do I tell conditioning from a fault that means I should stop?). And it changes the tuning, because a grounded edge close to the dee adds capacitance and more capacitance lowers the tank’s resonant frequency. Inserting a dummy dee into a model dee system dropped its resonant range by about nine percent, so a resonance measured without it is not the operating frequency (Anderson (1947), p. 9; 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?). El Cerrito in 1947 used one dee and no dummy dee at all, the chamber itself at ground, and made microamperes (Cressman (2006), p. 15). Houghton’s dee faces a grounded dummy dee (Yuly (2013), p. 3-4). The Rutgers 9-inch’s is a grounded bar in direct electrical contact with the chamber that also carries the ion source (Koeth, p. 2). COLUMBUS shortened its grounded electrode into a dummy dee because the region behind it is already free of electric field, so a short electrode does what a full grounded D would (Prechtl & Wolf (2020), p. 46). El Cerrito and the Mullins machine found beam without any of the shaping; the shaping helps later.

The lids and chamber are the RF return whether you plan it or not. The RF current that charges the dee every half-cycle has to flow back to the coil through whatever metal connects the grounded surfaces facing the dee to the coil’s cold end, its grounded end. On a single-dee machine that is the lids, the chamber wall, the flanges and the straps, in series, and their resistance lowers the volts per watt (What is this "Q" people talk about? How do I measure it, how good does it need to be, and is higher always better?). The Rutgers tank coil computed 50 mΩ of resistance and the assembled system behaved as if it had 800 mΩ. The return ran through a stainless chamber wall and stem support (Koeth (2005)). The Mullins return is two copper sheets about an inch wide, wedged by friction between the lids and the pole faces, with no bolted connection. It has worked at 60 W. Its resistance has never been measured, and the note says it should be before the planned amplifier upgrade (hosted note §4.2). A crude arrangement has carried 60 W on one machine; that does not establish that it is low-loss, or suitable for more power.

If it does not work. Blown amplifiers point at the load, and on a single-dee machine one load fault to look for is the dee touching a lid, which shorts the dee to ground and leaves the amplifier driving a short circuit. The Mullins dee is held only by its feedthrough and rests on loose pieces of Viton, a rubber. The log records two amplifiers lost on one day with “maybe dee touching lid” as the suspected cause, one incident on one machine and not a statistic (hosted note §2.2). A fixed dee mount is the first item on that machine’s deferred-maintenance list. Flashover at the dee edge under vacuum, a spark from the edge to ground, can be the lids bowing toward the dee under atmospheric pressure once the chamber is pumped, which narrows the gap. The Mullins lids close about a fifth of the nominal gap at atmosphere (hosted chamber-vacuum note, §6), and the Cyclotron Kids’ thin lids bowed enough to lower their flashover voltage (Baumgartner (2013), p. 2). A resonance that moves when the chamber is assembled is the dummy dee or the lids adding capacitance (Anderson (1947), p. 9). Beam that peaks with the source off-centre or dies in the first turns can be the gap’s electric field leaning where there is no symmetric counter-electrode. The Rutgers group traced a large initial vertical displacement to the gap field diverging from the source into the dee, and proposed pullers at the aperture, small shaped electrodes at that opening, as a cure (Koeth (2006), p. 7; 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?).

To understand it. The two-dee system has two coupled modes, two ways the pair can oscillate: one with the dees swinging together, both at the same voltage so that there is none across the gap, and one with them opposed. The drive has to select the second (The University of Washington 60-Inch Cyclotron: Progress and Status…, p. 76). A single dee against ground needs twice the dee-to-ground swing of a two-dee machine for the same gap voltage (Baumgartner (2013), p. 2), so conventions matter when comparing published dee voltages (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 energy gain per crossing depends on the dee’s angular width, the angle it spans around the centre, and the harmonic, whether the ion circles at the RF frequency or at a third or a fifth of it (I keep seeing "cyclotron resonance", "RF resonance" and "impedance matching". Are these the same thing? What has to match what?), and is maximal for a half-circle dee of 180 degrees (Smirnov (2021), p. 11, Livingston & Howard (eds.), p. 100). The RF return path’s resistance is the main part of the loss resistance that sets volts per watt. Broad, clean, clamped, plated contacts are the classical answer (Livingston & Boch (1952), p. 53), and bare steel in the path, a poor RF conductor since RF current flows only in a thin surface layer that thins as the frequency rises, cost the 37-inch a copper-plating job when it moved up in frequency (MacKenzie & Waithman (1946), p. 6).

Where the structure is a sizeable fraction of a wavelength, the dee and its stem, the conductor that feeds it, behave as a transmission line, a conductor along which the voltage differs from point to point at one instant. The designers then treat the dee, stem and liner, the grounded sleeve around the stem, as a quarter-wave resonator, a line a quarter-wavelength long that rings as a tank circuit does, whose frequency is set by its length, foreshortened by the dee’s capacitance (Livingston & Howard (eds.), p. 17, Livingston & Blewett (1962)). The complete RF circuit of a small machine, with its leads and internal structures, can still behave in more complicated ways than one coil and one capacitor (below; the dee-coupling chapter). The 9-inch’s transmatch, its matching network, used the dee’s own 70 pF as the tank capacitor and an eight-turn coil outside the chamber to resonate it (Koeth, p. 3). The Mullins coil is eleven turns of copper tubing at the feedthrough, outside the vacuum, across a dee-plus-feed capacitance that measured 128 pF (hosted rf-dee-source note, §2.4, §4.2). COLUMBUS matches its transceiver to a dee that looks like a 330 kΩ resistance at resonance through a pi filter, a matching network of two capacitors and a coil, outside the chamber (Prechtl & Wolf (2020), Prechtl & Wolf (2020), p. 44-45).

The two pictures are the same physics at different sizes. A circuit description, coil plus capacitor, is exact enough when every conductor is short compared with the wavelength. A distributed description, fields in a volume bounded by conductors, is needed when it is not. The classical reports therefore speak of quarter-wave lines and mode censuses, lists of every frequency at which the structure can ring, the small-machine theses of coils and picofarads. Your machine is on the coil side of that line, and will stay there unless it grows to the metre scale or the frequency climbs by an order of magnitude.

If it does not work. The chamber’s size enters in one way. Any conductor with a return path is a transmission line if it is long enough, and odd structures inside a vacuum chamber can resonate at frequencies you did not design. The 37-inch’s long rotor supports, the supports of its rotating tuning capacitor, acted as open lines, conductors long enough that the voltage at their far end differed from the voltage fed in, and stressed their insulators at three times the rotor voltage (MacKenzie (1947), p. 8). The 184-inch found a mode between its pole pieces with the chamber walls as the return (the vacuum-chamber chapter). A dee voltage that dips to zero at one specific frequency is the signature of a hidden resonant structure absorbing the power (MacKenzie (1947), p. 16). A dip or a second peak in a frequency sweep calls for a look at the leads and the structures inside before the amplifier is blamed. A resonance that is not where the coil and dee predict is more often a capacitance you did not count than a cavity effect. The dummy dee, the lids, the feedthrough and a probe are the usual ones (Anderson (1947), p. 9; Haas (2009), p. 64-65; 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?).

To understand it. The large machines took a mode census before applying power, exciting the structure from a separate oscillator and suppressing unwanted modes with traps, small tuned circuits that block one frequency. They found that the suppression was not complete with the dee shorted, as happens when a discharge connects the dee to ground (MacKenzie (1947), p. 7). They adjusted circuit elements so that the first higher modes would not fall on an oscillator harmonic, a multiple of the drive frequency that the oscillator also emits a little of (Smith (1960), p. 5). They built scale models of the whole resonant system before cutting metal (MacKenzie et al. (1948), p. 14, Anderson (1947), p. 16). The half-wave resonator form, a line a half-wavelength long rather than a quarter, lets tuning elements sit outside the main vacuum (Rainwater et al. (1971), p. 10).

Q sets how many volts a given power produces. In steady running the amplifier’s power replaces only what is lost, and the stored energy grows as the square of the voltage. Comparing like with like means the same capacitance, frequency and coupling; on that footing the voltage for a given power goes as the square root of Q (the dee-coupling chapter’s voltage formula). Q sets the power needed.

You measure it by sweeping. Drive the tank with a signal whose frequency you move slowly across its resonance and watch the dee pickup: the response is a peak, strong over a narrow band of frequencies and weak outside it. The centre frequency divided by the width between the two points where the pickup voltage has fallen to 70.7 % of its maximum is the Q. The 9-inch did exactly that, read 90 kHz wide at 13.6 MHz, and got 150 (Koeth, p. 4). Two details decide what number you get. First, a response read as voltage uses the 70.7 % points; a response read as power uses the 50 % points, since power goes as the square of voltage and 0.707 squared is 0.5. Second, and larger, there are two different Qs, and the connection decides which you are reading. The unloaded Q describes the losses inside the resonator itself. The loaded Q describes the coupled system as the amplifier sees it. The amplifier, once coupled, is a second place for the tank’s energy to go, so the coupled system loses energy faster and its Q is lower; at the best match the loaded Q is exactly half the unloaded value (Koeth (2005), p. 6-7). Swept through its own coupling with the amplifier matched, the tank reads the loaded Q: the 12-inch read 460 that way and inferred 920 unloaded (Koeth (2005), p. 6-8). A probe clipped on to make the measurement adds its own capacitance and moves the resonance, which is how Houghton found a two-percent disagreement between manual and analyzer readings (Haas (2009), p. 64-65). State the configuration with the number.

Higher is not always better. A higher Q means a narrower peak, the width being the centre frequency divided by Q, so the match and the tuning have to be held more precisely, and the thermal drift that every RF system suffers moves you off the peak sooner. The one small-machine source with a Q of 1,600 says that high Q demands precise, stable tuning (Chun (2003), p. 11-12). A higher Q also stores more energy in the tank for the same drive power, which is energy available to an arc. Houghton’s chain, at the other end, matched easily and tolerated drift, and gave less dee voltage per watt (Haas (2009), p. 64). A Q of a few tens through whatever tuner you have will find beam if the amplifier can supply the watts and survive the load. A Q of a few hundred from a clean copper tank and a short return path gives the same amplifier several times the dee voltage. A bench Q near a thousand falls when the tank is installed.

If it does not work. Low voltage per watt, once the tank is tuned and the match is good, is a Q problem, and the loss is seldom in the coil. Compute the coil’s resistance from its copper and you get tens of milliohms. Measure the assembled system and you get hundreds, because the return path runs through chamber wall, flanges, straps and feedthroughs in series (Koeth (2005)). The Mullins note describes “a low-Q system whose losses are distributed through the chain rather than concentrated in the coil’s DC resistance” (§4.3). Its friction-fit return strap has never had its resistance measured (§4.2). The checks are the joints, where the current crosses from one piece of metal to the next and a loose or dirty contact is a resistance in series. Clamped, clean, broad contacts (Livingston & Boch (1952), p. 53); no bare steel or nickel in the current path, which the 37-inch and a plating study both found costly (MacKenzie & Waithman (1946), p. 6, Fowler (1970), p. 4); and the shortest path from dee to coil to ground. A Q that reads differently each time is usually the measurement, not the tank: the probe loading, the coupling setting, or voltage versus power points. A Q that falls when the gas comes on or the voltage rises is loading by a discharge, a conducting path that takes energy from the tank and so reads as added loss, which is a different entry (People talk about RF "conditioning". What does that mean, and how do I tell conditioning from a fault that means I should stop?).

To understand it. The tank’s power is P = πfCV²/Q with V the peak dee-to-ground voltage and Q the resonator’s own loss Q, not a loaded Q read through the amplifier’s coupling; the 86-inch’s measured curve confirmed it (Livingston & Boch (1952), with its convention note). Here f is the frequency and C the tank capacitance. A bare copper tank on the bench reaches 900 to 1,600 (Koeth (2005), p. 6-8, Koeth, p. 4). The 9-inch measured 1,600 unloaded and 150 loaded in the machine (Koeth, p. 4). The Rutgers 12-inch’s installed system worked out near 130 from its series resistance (the dee-coupling chapter). The Mullins machine’s three historical measurements were 6, 30 and 34 in three different configurations. Its September 2026 measurement of the installed matcher and dee gave a loaded Q of about 62, with an internal Q, the resonator’s own, of about 160 on the assumption of a single mode (hosted rf-dee-source note, §4.3, §4.4). That note’s lesson for a successor, to budget for a loaded Q of 500 or more, is a design aim for a higher-voltage machine, not a prerequisite for a first beam; its own machine found beam in 2018, in an earlier configuration, and the 62 is a 2026 measurement of the installed system. Coil Q by itself has an optimum shape and conductor spacing, a length-to-diameter ratio near 0.4 and conductor diameter near half the turn pitch, the centre-to-centre spacing of the turns (Murphy (1999), p. 2-3, Murphy (1999), p. 2). Practical single-layer coils top out near 800 (Murphy (1999), p. 1). Silver plating does not automatically lower RF loss, since RF current flows in the surface layer where the plating is and commercial plating can run at half the conductivity of copper (Fowler (1970), p. 1). At critical coupling the loaded Q is half the unloaded Q, and that is also the condition of maximum voltage transfer (Koeth (2005), p. 6-7).

The 9-inch’s transmatch is a three-turn primary, the driven winding, wound around the eight-turn tank coil, with taps to find the 50 Ω point (Koeth, p. 3). The Mullins matcher in its current form is a series vacuum variable capacitor into the dee node, the point wired to the dee, with the coil from that node to ground. It replaced an earlier link-coupled transformer in an ammunition box (hosted rf-dee-source note, §4.1, §4.4). COLUMBUS uses a pi filter between its transceiver and the dee (Prechtl & Wolf (2020), p. 44-45). Houghton drives through an automatic antenna tuner, a radio operator’s self-adjusting matching box (Haas (2009), p. 64). All found beam. The coupling is one part of the larger decision, the whole matching network between a 50 Ω amplifier and a tank that looks like tens or hundreds of kilohms at resonance (I keep seeing "cyclotron resonance", "RF resonance" and "impedance matching". Are these the same thing? What has to match what?). The Rutgers equivalence was read in forward power, the power the amplifier sends toward the tank (Koeth (2005), p. 7).

The two differ in how they are adjusted and in what fails. The loop is adjusted by geometry: move it, turn it, change its area, and the coupling changes without touching the tank electrically, because the coupling depends on how much of the coil’s magnetic field the loop encloses. It leaves no wire between amplifier and dee, so any DC voltage placed on the dee, a bias against discharges for instance, stays off the amplifier. Its mutual inductance, the measure of how strongly the two windings are linked, can be measured with an ordinary meter by connecting loop and coil in series aiding and then opposing, end to end so that their fields add, then reversed (Koeth (2005), p. 5-6). Pushing a loop deeper stops helping once its own inductance dominates (the dee-coupling chapter). The tap or series capacitor is adjusted electrically, with a variable capacitor. That makes it the natural choice when the tuning has to be done from a knob, and it is the form that automatic tuners use (the dee-coupling chapter, citing Blodgett). The series capacitor and the tap sit in the high-voltage path and are the components that arc, and the cable behind them, a capacitor in its own right that holds charge at whatever voltage sits on it, stores some energy that an arc can release. How much depends on the voltage actually present at that point of the network, which for a low-power 50 Ω feed into a series capacitor is far below the dee’s. The record’s cautionary case, a deflector cable charged to 30 kV DC that stored half a joule (Ponter (2010), p. 43-49), is a different circuit, cited here only as the shape of the hazard at high voltage. At sub-kilovolt dee voltages neither failure is likely to be your first problem; at tens of kilovolts both are design items.

If it does not work. The choice between loop and tap is rarely why a machine has no beam; the match and the amplifier’s tolerance are. Reflected power that will not null means the coupling is too loose or too tight or the tank is off frequency. The two knobs interact, so alternate small moves of coupling and tuning rather than running one to its stop (I keep seeing "cyclotron resonance", "RF resonance" and "impedance matching". Are these the same thing? What has to match what?). An amplifier that fails on mismatch is a reason to prefer whatever arrangement you can match reliably and to protect the amplifier regardless. The Mullins machine’s 50 W final, its last stage, does not tolerate an unmatched load and lost ten to fifteen transistor pairs over the machine’s life, clustered around load faults rather than steady operation. The note calls reflected-power protection or a final that survives an open load the obvious upgrade (hosted note §3.2). A match that was fine cold and is lost hot usually means the tank has drifted with temperature rather than the coupling; check the tuning before touching the coupling (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?). A measured inductance that does not reproduce the resonance: handheld meters mislead on microhenries. The Mullins coil read 3 µH on an LCR meter, but the resonant frequency is fixed by the product of inductance and capacitance, so 9.1 MHz with 166 pF (the 128 pF terminal capacitance plus 38 pF in the matching adapter) implies about 1.8 µH, and the note suspects unzeroed test leads, whose own inductance adds to the reading (§4.4). Measure the tank by its resonance, not its parts.

To understand it. The L-network arithmetic, a series capacitor on the 50 Ω side and a shunt inductor, one from the dee node to ground, on the dee side, is the matching calculator’s job. Its warning is that the shunt inductor and the resonating coil are often one tapped coil whose synthesis is done on the bench. At critical coupling, the 50 Ω match, the loaded Q halves and the dee voltage is maximal; a reflected-power null read at the resonator’s own input, not through a lossy tuner, is a sufficient indicator of it (Koeth (2005), p. 6-7; the dee-coupling chapter). The classical reports chose the coupling point partly for its behaviour in a spark. An arc shorts the dee to ground, and the coupling decides what that short looks like to the amplifier. They preferred an arrangement that reflects a large resistive load back to the amplifier when the dee arcs, so the amplifier’s current falls rather than rises (Oak Ridge National Laboratory (1963), p. 182-183).

The 9-inch logged 16 W forward on a resonance run (census). COLUMBUS runs a 45 W marine transceiver (Prechtl & Wolf (2020), p. 44-45). The Mullins machine found its first resonances on a 5 W preamplifier and ran most of its beam era at 20 to 40 W (hosted rf-dee-source note, §3.1; the build log). The 12-inch, chasing kilovolts rather than a first peak, runs its 500 W for prolonged operation and has touched 2 kW (Koeth (2007), p. 3, Koeth et al. (2010), p. 19). The square-root law was measured on the 12-inch from 5 W to 1,300 W (Koeth (2005), p. 2-3) and on the 9-inch from 4 W to 60 W (Koeth, p. 4). The table collects the published power and voltage pairs; each is stated in its own convention, so compare within a row, not across rows. Losses in the cable and network beyond the meter can keep some of the accepted power from the resonator, and the beam’s share is its current times the voltage it gains, negligible at nanoamperes (the matching calculator’s note; dg-1368 for a machine where the beam is not negligible).

Machine	Forward power	Dee voltage	Convention	How the voltage was known
Houghton	15 W gave a measurable peak on the commissioning run (Haas (2009), p. 69); 26 W through its tuner (Yuly et al. (2010), p. 17-19)	about 1.7 kV at 26 W	peak-to-peak	pickup calibrated at 11,300 to one, recalibrated at every frequency change (Haas (2009), p. 65-66)
9-inch	16 W on a resonance run (census); 60 W at the top of its measured range (Koeth, p. 4)	about 1.7 kV at 60 W	peak	rectifier and divider charging a capacitor to the peak (Koeth, p. 4); square-root law checked from 4 to 60 W (Koeth, p. 4)
Rutgers 12-inch	500 W for prolonged running; 2 kW touched (Koeth (2007), p. 3, Koeth et al. (2010), p. 19)	8.4 kV at 2 kW	peak	pickup calibrated at 3,710 to one against a probe, linear to 1,300 W (Koeth (2005), p. 3-4); square-root law checked from 5 W to 1,300 W (Koeth (2005), p. 2-3)
COLUMBUS	45 W marine transceiver (Prechtl & Wolf (2020), p. 44-45)	not given in the sources used here	not given	not given
Mullins	5 W preamplifier for the first resonances; 20 to 40 W in the beam era (hosted rf-dee-source note, §3.1)	“~800 V nominal, uncalibrated”; a 2026 cold, small-signal estimate of 400 to 1,000 V at 10 W (§4.4, §5)	nominal; no convention established	nine-turn pickup used for peaking and tuning, never calibrated; the 2026 figure is an estimate from stored energy

The direct way to measure it is a high-voltage probe, a divider rated for kilovolts, on the dee stem at low power. The probe adds capacitance, so it loads the tank and shifts the resonance a little, and it fails quietly at higher power, as the Rutgers probe did above about 200 W (Koeth (2005), p. 3-4, Haas (2009), p. 64-65). The working way is a small pickup whose signal is a fixed fraction of the dee voltage, calibrated against the direct probe at low power and then trusted on the square-root law. The Rutgers pickup calibrated at 3,710 to one, dee volts per pickup volt, and stayed linear to 1,300 W; Houghton’s calibrated at 11,300 to one and had to be recalibrated at every frequency change (Koeth (2005), p. 3-4, Haas (2009), p. 65-66). The 9-inch used a rectifier and divider instead, charging a capacitor to the peak and reading it through a resistor chain (Koeth, p. 4). The beam itself gives an independent check, with assumptions attached. If the species, the starting energy, the crossing phase, the point in the RF cycle at which the ion crossed, and the geometry are known, the radius of an ion’s first half-turn implies the gap voltage it crossed, because in a known magnetic field the radius follows from the energy, and that energy came from the one crossing (Koeth et al. (2010), p. 33); it is a cross-check on the electronics, not a meter reading. The Mullins machine has the pickup, a nine-turn coil on a feedthrough, and the note states that it was always “a peaking and tuning tool”. An attempt to calibrate it against a high-voltage probe did not yield a calibration. Every figure ever quoted for that dee is relative or estimated; the stated value is “~800 V nominal, uncalibrated” (§5). The pickup found and followed the operating point without establishing an absolute voltage, which is adequate for a first beam and not for characterizing the machine. Its September 2026 measurements, which the note calls cold and small-signal, meaning the assembled tank at low RF level with no discharge and no beam, put the stored energy at 10 W near 27 µJ and the dee between 400 and 1,000 V, an estimate, not a calibration (§4.4).

If it does not work. Voltage that stops following the square root of power as drive rises is the warning sign. It has three ordinary causes: a probe or pickup saturating, reading no higher though the voltage still rises, the tune walking with heat as the warming metal moves the resonance, or a discharge loading the tank (Why can't I just drive the dee with an RF amplifier, or step the voltage up with a transformer? What are the resonant circuit and the matching network actually doing?; People talk about RF "conditioning". What does that mean, and how do I tell conditioning from a fault that means I should stop?). More power fixes none of them. Beam that does not follow the voltage is a separate observation. The Mullins log found beam current responding weakly to RF power once on resonance, with more drive shifting the whole sweep rather than sharpening the peak, and made no model of it (§3.3). Power that heats the amplifier and not the dee is a mismatch or an untuned tank (I keep seeing "cyclotron resonance", "RF resonance" and "impedance matching". Are these the same thing? What has to match what?). Numbers that will not compare are usually conventions. Peak, peak-to-peak and dee-to-dee differ by factors of two and four, peak-to-peak being twice peak and a two-dee machine’s gap voltage twice each dee’s swing, and a published pair is only comparable within its own machine (the dee-coupling chapter’s table note; dg-288’s correction).

To understand it. The voltage formula, V = √(2PL/RsC) at match, with P the power, L the coil’s inductance, C the tank capacitance and Rs the series resistance of the whole RF path, is the dee-coupling chapter’s. The only levers at a fixed frequency are lowering Rs or raising the ratio of inductance to capacitance (Koeth (2005), p. 8). The X-ray endpoint method reads the peak dee voltage from the highest-energy photons electrons make crossing the gap. An electron crossing the gap gains the gap voltage in energy and, striking metal, makes X-rays of at most that energy. In the MSU setup it worked only above about 30 kV, because the natural emission, the electrons the gap’s own surfaces release without being supplied, was too weak below that (Miller & Kashy (Michigan State University Cyclotron Laboratory), p. 1, Miller & Kashy (Michigan State University Cyclotron Laboratory), p. 1). It is a professional calibration and, at the voltages where it works, a reminder that the dee gap is an X-ray source (Can the machine make radiation, or hurt me some other way, before I've even detected a beam?). Beam loading, the power the beam itself takes from the tank, becomes a design term at microamperes and hundreds of keV (the matching calculator). The 86-inch’s power budget, P = πfCV²/Q, is the same square law written for the resonator (Livingston & Boch (1952)).

The textbook’s picture is a ladder: the magnet fixes the height, the voltage is the rung spacing (Prechtl & Wolf (2020), p. 41-42; 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?). The literature’s tens of kilovolts belong to machines reaching megavolts in a few hundred turns with extraction, taking the beam out of the chamber, in mind. The 1958 census of small research machines ran 10 to 30 kV dee-to-dee (Howard (1958), p. 61), and the Iowa State student machine 10 to 12 kV for 1.5 MeV (McGuire (1961), p. 9). COLUMBUS documents its proton run at 1,000 V amplitude (census; Prechtl & Wolf (2020), p. 71). Houghton reported 800 V and 1.7 kV peak-to-peak from 10 and 26 W (Yuly et al. (2010), p. 17-19), later up to 3 kV peak-to-peak (Yuly (2013), p. 3-4). Niell’s second machine quotes 1,300 V (census). The 9-inch reached about 1.7 kV peak at 60 W (Koeth, p. 4). The Mullins 2026 estimate is 400 to 1,000 V (hosted rf-dee-source note, §4.4). The Rutgers 12-inch, at 8 to 10 kV, is the amateur-origin machine that crossed into the literature’s range (Koeth (2007), p. 3).

The low voltage bought several things. A 5 W preamplifier, a 50 W hobby board, a marine transceiver or a 100 W laboratory amplifier is enough (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?). A vacuum feedthrough rated for 2 kV and an off-the-shelf variable capacitor hold it; COLUMBUS’s dee amplitude is bounded at 3 kV by its feedthrough’s rating (Prechtl & Wolf (2020), p. 42). Electrons crossing a vacuum gap strike metal with the gap’s voltage in energy and make X-rays of up to that energy. The voltage sits far below the tens of kilovolts at which a vacuum gap becomes a serious X-ray source, which reduces the hazard and does not demonstrate the safety of the complete apparatus. The site treats any gap above about 15 kV as an operating X-ray source, and an RF system that will hold kilovolts is surveyed from its first power-up, before any voltage is raised (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?). COLUMBUS’s “on the safe side below 2–3 kV” is its authors’ judgment for their apparatus, not a measurement (Prechtl & Wolf (2020), p. 41). Spark conditioning, raising the voltage gradually through the early sparks (People talk about RF "conditioning". What does that mean, and how do I tell conditioning from a fault that means I should stop?), is a smaller part of operation. And the resonator can be lossy and still work, since the volts needed are few (What is this "Q" people talk about? How do I measure it, how good does it need to be, and is higher always better?).

The cost is turns. An ion crosses the gap twice a turn and gains the gap voltage at each crossing, so at a kilovolt a 150 keV proton makes of order a hundred turns rather than ten, and the ideal count is on the path-length calculator. Three things scale with that. Gas. A hundred turns is tens of metres of path, each metre another chance for the ion to strike a gas molecule and be lost from the beam, and the vacuum has to be an order of magnitude better than a ten-turn machine’s for the same survival. COLUMBUS’s textbook works the trade for its own 16 keV target, where halving the voltage doubled the path to the edge of what its pressure allowed (Prechtl & Wolf (2020), p. 54-55; 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?). Phase. An ion circling a little slower or faster than the RF arrives a little late or early at each crossing, and the slip adds up turn by turn; at a quarter of an RF cycle the gap voltage stops pushing it forward. More turns against the same ninety-degree budget means a narrower resonance, the magnetic field held closer to its exact value, and a stricter field profile, less variation of that field with radius. The Houghton record shows the ceiling directly: at 800 V peak-to-peak no beam peaks appeared above about 0.5 T, where a higher field means more energy at full radius and so more turns at the same voltage, more than the 44 orbits that worked (Yuly et al. (2010), p. 21; 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?). The first turn. A low dee voltage makes a small first orbit, since the radius follows from the energy of one crossing, so a source housing has to be small or absent for the ion to clear it. COLUMBUS’s protons clear its chimney, the tube that houses the source, from 200 V at its low magnetic field, and the Rutgers 12-inch at a tesla needed about 170 W before its first turn cleared the chimney at all (Prechtl & Wolf (2020), p. 42-43; Koeth (2006), p. 4; 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 bare filaments of the Mullins and Houghton machines, with no housing to clear, are part of how they ran so low. The result is beams of nanoamperes rather than microamperes and energies of tens to a couple of hundred keV, which is what those machines set out to demonstrate (census).

If it does not work. The low-voltage machine’s failures are the many-turn failures. Beam near the centre that dies before the collector is the gas, phase or focusing budget, focusing being what keeps the ions from drifting up or down into the dee surfaces, running out over the extra turns (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?). No beam below some drive level and beam above it is in the Mullins log as “below about 70 mV drive, no output at all”, drive being the signal fed to the amplifier. It is in the Rutgers record as an abrupt cutoff at 170 W (hosted note §3.3; Koeth (2006), p. 4). The Rutgers case was modelled and matched the chimney-clearance prediction. The Mullins case was not modelled, and several mechanisms produce a threshold: first-orbit clearance, a minimum voltage to climb through the low-voltage discharge band, a range of dee voltages in which electrons bouncing across the gap in step with the RF absorb the drive (People talk about RF "conditioning". What does that mean, and how do I tell conditioning from a fault that means I should stop?), and a phase budget that closes as turns multiply (Fulbright (1961), p. 4, Gonski (2013), p. 1). A dee that will not rise above a few hundred volts may be sitting inside that discharge band, which is where a sub-kilovolt dee operates (MacKenzie & Waithman (1946), p. 12; People talk about RF "conditioning". What does that mean, and how do I tell conditioning from a fault that means I should stop?). For the turn-count causes, the shared remedy is more volts per turn, at the square root of the power (Livingston & Blewett (1962), p. 172, Koeth (2005), p. 2-3). It is not a remedy for a dee voltage clamped by a discharge or load change you have not identified; that is diagnosed first, with the drive off (People talk about RF "conditioning". What does that mean, and how do I tell conditioning from a fault that means I should stop?). And it does not correct a mistuned frequency, an unsuitable field or a geometric obstruction, which have their own entries. The hosted note’s expectation that ten times the power would give three times the voltage, the square root of ten, is “right in form”, with the observation that beam did not follow (§5).

To understand it. As an ion gains energy its mass rises and it circles a little slower, so against a fixed RF it falls behind a little each turn. The fixed-frequency energy ceiling itself grows only as the square root of the dee voltage, because the accumulated relativistic slip is spent over the turn count (Humphries (1986), p. 530-531). At amateur energies that ceiling is far away, and the binding limits are the three above. Extraction, if it ever comes, wants turn spacing, the radial step between one turn and the next, because a deflector has to catch the last turn without intercepting the one before. Spacing at a given radius is proportional to the energy gain per turn (Kleeven & Zaremba (2018), p. 44), so the extraction literature wants kilovolts. The gap’s clearance and the magnet gap trade against voltage at the top end (Livingston & Howard (eds.), p. 65). At the bottom end the multipactor band, the low-voltage discharge band, sets a floor the drive must climb through (Smith (1960), p. 4; the dee-coupling chapter’s discharge section). The planned path for the Mullins machine, a 100 to 500 W amplifier toward 5 to 13 kV, is the ordinary next step. It is also the point at which the X-ray survey, the feedthrough rating and the amplifier protection all become design items at once (hosted note §3.1; safety page).

Inserting a dummy dee alone dropped a model dee system’s resonant range by about nine percent (Anderson (1947), p. 9). The Mullins lids deflect 0.033 inch at the centre, closing about a fifth of the nominal gap. A free-floating dee that sags 0.05 inch moves the tank capacitance by more than ten percent, which the hosted note names as a plausible contributor to that machine’s day-to-day retuning (hosted chamber-vacuum note §6; simulation-models note §6). Energizing the magnet squeezes the lids a little further as the poles pull toward each other (Koeth, p. 5). A probe clipped on to measure the dee adds picofarads and shifts the resonance by percent (Haas (2009), p. 64-65). Admitting gas and striking the source, turning it on, is what brings the conducting medium (Livingston & Blewett (1962), p. 188; People talk about RF "conditioning". What does that mean, and how do I tell conditioning from a fault that means I should stop?), and the beam itself loads the tank by its current times its energy, negligible at nanoamperes (the matching calculator). The 9-inch pumped transformer oil through its coil to hold frequency, the Cyclotron Kids cooled theirs for the same reason, and Houghton automated the retuning (Koeth, p. 4, Heuer & Baumgartner (2009), p. 23, Koeth et al. (2010), p. 21). Warm magnet coils move the magnetic field too, which moves the cyclotron resonance, the ions’ circling frequency, rather than the RF one, the tank’s (It worked yesterday. Why doesn't putting every knob back where it was bring the beam back?). A gap that sparks at higher power either conditions, holding more voltage after each spark, or does not, and the low-voltage discharge band (People talk about RF "conditioning". What does that mean, and how do I tell conditioning from a fault that means I should stop?) loads the tank until the drive climbs through it (MacKenzie & Waithman (1946), p. 12). A null on the reflected-power meter is a statement about that point in the chain, after whatever attenuators and cables sit between it and the tank (the dee-coupling chapter, practice section). The 128 pF the Mullins chain met is about a third of the 387 pF of the plastic bench capacitor it had been tuned against, and the dee alone measured 100 pF (hosted rf-dee-source note §2.3).

The bench result is a starting point. Tune with every electrode in place, because “a resonance measured on a bare dee is not the operating frequency” (Anderson (1947), p. 9).

If it does not work. Four different things look like “it changed”. They are categories of evidence that narrow the search, not labels for a unique cause, and each points somewhere different rather than at indiscriminate retuning. The resonance shifted: the peak of the pickup is at a new frequency and is as tall as before once you find it. Retune, by frequency or by the capacitor, and note how far it moved. The direction and size point at the cause: down for added capacitance, walking during a run for heat. The match changed: the peak is where it was but reflected power has risen at it. The coupling is the first place to look. The losses rose: the peak is where it was, the match nulls, and the pickup is lower for the same forward power. Something is absorbing power, a discharge, a hot joint, gas, and more drive is the wrong answer until the something is found (What is this "Q" people talk about? How do I measure it, how good does it need to be, and is higher always better?, People talk about RF "conditioning". What does that mean, and how do I tell conditioning from a fault that means I should stop?). The instrument moved: a probe added or removed, a cable changed, a meter reading at a different plane. Houghton’s two percent disagreement between manual and analyzer readings was the probe’s capacitance (Haas (2009), p. 64-65). The Mullins log’s “wiggling RF connection to tuning coil, and finding right resonant frequency” after an amplifier change is the same sorting done by hand (hosted note §2.2). Change one thing between readings, and log the pickup, the reflected power and the frequency together each time.

To understand it. The two architectures answer the drift problem differently. A self-excited oscillator, one in which the tank itself is the frequency-setting element, takes its frequency from the tank and follows the drift automatically, needing a trimmer, a small adjustable capacitor, to hold the cyclotron condition, agreement with the ions’ circling frequency. A driven system, in which a separate signal generator sets the frequency and an amplifier delivers it, holds the frequency and must be re-matched as the tank moves, by hand or by a phase-comparison servo driving a trimmer capacitor (the dee-coupling chapter; architecture section; Koeth et al. (2010), p. 21; Livingston & Blewett (1962), p. 188). The large machines modelled their RF systems at reduced scale before building and still budgeted for retuning (Anderson (1947), p. 16, Goodman (1958), p. 25). The thermal fixes are documented at every scale: cooled coils, stable cooling-water temperature, and closing the loop (the dee-coupling chapter, practice section). Lid deflection under atmosphere is an RF problem before it is a vacuum one (the lid-deflection calculator; the vacuum-chamber chapter, lids section).

An unexpected discharge may be a clearance problem, damaged insulation, an unwanted electron discharge, or another fault. The machine’s voltage, pressure, RF behaviour and protection all enter. The physics behind the controlled version is settled. Fresh surfaces carry whiskers, microscopic metal points at which the electric field concentrates, and particles that emit electrons, and a spark starts where electrons are emitted; each spark in the early regime is overwhelmingly likely to raise that site’s breakdown field, the field at which it next sparks, with the gains shrinking toward a limit (Werner (2004), p. 91-92). Fresh surfaces also carry gas that the first RF heating drives off, so the pressure rises in bursts and settles. Livingston and Blewett’s rule is that “no amount of smoothing or polishing will eliminate the necessity of some high-voltage conditioning under vacuum” after every opening (Livingston & Blewett (1962), p. 189). Within a procedure such as Wouters’, with its limits set beforehand and the protection in place, the expected course is a spark rate that falls and pressure bursts that decay. The AMIT cavity logged about a hundred arcs over a hundred hours with the rate falling below one an hour (Gavela et al. (CIEMAT), p. 3). The 63-inch called its RF solved only when it held 75 kV “for long periods” rather than touched it (Howard (ed.), p. 15). The rating is what the machine holds quietly, not what it reaches between sparks (Livingston & Boch (1952), p. 24).

The Mullins record lacks that amplifier protection and names it the obvious upgrade after ten to fifteen transistor pairs (hosted rf-dee-source note, §3.2). A spark shorts the dee to ground, the match is lost while it lasts, and the power the tank no longer accepts comes back at the amplifier. A sub-kilovolt dee is far below the voltages where the X-ray hazard appears, and the survey is how you know that for your machine rather than assume it.

The behaviours that are not surface conditioning, and what the record did about them: The voltage sits at a few hundred volts and will not rise, perhaps with a blue glow, while the amplifier delivers power. One documented cause is the low-voltage electron discharge, multipactor, electrons bouncing between the dee and the facing ground in step with the RF and knocking more electrons out of the metal at each impact, and its relatives, which the classical machines found living in a bounded voltage band and absorbing the drive (Livingston & Blewett (1962), p. 188, MacKenzie & Waithman (1946), p. 12, Smith (1960), p. 4). Those machines dealt with it by design: a DC bias on the dee, a steady voltage across the gap that pushes the electrons one way so they cannot bounce back and forth in step with the RF (Smith (1960), p. 4, MacKenzie et al. (1948), p. 23, Woo (1970), p. 13); less free volume around it; and, where the main oscillator was self-excited, taking its feedback from the dee itself and so unable to start into a dee loaded by the discharge, a small independent oscillator to push it through the band (MacKenzie & Waithman (1946), p. 12). One report describes a ring-down test, cutting the drive and watching the dee voltage decay, that shows the band’s edges on a given machine (MacKenzie et al. (1948), p. 23; Fulbright (1961), p. 2; Fulbright (1961), p. 4; the dee-coupling chapter’s discharge section). The same symptom can have other causes, a shorted or touching dee among them, and applying more RF power to push through an unidentified discharge is not a diagnostic method; identify it first, with the drive off. Running longer does not condition it away either. A spark rate that does not fall, or any discharge you cannot account for, is a reason to shut down and look, not something that earns the name “fault” after a trial period. Look for a particle, a sharp edge, a loose piece, a dee touching a lid (hosted note §2.2). Pressure that rises and stays up is gas being made faster than it is pumped, by a discharge or a hot surface. Wouters’ procedure stops at 10⁻⁴ torr for that reason (Wouters (1949)). Anything hot that should not be. An amplifier transistor at 190 °F is in the Mullins log beside a failure (§3.2), and a nickel-plated coil ran at 350 °C in one study (Fowler (1970), p. 4). Arcing outside the vacuum, at a feedthrough, in a cable, across air gaps, is never conditioning. The ORNL source-test unit’s dee voltage was capped by a stem spacing in air, not by any vacuum gap (Howard (ed.), p. 23), the air along the stem outside the chamber sparking first, and the Rutgers deflector’s persistent arcing was the stored energy in its coax, the cable feeding it, which holds charge as a capacitor does (Ponter (2010), p. 43-49). A match that has changed during the session is drift or a changed load, not conditioning (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?).

If it does not work. The stop-and-review criteria are the ones the record wrote down, and they are specific to equipment rather than universal. Stop when the amplifier’s own protection trips, or when there is none and the load has become unknown. Stop when the pressure exceeds the figure you set beforehand, Wouters’ 10⁻⁴ torr being the historical one (Wouters (1949)). Stop on any discharge you cannot explain, and open the chamber expecting to find something physical. Stop on any smell, heat or sound from outside the vacuum. Stop if a survey instrument reads above background anywhere a person stands. Then review before resuming. What the forward and reflected power, the pickup, the pressure and the spark rate did over time, in the log, is the evidence that separates a conditioning trend from a fault. The Mullins log’s “blew two RF amps, maybe dee touching lid?” was followed by opening the chamber and finding the Viton spacers out of position, not by more drive (§2.2). “Conditioning sometimes appears in the literature” is not a reason to run through a problem; the literature’s conditioning was done on interlocked machines, with predefined limits, vacuum and reflected-power interlocks, and the shielding in place. An unresolved electrical problem is the default reading until a controlled conditioning process is established.

To understand it. The large machines automated what the small ones do by hand. An interlock is a circuit that cuts the drive by itself when a reading leaves its bounds. One on the ratio of dee voltage to oscillator current, which an arc holds low because the dee voltage collapses while the current does not, cuts the drive and recycles a second later so the vacuum can pump away the discharge products (Smith (1960), p. 7). A fast interlock acts on reflected power (Gavela et al. (CIEMAT), p. 3). Spark detection reads a microsecond collapse of the dee voltage and ramps back automatically (Gold & Sabaiduc (Best Cyclotron Systems), p. 2). Every dee spark is a system-wide transient that can propagate into the amplifier, so protection is layered by speed (Smith (1960)). Deliberate conditioning on the production machines ran to hundreds of thousands of sparks and roughly a hundred hours (Smith (1960), p. 4, Röcken et al. (Varian Medical Systems Particle Therapy), p. 1). A conditioned gap holds several times what it first held and loses some of that at every air exposure (the dee-coupling chapter; the safety page on dark current). The breakdown regime depends on pressure: vacuum breakdown, started by electrons drawn from the metal surfaces themselves, below about 10⁻⁵ torr and gas breakdown, the gas between the electrodes ionizing, above about 10⁻⁴. A gas-fed small machine often runs in the grey zone between (Werner (2004), p. 23; 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?).