The Vacuum Budget of a Cyclotron

A cyclotron's vacuum requirement is set first by its beam, not by a rule of thumb. The target pressure follows from how much of the beam survives the spiral without picking up an electron; the gas the pump has to remove is mostly the hydrogen the ion source admits on purpose; and the pressure that matters is the one inside the dee, behind the slots, which no gauge reads directly. Those three facts make the whole system estimable to first order before a pump is bought: feed rate in, effective pumping speed, chamber and dee-interior pressure, surviving beam out. For the site's reference point (0.6 T, protons to 150 keV, 1 kV on the dee) the answer is: a 0.3 sccm source against 140 L/s of effective hydrogen speed gives about 3 × 10⁻⁵ torr over base, at which 75% of a proton beam survives its 30 m spiral and under half of an H₂⁺ beam does; five times the dee voltage or five times the pumping speed puts the proton beam above 90% and the H₂⁺ beam near 80%. This page works that budget at the site's generic reference point and shows where the published record says small machines get it wrong. The design guide's vacuum domain holds the 157 sourced rules behind it; the vacuum calculator runs the survival integral for any machine.

Elsewhere: vacuum technology in general is O'Hanlon's User's Guide and the resources page; source hardware is ion sources; scattering short of loss is beam quality; chamber mechanics is lid deflection.

The pressure target comes from the beam, not from a rule of thumb

A fusor runs at 10⁻² torr; a vacuum-tube rectifier is hard vacuum at 10⁻⁶. A cyclotron sits between them for a reason that has nothing to do with the hardware and everything to do with the ion's trip. A proton at a few tens of keV passing a hydrogen molecule can capture one of its electrons. The neutral atom that results no longer bends in the magnetic field; it flies straight to the wall. The loss is not a degradation of the beam, it is a subtraction from it, and it compounds along the whole path.

The arithmetic is the calculator's: with gas number density n = p/k_BT and a capture cross-section σ, the beam's mean free path is λ = 1/nσ and the fraction surviving a path L is exp(−L/λ). Smirnov gives the same relation as a time-step rule, dN = σnNv dt, with n[m⁻³] = 3.3 × 10²² p[torr] (dg-578). What makes a cyclotron unforgiving is L. The beam does not cross the chamber once; it spirals through every turn the dee voltage allows, and the path-length calculator sums those circumferences to tens of metres for a tabletop machine. At the reference point — 0.6 T, protons to 150 keV at a 9.3 cm final radius, 1 kV on the dee with two gap crossings per turn — that is 75 turns and 29.6 m of path, an idealized lower bound that credits the full peak voltage at every crossing; real gain per turn is less and the path correspondingly longer. Raise the dee voltage to 5 kV and it is 15 turns and 6.1 m. The vacuum requirement scales with that length: every factor the RF system gives in dee voltage is a factor the vacuum system gets back.

Everything in that formula is known except σ, and σ is where a design goes wrong. The gas-kinetic mean free path, λ_gas = k_BT/(√2 πd²p), describes a molecule colliding with other molecules, and for hydrogen at 10⁻⁵ torr it is about 9 m (molecular diameter 0.274 nm, O'Hanlon App. B.2); it is the number a vacuum text prints and it says nothing about a proton. The beam's mean free path uses the capture cross-section, which for a 10 keV proton in hydrogen is 8.7 × 10⁻¹⁶ cm² (Barnett 1990, p. A-28): λ ≈ 35 m at 10⁻⁵ torr, and 17 cm at 2 × 10⁻³. The census carries the case of the wrong σ. An MIT thesis set the requirement correctly, "an acceptable vacuum would allow for a mean free path an order of magnitude larger than the expected flight distance," about 300 m for its design (dg-460), and then read from its own plot a mean free path of 5 km at 2 × 10⁻³ torr (Dewan 2007, p. 11), a figure that implies a cross-section near 3 × 10⁻²⁰ cm², four orders of magnitude below the measured one. The machine reached 2 × 10⁻³ torr in testing, and the record reports no beam; whatever else the record does not say, at that pressure a proton's capture mean free path is shorter than one turn. The trap is general, the rule was right, and the cross-section was not. Nothing else on this page rests on that thesis: it is quoted for the criterion it states, and the design guide's rule from it (dg-460) now carries a dated correction withdrawing its pressure figure.

The census also shows what working machines settled on. Every beam-producing entry that reports a base pressure (6 of them, from Niell's estimated 10⁻⁵ torr in 1995 to COLUMBUS at 7.5 × 10⁻⁷) sits in the 10⁻⁷–10⁻⁵ torr band with gas off, and runs an order of magnitude higher with the source gas on (comparison table). Livingston and Blewett give the same pair for the MIT cyclotron: "with no gas flow, chamber pressures of better than 1 × 10⁻⁶ mm Hg are obtained. With the deuterium gas flow from the ion source, the operating pressure is about 2 × 10⁻⁵ mm Hg" (dg-370). Wouters' 1949 recipe for a 6-inch machine is the same band stated as thresholds: 10⁻⁵ before starting, no worse than 10⁻³ during RF bakeout, and operation "can be attempted with a pressure of 10⁻⁴ mm or less" with source and RF on (dg-465). Modern research machines run near 10⁻⁷, and Smirnov names the second reason for it: vacuum holds voltage as well as beam (dg-577).

Species changes the budget: H⁺ against H₂⁺

The capture cross-section is not a constant. For protons in hydrogen it rises from 4 × 10⁻¹⁶ cm² at 1 keV to a peak near 10⁻¹⁵ at 7 keV, then falls nearly three orders of magnitude by 200 keV. The recommended values from the Oak Ridge compilation (Barnett et al. 1990, p. A-28; stated accuracy 10% above 100 eV):

A beam spends its early turns where σ is largest and its late turns where σ is negligible, so the right calculation integrates σ(E) along the orbit rather than picking one value. The calculator's orbit mode does that, turn by turn, with the table above. For a proton machine the answer is close to the single-value estimate anyway: across a 2–150 keV spiral the turn-weighted average lands near 10⁻¹⁶ cm², and at the reference point the integrated survival at 10⁻⁵ torr is 89.9% against 90.7% for a flat 10⁻¹⁶. The simple model is adequate for protons, and conservative if the single value is taken from the low-energy end.

The molecular ion is a different case, and an internal hydrogen source makes both species — more of the molecular ion when the arc is starved of gas (Forringer 2004; see species). H₂⁺ is destroyed in hydrogen by capture and by collisional dissociation, and the total destruction cross-section stays near 8 × 10⁻¹⁶ cm² from 1.5 to 20 keV per nucleon before it begins to fall, reaching 3.8 × 10⁻¹⁶ at 50 keV/amu (Barnett 1990, p. G-46; accuracy 20%, and the compilers note that ion-source conditions alone shift the measured values by up to 10%). There is little high-energy relief within a tabletop machine's range. At the reference point, an H₂⁺ beam taken to the same 9.3 cm radius (75 keV, since the heavier ion reaches half the energy at the same rigidity) survives 71% at 10⁻⁵ torr and 51% at 2 × 10⁻⁵ with 1 kV on the dee, where a flat 10⁻¹⁶ would have predicted 95% and 90%. Five kilovolts on the dee restores 93% at 10⁻⁵. A builder who sees the H₂⁺ peak fall away as gas is admitted while the proton peak holds should suspect this cross-section before the tuning, though admitting gas changes the source's species mix too.

H⁻, the species commercial machines accelerate for stripping extraction, is the extreme case: its stripping cross-section "is maximal for the energy range (0.1–300) keV," and the compact AMIT design loses (14.6 ± 1.5)% of its beam to residual gas at ~10⁻⁴ hPa (dg-599; treated on the extraction page, and not a concern for a positive-ion machine).

The ion source is the gas load

A vacuum text's gas-load chapter is about outgassing: water leaving the walls, air permeating the O-rings. A cyclotron's gas load is something the builder turns on with a valve. The internal source needs hydrogen at 1–10 Pa inside its chimney to sustain an arc (Wolf, dg-372), and everything the arc does not ionize leaks out of the slit into the chamber. Source gas efficiency is 10–20% for a poorly confined discharge and 50% at best (dg-380), so most of the feed is a gas load by design. Livingston and Blewett's conclusion for the MIT machine was that "the ion-source gas load, not outgassing, sets the working pressure," and the design response was to put the pumping speed close to the dees (dg-370). The Carnegie designers anchored an entire 140-inch vacuum system to the same number: "if 200 ml/hr is considered as a maximum rate of gas injection, this results in … 0.042 liter-mm/sec" (TID-454 p. 136, dg-843).

The unit conversion is the one a builder actually needs. A standard cubic centimetre per minute is 1.69 Pa·L/s (O'Hanlon App. A.3), which is 1 sccm = 0.0127 torr·L/s; Carnegie's 200 ml/hr is 3.3 sccm. Published small-source feeds bracket that: a Penning source's housekeeping consumption is 0.2–0.6 sccm (dg-372), Forringer's MSU test stand held its chamber near 4 × 10⁻⁵ torr with 2.5 sccm into the chimney (dg-414), and Rovey's laboratory Penning source maps 1, 2 and 3 sccm to 2, 5 and 16 × 10⁻⁵ torr in its chamber (Rovey et al. 2007, Table I). Since the chamber pressure with gas on is Q/S_eff above base, each of those is a measurement of the test stand's effective pumping speed, with one caveat that applies to every hydrogen pressure on this page: an ionization gauge is nitrogen-calibrated, and its relative sensitivity to H₂ is 0.42–0.53 (O'Hanlon Table 5.1), so an uncorrected reading understates hydrogen pressure by about two; Forringer's works out near 800 L/s, which is a large pump on a small chamber, and explains why a builder with a 100 L/s pump cannot reproduce his pressure at his flow.

The gas window has a floor as well as a ceiling. Below some flow the arc starves: "the arc voltage increases with decreasing gas flow … until the discharge becomes unstable" (dg-607). The Houghton record documents the result as a chamber-pressure band with an optimum inside it — 10⁻⁶ to 10⁻⁴ torr for the machine to operate at all, peak current near 10⁻⁴ (dg-405), and in a later thesis a narrower 1–3 × 10⁻⁵ torr where current is best (dg-403). Those are two numbers from two theses on one machine, an operating window and an optimum within it, and a reader should not average them. The shape is general: the source needs gas, the beam needs its absence, and the vacuum system's job is to make the source's pressure and the chamber's pressure as different as possible. A tight-fitting insulator between the discharge region and the chamber (dg-414) and a smaller hood opening (dg-1289) both widen that ratio; in a compact rig where the source sits open in the chamber, the source pressure is only about twice the chamber pressure (dg-409) and the window collapses toward a single compromise pressure.

Outgassing still sets the base pressure, and the base pressure is what the gas-on pressure is added to. Unbaked, uncleaned stainless outgasses of order 10⁻⁵ Pa·m/s after ten hours of pumping (O'Hanlon, dg-441); an unbaked Viton O-ring starts near 10⁻³ Pa·m/s, two orders worse per unit area, and a 150 °C bake cuts it 2500-fold until the next air exposure reloads it with water (dg-443). The USPAS comparative table has aluminium at 80, unpolished stainless at 266 and slightly rusty mild steel at 58,520 (all ×10⁻¹⁰ mbar·L·s⁻¹·cm⁻² after one hour), with the instruction to use such data "for comparative purposes only" (dg-456). The rusty steel entry is the one that matters for a builder with a yoke-as-chamber design: an unprepared, rusting steel surface is not a vacuum surface, whatever a cleaned and plated one may be. The Washington 60-inch measured the effect directly: installing copper liners and RF loops "approximately tripled the interior surface area" and raised the base pressure to match (dg-1348).

Pump speed is what arrives at the chamber, not what the nameplate says

A pump rated 150 L/s does not pump the chamber at 150 L/s. Between them is a port, a valve, perhaps a baffle, and each is a conductance C in series with the pump's speed S; the effective speed at the chamber is

so a conductance equal to the pump speed halves it, and no conductance can raise it above the smaller of the two. The Carnegie report states it as S_net = 1/(1/S_pump + 1/C) and works a network of them (dee interior, stub line, side outlets, condenser box) as series and parallel resistances (TID-454 pp. 134–136, dg-840). Its conductance formulas are in inch units and carry deliberately conservative constants: a long duct passes S = 400 A²/(O·L) L/s for air, with A the cross-section in square inches, O the perimeter and L the length in inches (dg-837), and an orifice small relative to its surroundings passes 75 A (dg-839). In SI the orifice limit is 11.6 L/s per cm² of aperture for air at room temperature, and no structure in molecular flow can exceed it (O'Hanlon ch. 3, dg-450).

Hydrogen changes the numbers in a way that is easy to get backwards. Molecular-flow conductance scales as √(T/M), so every aperture and duct passes hydrogen √(29/2) ≈ 3.8 times faster than air; Carnegie's side-arm conductances go from 24,800 to 94,000 L/s when the gas is hydrogen (TID-454 p. 138). The pump does not follow: "the fact that the conductances are considerably greater for hydrogen, therefore will have very little effect toward increasing the net speed" where the pump, not the duct, is the bottleneck (dg-844). For a small machine with a short, fat port this is usually the case, and the consequence is that the pump's hydrogen speed is the figure to look up, which for a turbopump is the one the datasheet is least eager to print (see the pumps section).

Two sizing rules from the hosted record bracket the pump. Livingston and Blewett: "a good rule of thumb is to provide a pumping speed of at least 1 liter/sec at 10⁻⁵ mm Hg per liter of volume," with the roughing pump sized to reach diffusion-pump backing pressure in 15–20 minutes (dg-432). The Carnegie method is stricter and more useful: size by throughput at the operating pressure — tabulate Q = p·S for each candidate pump against the system's effective conductance and require margin over the known gas load (dg-842). On that test "with 20-in. diffusion pumps there is little excess available" and the 32-inch pumps were chosen. Oak Ridge's design study derated installed speed to 25% of mouth speed for baffles and valves (dg-906); Carnegie's own equipment list shows a 15,000 L/s pump delivering 8,000 L/s through its refrigerated baffle (NYO-780 p. 80). A builder who reads the pump's rated speed as the chamber's speed through a baffle, a valve and a duct has overestimated by a factor of two to four.

The pressure that matters is inside the dee

The beam spends most of its time inside a copper box. A dee is a hollow half-cylinder open only along its accelerating edge, and gas that enters it — the source sits at the gap, so some of the feed, taken here as half, goes straight in — must leave through that same opening, against whatever conductance the dee aperture presents. The dee-interior pressure is the chamber pressure plus Q_dee/C_aperture, and since the beam is inside a dee for most of every turn, it dominates the pressure the survival integral should use. A gauge on a chamber port reads something lower. Molflow+ exists to compute the difference (modelling tools); the arithmetic here is the zero-dimensional version.

The Carnegie designers treated the dee as the first node of the network: the pumping speed available inside the dee was worked at 6,500 L/s for a 140-inch machine, and the report's recommendation is to perforate "internal RF structures — dee back, stub-line walls, internal bracing — wherever structurally and electrically tolerable," so that "this additional pumping speed then can be considered as being in parallel with that through the opening at the mouth of the dee" (TID-454 p. 129, dg-841). Oak Ridge perforated the peripheral dee walls of the 86-inch "to permit high pumping speed" (dg-361), and Carnegie drilled "numerous holes" in its pole-tip liners so the volume behind them pumped instead of trapping gas (dg-647).

At tabletop scale the aperture is large relative to the feed, and that is worth stating because it is the one place the budget comes out comfortable. A dee opening 2 cm high by 18 cm wide passes hydrogen at up to 11.6 × 3.8 × 36 ≈ 1,600 L/s, the thin-orifice upper bound that lips and stems only reduce; half a sccm entering the dee raises its interior about 4 × 10⁻⁶ torr above the chamber. That is a correction, not a crisis, for a machine running at 2 × 10⁻⁵. It becomes one the moment the dee is closed: a dee with a solid back and a narrow aperture gap, or a dee that fills the chamber so closely that the gap between dee and pole is the only path to the pump, turns that 1,600 L/s into a few tens, and then the interior runs an order of magnitude above the gauge while the builder lowers the chamber pressure and wonders why the beam does not improve. The same trap takes a second form: a volume that is sealed from the chamber except through a fine path, a blind tapped hole or a trapped O-ring groove or a closed liner, is a virtual leak, and its pressure decays on its own schedule regardless of the pump (dg-458, dg-356).

Gauge placement follows from the same picture. Oak Ridge mounted its ion gauge "where conductance to pumps and to tank are comparable so it reads representative pressure," did not switch it on until the tank was below 0.5 micron, and gave the filament some shielding from the magnet (dg-475). A gauge on the pump port reads the pump; a gauge on a dead-end stub reads the stub.

The budget at the reference point

The site's reference point is a representative tabletop machine: 0.6 T on 8-inch poles, protons to ~150 keV, an internal hydrogen source. The numbers below are computed from that point with the site's calculators and the ORNL-6086 cross-sections, not taken from any one build; the census row at the end is the cross-check. Assumed: every gap crossing at peak voltage; a 10 cm diameter, 10 cm long pump port with nothing in it; the pump's hydrogen speed equal to its rated speed; half the source feed entering the dee; gauge readings already corrected for hydrogen; and pressures quoted as the increment over a base in the 10⁻⁶ decade.

• Hydrogen. "The main difference between the turbomolecular pump and the diffusion pump is the low hydrogen compression ratio in the turbo pump" (O'Hanlon p. 209). USPAS gives typical turbopump compression ratios of 10⁸–10⁹ for nitrogen but only 10²–10⁵ for hydrogen (Bertolini 2004, slide 122), so a turbopump's ultimate pressure under a hydrogen load depends on its backing pressure far more strongly than a diffusion pump's, whose light-gas compression is also finite. The hydrogen speed, not the nitrogen speed, is the datasheet figure to design to.
• Backstreaming. A diffusion pump puts oil vapour toward the chamber unless baffled, and Carnegie's refrigerated baffle cost it half its speed (NYO-780 p. 80). The proven amateur recipe at the 15 cm scale is diffusion pump plus liquid-nitrogen cold trap for 10⁻⁶ torr (dg-471); Argonne found a Freon-cooled baffle sufficient for operations and kept its LN₂ trap "for vacuum test purposes" (ANL-5907 p. 7). A turbopump with a dry backing pump has no oil in the high-vacuum path at all.
• The roughing pump's oil. The oil-sealed rotary-vane pump that backs either kind backstreams its own oil into the chamber if it is allowed to rough below 10–15 Pa. "The '100-mTorr rule'" cuts both ways: do not open the high-vacuum pump to the chamber above its crossover pressure, and do not keep roughing directly once the chamber is below 100–150 mTorr (O'Hanlon, dg-445); the pump's own limits and an interlocked valve sequence decide the exact point. A scroll pump is clean but "permeable to light gases" (Bertolini 2004, slide 110), which matters when the gas is hydrogen.
• Forepressure. A diffusion pump has a critical forepressure of 25–75 Pa above which its jets collapse and the inlet pressure "rises uncontrollably" (dg-440). Carnegie's automatic sequence cut the heaters when forepressure reached 50 micron and opened a bleeder valve as the mechanical pump shut off so oil could not migrate back (dg-847, dg-846). A turbopump tolerates a higher backing pressure; it needs the same vent-valve interlock, so that a stopped backing pump cannot feed oil back through it.
• Time and attention. A diffusion pump needs its oil level checked and its trap kept cold; the Harvard quarter that lost three days to a cold-trap refrigerator and a fourth to low oil is the cautionary record (dg-1153, dg-1154). Livingston and Blewett's practice was to let diffusion pumps "cool for a half-hour before admitting air" (Livingston & Blewett p. 181); the pump's own manual sets the figure, since air on hot oil degrades it. A turbopump on a small chamber is ready in minutes and stops in minutes. Against that, a diffusion pump has no moving parts, and it is what turns up on the surplus market and in donations — the census's two donated pumps were both diffusion pumps.

Venting discipline is common to both. Oak Ridge injected dry air at the mechanical pump's outlet in place of a refrigerated inlet trap and vented the tank only with dry air "to minimize the amount of moisture entering the tank and thereby to reduce the time required for the next pumpdown" (dg-474); a vacuum lock for the source and probe, so the chamber is not vented for every filament change, is the same saving in a different place (dg-1350). Carnegie's analytic bound on pump-down, 15,000 litres from atmosphere to 45 micron in 30 minutes and then to 4 × 10⁻⁶ in 3 more, "neglecting outgassing and assuming a perfectly tight system" (dg-845), is the shape of every pump-down curve: the roughing stage is volume-limited and fast, the finishing stage is outgassing-limited and slow, and a curve that departs from last month's curve is the first leak detector (dg-650).

Voltage holding is a vacuum function

The dee carries kilovolts of RF across a gap of a centimetre or two, and whether that gap holds depends on what regime the pressure puts it in. Werner's summary is the map: "for typical cases of interest, 'vacuum' pressure is lower than 10⁻⁵ torr, and 'gas' pressure higher than 10⁻⁴ torr". Below the first the physics is vacuum breakdown, governed by field emission and particulates on the electrodes; above the second it is gas breakdown, governed by the pressure–distance product; and the decade between is a grey zone (dg-276). The figures are indicative: where the boundaries fall for a given gap depends on the gas, the electrode surfaces and their conditioning, and the RF frequency. A cyclotron with gas on runs in or near that grey zone by necessity, which is why Wouters' thresholds put a ceiling on bakeout pressure (10⁻³) and on operating pressure with RF applied (10⁻⁴) (dg-465).

Gas breakdown organizes by pd, not pressure alone; a glow runs at a few hundred to 1500 V with most of the drop across a millimetre-scale cathode sheath (dg-396), and in a DC gridded device at low pressure the ion mean free path sets whether it can strike at all: at 2 mTorr the ion mean free path is ~7 cm and striking voltages reach tens of kilovolts, at 20 mTorr it is 0.7 cm and striking is easy (dg-398). The failure many builders meet first is neither of these but multipactor: the resonant electron discharge that "holds the D potentials down to a few hundred volts" and, "unless the loading is removed," keeps the chamber "in the low-voltage, blue-glow discharge condition indefinitely" (Livingston & Blewett p. 188, dg-251). It liberates gas as it heats surfaces, and breaking it takes fast pumping and an oscillator that can drive through it. Wouters' conditioning rule is the procedure: RF in short bursts at reduced power, never left on through a glow, power and duration raised gradually until the vacuum stays below 10⁻⁴ with ~2 kV steady (dg-277). The RF page treats the electrical side; the vacuum side is that every one of these thresholds moves with pressure, and that a high-voltage gap in vacuum can emit X-rays from field emission and dark current whether or not it visibly sparks; the safety page treats any vacuum gap above roughly 15 kV as a source to survey.

What the record says leaks

The construction reports are unusually candid about where their leaks were, and the answers repeat. Carnegie, after helium-testing every subassembly on delivery (dg-648): "only two leaks were detected, and these were in the gasket seals. They were believed to be due to non-uniform thickness of gasket material" (NYO-780 p. 24, dg-649). Washington: "initial testing of the system disclosed two leaks in welds, both of which were in stainless to mild steel joints"; the same-metal welds were tight (AECU-1951 p. 37, dg-1347). The Oak Ridge test cyclotron's worst leaks were "in very inaccessible locations" in internal water-cooling tubes built by an outside shop (dg-951). Gaskets, dissimilar-metal welds, and anything carrying water inside the vacuum: that is the order three construction records found them in, and a reasonable order to look.

Elastomer seals usually set the floor. ISO and KF flanges with Viton O-rings are "rated to 1 × 10⁻⁸ torr (better suited to 1 × 10⁻⁶ torr)" and limited to ~150 °C bakes (Bertolini 2004, dg-454), and since the budget above wants a base in the 10⁻⁶ decade, that floor is close enough to the requirement that O-ring count and condition matter: squeeze toward the heavy end of the gland chart for static seals, a 16 RMS groove finish, no grease (dg-434, dg-430, dg-444). The double-gasket flange with a pumped interspace, which Livingston and Blewett describe as making it "possible to test the seal for vacuum-tightness quickly and with certainty," was standard at Berkeley, Washington, Carnegie and Oak Ridge (dg-433, dg-1346); on the big lid of a small machine it is the one place the practice still pays.

The acceptance test the records used is rate of rise, alongside the base pressure rather than instead of it. Oak Ridge declared the 63-inch tight at 10⁻⁵ mm Hg with "a rate of rise of 0.00025 microns/sec" valve-off (ORNL-1339 p. 12, dg-794); the same measurement, watched long enough, helps separate a leak from outgassing, since "a molecular leak causes a linear increase in pressure with time" while outgassing rises toward a steady value (dg-447); a virtual leak can mimic either, and helium testing settles what the curve cannot. Helium leak-checking an elastomer-sealed system has its own trap: helium permeates a Viton O-ring in about twenty minutes, after which the background rises and stays up until the gaskets degas, so "take a break rather than chase phantom leaks" (O'Hanlon, dg-448).

Where the time goes

The professional operating records put vacuum at the top of the maintenance ledger. At NRL in 1969, power supplies took 10.2% and vacuum 9.3% of all scheduled hours, far ahead of RF at 1.6% and ion-source work at 1.0% (NRL-MR-2103 p. 33, dg-1139); Oak Ridge's 86-inch lost time "from leaks in the vacuum system, electrical difficulties, mechanical problems … in that order" (ORNL-1196 p. 20); Harvard's biggest single loss in a quarter was the cold-trap refrigerator (dg-1153). None of these was a design fault. They were housekeeping on a system that has to be right every day.

The amateur census does not record vacuum as the reason any build stopped — the one stalled entry stopped on laboratory rules, with its vacuum complete. What it records is vacuum as the open item on builds that have not reached beam: a project whose 10⁻⁵ torr target has been "not yet met" since 2018, with a contamination event along the way (The Cyclotron Project); the MIT machine's marginal 2 × 10⁻³ torr (MIT 2007); a 1958 school machine whose source ran "at the edge of usable pressure" and whose pump "would do at least 10⁻⁶ Torr when it was cooperating" (Central High); a Houghton thesis reporting that "the chamber and foreline setup does not allow the pressure to get low enough to produce the mean free path necessary for acceleration" (Haas 2009, p. 72). A builder budgeting a machine should budget the vacuum system as the professionals' ledger suggests: the subsystem most likely to be the reason today's run does not happen.

Go deeper

Before buying a pump, in the order the budget runs:

1. Species and dee voltage → turns and path length (path-length calculator).
2. Path length and pressure → survival, along the orbit (vacuum calculator); pick the pressure for the loss that is acceptable.
3. Source feed in sccm → throughput in torr·L/s (×0.0127).
4. Throughput ÷ target pressure → effective hydrogen speed needed; then the port and baffle conductances a real pump must beat.
5. Dee aperture conductance → the interior excess; perforate what can be perforated.
6. Gauge where conductance to pump and chamber are comparable; correct it for hydrogen.
7. Helium-test each subassembly; accept by rate of rise; log the pump-down curve.
8. Safety review before RF: HV, X-rays, hydrogen.

• Vacuum & beam survival calculator — the survival integral in simple and along-the-orbit modes, with the ORNL-6086 cross-sections built in.
• Design guide: vacuum domain — the 157 sourced rules behind this page; seals and chamber are the adjacent domains.
• TID-454, Report 4 (pp. 129–151) — the complete worked conductance network and throughput sizing of a cyclotron vacuum system, hosted.
• UCRL-476 pp. 6–10 and NYO-780 pp. 19–24 — the small-machine thresholds and the leak-test-everything record.
• Ion sources: gas feed — the other end of the feed line.
• Modelling tools — Molflow+ for the pressure at the beam rather than at the gauge.
• Resources — the vacuum practitioner communities and surplus sources for pumps and gauges.

Sources

• C. F. Barnett et al., Atomic Data for Fusion, Vol. 1: Collisions of H, H₂, He and Li Atoms and Ions with Atoms and Molecules, ORNL-6086/V1, 1990 — H⁺ + H₂ electron capture p. A-28; H₂⁺ + H₂ total destruction p. G-46. OSTI full text (public-domain ORNL report), retrieved 2026-08-23.
• J. F. O'Hanlon, A User's Guide to Vacuum Technology, 3rd ed., Wiley, 2003 — conductance (ch. 3), diffusion and turbomolecular pumps (chs. 11–12), outgassing (App. C), molecular diameters (App. B.2), unit conversions (App. A.3). Library entry.
• L. R. Bertolini, Accelerator Vacuum and Mechanical Engineering, USPAS course notes, 2004 — pump comparison, compression ratios, comparative outgassing table, elastomer flange ratings. Library entry.
• D. Rose, "Design of Cyclotron Vacuum System," Report 4 in Cyclotron Component Design Technical Reports, TID-454, Carnegie Institute of Technology, 1952 — hosted; pp. 129–151.
• Carnegie Institute of Technology Synchro-cyclotron Construction Report, NYO-780, 1952 — hosted; vacuum section pp. 19–24, equipment list p. 80.
• L. F. Wouters, General Recommendations for Design of Small Cyclotrons, UCRL-476, 1949 — hosted; pp. 6–10.
• The University of Washington 60 Inch Cyclotron, AECU-1951, 1951 — hosted; vacuum pp. 30–37.
• R. S. Livingston et al., The Oak Ridge 86-Inch Cyclotron, ORNL-1196, 1952 — hosted; pp. 9, 20, 41–45.
• The Argonne 60-Inch Cyclotron, ANL-5907, 1959 — hosted; vacuum system pp. 6–7.
• ORNL-1339 (commissioning cluster, rate-of-rise acceptance p. 12) and ORNL-3540 (hosted, pump derating p. 158).
• Cyclotron Branch, NRL, Report of Cyclotron Operation, July–December 1969, NRL-MR-2103 — hosted; outage table p. 33. Harvard Cyclotron Laboratory quarterly report, 1964 Q3 — same cluster.
• M. S. Livingston & J. P. Blewett, Particle Accelerators, McGraw-Hill, 1962 — ch. 5, pp. 181–200: pumping-speed rule, MIT pressures, multipactor, double gaskets. Library entry.
• G. R. Werner, Probing and Modeling Voltage Breakdown in Vacuum, Cornell dissertation, 2004 — breakdown regimes, p. 23. Library entry.
• B. Wolf (ed.), Handbook of Ion Sources, CRC Press, 1995 — Penning source operating data, Table 5.5; gas efficiency. Library entry.
• J. L. Rovey, B. P. Ruzic & T. Houlahan, "Simple Penning Ion Source for Laboratory Research and Development Applications," Rev. Sci. Instrum. 78, 106101, 2007 — Table I. Library entry.
• E. R. Forringer, Phase Space Characterization of an Internal Ion Source for Cyclotrons, MSU dissertation, 2004 — pp. 17–29. Library entry.
• P. Calvo et al., "Beam stripping interactions in compact cyclotrons," Phys. Rev. Accel. Beams, 2021 — H⁻ loss formalism and the AMIT figure. Library entry.
• V. Smirnov, "The Cyclotron and Its Modeling," Phys. Part. Nuclei 52, 2021 — pp. 14, 70. Library entry.
• A. J. Loucks (2007), D. Haas (2009), N. A. Fuller (2013), Houghton College theses, and M. Yuly, "The Houghton College Cyclotron," Cyclotrons 2013, WE1PB01 — pressure windows and the vacuum-limited run. Library entries lib-008, lib-003, lib-005, lib-041.
• G. M. Miley & S. K. Murali, Inertial Electrostatic Confinement (IEC) Fusion, Springer, 2014 — glow-discharge pd scaling, pp. 86–94. Library entry.
• L. Dewan, Design and Construction of a Cyclotron Capable of Accelerating Protons to 2 MeV, MIT S.B. thesis, 2007 — vacuum requirement pp. 9–11. Library entry.
• Census entries cited by anchor are sourced on the builds page, each to its own public record.