Shielding a Small Cyclotron

The accelerator-shielding literature is written for machines that make neutrons by the billion behind metres of concrete, and it is tempting either to read that as the standard a small cyclotron must meet or to dismiss it as irrelevant. Both readings are wrong. What a machine emits is set by what its beam, its target and its structure can actually drive — which for a proton machine on ordinary targets below about 1 MeV shuts the (p,n) channels, but says nothing about prompt gamma rays, and nothing at all about a machine running deuterons. The workflow from the big-machine literature transfers well and is better than anything an amateur is likely to invent: design from the source terms you can credibly produce, build the estimate as a chain you can check link by link, verify it by survey, and expect the result to leak out through the holes rather than through the wall. The source terms and the empirical formulae do not transfer; only the method does.

Where this sits among the neighbouring pages. Safety covers the seven hazard classes of a small accelerator project and carries the distance-and-attenuation intuition figure this page assumes; Legal covers dose limits as regulation, licensing and notification, by jurisdiction; and residual radiation and personnel dose hosts the measured activation and dosimetry data.

What your machine can actually emit

Shielding starts as a question about nuclear thresholds, not about materials. Where a reaction's threshold sits above the energy a projectile can actually reach, that channel is not part of your source term — for that projectile, that nuclide, and that maximum credible energy. It is a hard kinematic floor rather than a probability argument, and it is also a narrow claim: it rules out one channel, not X-rays, not prompt gammas, not a later change of species, and not an impurity you did not know was in the gas bottle. The care is all in “actually reach”: a shield must be designed against the maximum credible energy, not the nominal one. Voltage overshoot during conditioning, RF transients, energy spread, a biased target, an impurity in the gas bottle and a later decision to change species all move that number, and every one of them moves it upward.

X-rays come first, and they do not need a beam. A vacuum gap under sufficient voltage emits bremsstrahlung wherever field-emitted electrons land on a surface — so the ingredients are an accelerating potential, an electron current and something for the electrons to strike, not merely a gap. The bremsstrahlung endpoint cannot exceed the electron energy, which is why the practical monitoring onset in the amateur literature sits around 18–20 kV on electrodes (dg-559 — citations in this form point to a Design Guide rule, each of which carries its own formula, verbatim quotation and page-level source citation): below roughly 10–15 keV the photons are largely absorbed by the chamber wall, the glass and the air before reaching anyone.

A dee at a kilovolt is therefore not in that territory — but an RF system rebuilt toward 5–13 kV is approaching it, and conditioning transients and field emission routinely exceed nominal electrode voltages. That is the sequence to plan for: the X-ray hazard arrives with the RF upgrade rather than with the beam, which is why the safety page puts a survey meter before a beam diagnostic.

Proton-induced neutrons need a threshold crossed. Among the common, stable light targets the lowest door is ⁷Li(p,n)⁷Be at 1.881 MeV, and near that threshold the neutrons emerge with energies capped around 100 keV — which is why the reaction serves as a soft neutron source. Radioactive targets change the picture: a tritiated target opens a (p,n) channel lower still, so “lowest” here means lowest among the materials an amateur is likely to have.

Structural metals sit higher, but quote them per nuclide, not per element. ⁶³Cu(p,n) needs about 4.2 MeV (dg-884) — and natural copper is only 69% ⁶³Cu, the other 31% being ⁶⁵Cu, whose (p,n) door opens lower. Citing the majority isotope's threshold understates the element. Every natural material is a mixture, and the shield has to answer to the most permissive constituent, not the most abundant one. The energy-band page makes the same argument from the experimental side, with its thresholds retrieved from the NNDC Q-value calculator: every beam in the documented amateur census sits at less than half the ⁷Li threshold, as of its August 2026 review.

Deuterons break the whole argument, and not only on deuterated targets. This is the most important qualification on this page. A low-energy deuteron sheds its loosely bound neutron readily in the field of a light nucleus, so breakup and stripping proceed efficiently wherever the Coulomb barrier is low and the (d,n) Q-value is favourable. ⁹Be(d,n) is exothermic and is one of the most prolific neutron reactions available to low-energy accelerators — second only to Li(d,n) between roughly 1 and 3 MeV — and much of its yield lands below 1 MeV. Lithium, deuterium and tritium behave similarly.

So a deuteron machine is a neutron source almost regardless of what you aim it at. Beryllium windows, lithium targets, deuterium adsorbed on a previously-used target, and D–D on the residue in the chamber all qualify. Changing species from protons to deuterons is a categorical change to the shielding problem, and it must be re-analysed rather than extrapolated.

Two amateur-scale figures are worth knowing and worth handling carefully. Detectable D–D output is reported from around 15 kV on a fusor cathode (dg-543) — but that is a detectability observation, not a physical threshold, and it depends on ion current, detector efficiency, background and geometry, none of which transfer directly from a fusor cathode to a cyclotron target. And the amateur fusion literature puts the point where an operator needs both neutron and X-ray shielding at roughly 6 × 10⁵ n/s (dg-560). Treat that as one community's rule of thumb at an assumed working distance, not a universal threshold: dose depends on distance, occupancy, directionality, moderation and room scatter, so a weaker source at arm's length or in an occupied room can demand more shielding than a stronger one across a basement.

Thresholds are properties of specific nuclides, not of materials in general. “Copper does not activate” is not a fact; “⁶³Cu(p,n) is closed below 4.2 MeV, and ⁶⁵Cu opens lower” is. And closing the (p,n) channels does not close everything: radiative capture and prompt-gamma reactions run at sub-MeV proton energies — ⁷Li(p,γ) emits 17.6 MeV gammas, as the energy-band page records — and any neutron field, once present, activates by capture. Work out the reactions your own beam, on your own target and structure, can drive; redo it whenever the machine gains energy or changes species; and design against the result rather than against the nominal beam.

Design from source terms; verify by survey

Order matters here, and it is easy to get backwards. Primary shielding must be designed before the machine runs, from the maximum credible source terms worked out in the previous section — you cannot measure a spectrum you have not yet produced, and being inside the enclosure to measure it is the thing the enclosure exists to prevent. Survey then does two jobs: it verifies the design, and it lets you refine shielding for the residual and scattered fields that only exist once the machine has run.

That second job is where the collection's sharpest rule applies: size residual gamma shielding from the measured line energies rather than from a worst case (dg-868). When Oak Ridge surveyed the Berkeley 184-inch to find out what a high-intensity machine leaves behind, the residual spectrum proved to be dominated by lines at 510 and 810 keV, and at those energies the report gives a lead half-thickness of about 0.6 cm and about 4 cm in concrete, concluding that 2 cm of lead reduces that field by an order of magnitude. Its own summary is that “shielding against this radiation is also not very difficult.”

Those thicknesses are narrow-beam attenuation figures for that specific residual gamma field. In a broad-beam geometry, with scatter and buildup, with higher-energy prompt gammas present, or with secondary radiation from the shield itself, 2 cm of lead will deliver less than a factor of ten in dose rate. Half-thickness tables size a shield against a known line; they do not bound a mixed prompt field.

In plainer terms: a half-thickness figure assumes a pencil of radiation aimed straight at a slab (narrow beam). A real enclosure sees radiation arriving from many directions, bouncing off surfaces (scatter), and the shield itself re-emitting some of what it absorbs (buildup). All three deliver more dose to the far side than the table predicts, so the tabulated thickness is a floor and not an answer.

Buildup has a consequence that is worth stating on its own, because it is the opposite of what intuition suggests. Adding material to a shield can make the reading behind it worse. Measuring concrete and water attenuation at the Berkeley 184-inch in 1947, Moyer’s group found that a hydrogenous layer placed after a dense one raised the ionization reading rather than lowering it — by about 60% for paraffin following iron, and 100% following lead (dg-1118). Fast neutrons slowed in the dense layer become far more effective at depositing energy in the hydrogenous one, and some of that comes back out. The lesson is not that paraffin is bad; it is that layer order is a design variable, and a composite shield cannot be sized by adding up the layers’ individual attenuations.

The general point survives the caveat, though, and it is what makes measurement worth the trouble: an unknown spectrum can only be over-specified. That is the mechanism by which amateur projects come to believe they need a concrete vault — not because the machine is energetic, but because nobody has characterised what it emits, and the only safe assumption in ignorance is somebody else's worst case.

Three techniques from the collection are procedurally simple, and all three belong to the verification step rather than the design step. Simple is not the same as casual: each needs an appropriately calibrated instrument, controlled access while it is in use, and someone competent to interpret what it reads.

• A collimator made of lead bricks. Berkeley scanned a bombarded target assembly past a 1/8-inch slot between lead bricks with a counter behind it, turning a survey meter into a crude imaging instrument that says where the activity is (dg-685).
• A detector in a lead pig with a plugged hole. Oak Ridge localised activation with a collimated NaI crystal in a lead housing, using the plug to take a background reading without moving the instrument (dg-869) — the discipline being that a shielded detector measures a direction, and the same detector unshielded measures a room.
• Survey the machine's own surfaces. Where activation concentrates on dee edges and liners tells you where the beam is dying (dg-695). Activation maps the beam losses that both activate the surveyed material and stay detectable after cooling — so it is a strong clue to the beam-loss map rather than identical to it. Prompt X-rays, prompt gammas, neutrons and non-activating losses can each be distributed differently.

The estimate is a chain

ORNL-3540, the 1963 proposal for an 810 MeV machine that was never built, is the only document in this collection that treats shielding as an engineering deliverable with a budget rather than a regulatory afterthought — a proposal has to justify itself, so it shows the reasoning a built-machine report would compress into a wall thickness. Its method is a chain with a checkable link at each stage (dg-914):

1. Dose limit — the design target, chosen before anything else.
2. Source term — how much of what, emitted where.
3. Attenuation — what the proposed material and thickness do to it.
4. Secondary buildup — what the shield itself then emits and scatters.

The value is not the arithmetic; it is that a wrong answer can be localised. A single number for “wall thickness” cannot be debugged. Four linked numbers can, and the report is explicit that each link should be checked independently.

Two design decisions in the same chapter are worth adopting whole. Separate the radiation components by the question each one answers (dg-915): the penetrating high-energy component sets bulk shield thickness, while the soft, scattered component sets what happens at doors, ducts and corners. Treating them as one quantity guarantees over-building one and under-building the other. And design to the general-population limit, not the occupational one (dg-913), in every area that is regularly occupied. For an amateur machine in a domestic building, where the people on the other side of the wall have not consented to anything and are not monitored, that is the only defensible target. How much stricter the public limit is depends on jurisdiction and era — under current US federal limits the ratio of annual occupational to public dose is far larger than the factor of ten this 1963 report assumed — so take the relationship from the method and the numbers from Legal and your own regulator.

Shields leak at their penetrations

A shield wall is the easy part. Every real enclosure has holes in it — a door to get in, a duct for cables and cooling water, a line of sight for a beam or a probe — and those holes, not the wall, decide what the shield achieves. ORNL-3540 gives a quantitative method for them that scales down cleanly, because it is geometric rather than energetic (dg-917).

Duct transmission depends strongly on the ratio of length to radius, z/a, not on length alone: a long narrow duct is a good shield, a short fat one is a window. At a bend, scattering creates a fresh source of neutrons on the far side, and the measured attenuation across the bend is approximately ⅓ csc θ, where θ is the angle of deviation and the empirical ⅓ accounts for the angular distribution and albedo of the reflected neutrons. For a 90° bend that expression alone gives about 0.33.

A further factor of three is available for the price of some duct: extend the entering leg past the bend rather than stopping it at the corner, so a neutron travelling straight hits a dead end instead of finding the next leg. The two together are what produce the ~0.1 per-bend figure the report tabulates — 0.33 from the turn, times roughly ⅓ from the extension. The 0.1 already includes the trick; it is not 0.1 and then a further factor of three. Reading it as both would underpredict streaming several-fold, which is the wrong direction to be wrong in.

The report works its own personnel maze as an illustration, modelling the 5 × 10 ft passage as a circular duct of equal area. Total transmission is the product of the individual elements — which is the whole method in one sentence:

Method to imitate; numbers not to reuse. The table below is one worked geometry from one report, for the low-energy neutron atmosphere of one experiment room. Its value is the demonstration that elements multiply — not the figures in the right-hand column.

Multiplying the seven tabulated elements gives about 3 × 10⁻⁹. That figure is arithmetic on the report's own numbers rather than a value read from its table, whose printed total is illegible in the available scan.

The report scopes this method explicitly, and so must anyone reusing it: the duct-and-maze calculation “applies for low energy neutron, such as constitute the neutron atmosphere within the experiment room.” It is not a method for the penetrating high-energy component, which is what bulk wall thickness is for. This is dg-915 in practice — the two components need different calculations, and using the easy one for the hard job is the classic way to build a shield that fails at exactly one energy.

Three more penetration rules from elsewhere in the collection, all cheap:

• Step your joints. Shield doors and removable plugs get stepped, labyrinth edges so that ordinary construction tolerances cannot produce a straight-through gap (dg-919). The step is what makes a millimetre of misalignment harmless instead of load-bearing.
• Stagger removable layers. Carnegie stacked removable shielding in two offset layers precisely so that no crack ran straight through (dg-653). Two imperfect layers beat one perfect one, because the second one's flaws are somewhere else.
• Put beam-defining apertures inside the wall. Rochester placed the beam-defining slit within the shield wall itself, because the slit system intercepts most of the beam and therefore becomes a source (dg-966). Anything that stops beam belongs on the shielded side of the boundary — which is also why the in-vacuum components the beam strikes are the hottest objects in the building (dg-874).

Machine materials become radiation sources

What a machine is made of determines what it becomes under irradiation, and that is a decision taken at the drawing board or not at all (dg-864). Shielding added later attenuates what a component emits; it cannot change what the component is.

The measured evidence is sharper than the principle suggests, and it tracks the alloying elements rather than the base metal. Under identical irradiation at Berkeley, stainless steel produced two long-lived isotopes — Cr-51 at 27 days and Mn-54 at 300 days — where plain iron produced only the Mn-54 (dg-865). The chromium is what makes the difference, and the nickel in stainless brings 71-day Co-58 with it. Aluminium, in that survey and under those conditions, yielded no long-lived activities — a report-specific observation rather than a property of aluminium, which under harder irradiation can produce long-lived ²²Na and ⁷Be.

So the report's construction advice is specific: use as much aluminium as possible and very little stainless steel. It also quantifies the short-lived penalty for copper — the Cu-64 yield from copper ran about 50 times the Na-24 yield from aluminium, a ratio the authors put as good to within a factor of two. A material can be the right choice not because it activates less in total, but because what it becomes dies sooner, and because the marker nuclide follows an alloying element you may not need.

That reasoning applies hardest to beam-intercepting hardware — probes, slits, beam stops, septa — where activation is a selection criterion alongside strength and machinability (dg-939). And you can find out what your own machine does empirically: hang witness foils of candidate materials at mapped positions before a run and count them afterwards (dg-866).

Those specific inventories are 730 MeV data at roughly a microamp, produced by spallation channels that sub-MeV protons cannot open — so those nuclides do not transfer, though the reasoning does. “Closed” applies to the spallation routes and not to everything: radiative capture and prompt-gamma reactions run below 1 MeV, and once any neutron field exists — from deuteron operation, say — capture activation follows wherever the neutrons go. See the scope note on the residual-radiation page, which carries this caveat above every number.

The cheapest shielding is earth, geometry and time

Before buying attenuation, spend the free kinds.

Earth. Oak Ridge planned its proposed 48-inch machine's room “mostly below ground” and let the soil do the work (dg-962). A basement, a berm or a partly buried enclosure is shielding that costs excavation once and nothing thereafter, and it shields in every direction at once rather than the one you thought of.

Geometry. Distance is exact and free, and the attenuation figure on the safety page shows how quickly it pays. Rochester's neutron time-of-flight work kept flight paths under about 1.2 m partly so that the room, rather than the resolution equation, set the layout (dg-994) — a reminder that the enclosure is a design constraint on the experiment, not just a container for it.

Time. The Crocker Laboratory crew treated handling time as the primary dose control and choreographed it to the minute — target setup about three minutes, removal about one, dismantling under one, behind a two-inch lead-glass shield with the sides deliberately left open for tools (dg-871). They also found that in target handling the hands take roughly ten times the whole-body dose (dg-872), which means a badge on the chest is measuring the wrong thing for that task. And the short-lived component decays fast: at the 184-inch, initial levels under 8 r/hr fell to about 10 mr/hr in 48 hours — a factor of several hundred for the price of two days. Waiting is a shield, within limits: that residual 10 mr/hr is still a controlled radiological area rather than a safe one, the decay curve belongs to that machine's nuclide mix and not yours, and entry should be governed by what a survey says and what the half-lives are, never by elapsed time alone.

Two more decisions belong in this category rather than in a materials budget. Sequence commissioning around the shielding you actually have. Davis did all its early work on a species its enclosure could contain and deliberately declined to accelerate protons until the vault was complete (dg-818). The transferable rule is the sequencing, not a heuristic that heavier or slower is safer — it is not. Deuterons and alphas open neutron channels at energies where protons open none, so the safe-first species is whichever one your computed source terms say is quietest, which may well be the lighter one.

Interlock the access. Carnegie wired doors and enclosures so they could not open unless the oscillator was off (dg-654) — a 1950 instance of the right instinct, and not a sufficient modern specification. A fail-safe accelerator interlock should remove and verify the removal of every hazard the access exposes: RF, high voltage, the ion source and beam, plus the stored energy that outlives them all, and it should prevent operation while access is open rather than merely reacting to it. Residual radiation does not respond to an interlock at all, which is what survey and waiting are for.

When you do buy material, ORNL-3540's own approach was to trade construction methods on delivered cost per unit attenuation rather than on cost per tonne (dg-920) — which is how a study ends up choosing solid low-strength concrete over more exotic options.

Assume your estimate is low

The most useful sentence in ORNL-3540's shielding chapter is an admission: assume the shielding estimate will prove low and the experiment space too small, and design the margin and the expansion room in from the start (dg-912). The same chapter tells you to leave a designed-in recovery path so that a maze or penetration found inadequate can be fixed without rebuilding the enclosure (dg-918).

That expectation is not pessimism; it is what the record shows. The same laboratory set out to grind a magnet's pole faces flat to ±0.01% and reported 0.05% after a further half-year of work (the test-cyclotron seam). Estimates in this field land short, and the designs that survive are the ones with somewhere to put the difference.

One last piece of method, for the situation an amateur is most often in. When your problem has no literature, adapt the quantitative methods of the nearest mature field — and say in writing that you did (dg-916). ORNL did exactly this for subproblems its own field had not addressed. Borrowing a method and labelling the borrowing is honest engineering; the failure mode is borrowing it silently and forgetting which assumptions came with it.

Where this page stops

Deliberately excluded, with somewhere better to go:

• Dose limits, licensing and notification — regulatory, jurisdictional and dated. Legal carries the US federal overview and all 51 jurisdictions, cited and dated. Nothing on this page is legal advice.
• Hazard identification — the seven hazard classes, the survey-meter discipline and the attenuation intuition figure live on Safety.
• Measured activation inventories and dosimetry practice — the two hosted studies, with their energy scope stated above every number.
• Dose arithmetic. There is no calculator here and there should not be. The professional standard for this work is NCRP Report No. 144, Radiation Protection for Particle Accelerator Facilities (2003), which revised and expanded NCRP 51 (1977) — whose own title, Radiation Protection Design Guidelines for 0.1–100 MeV Particle Accelerator Facilities, is worth noticing: the standard's stated range starts at 100 keV, well inside amateur territory. Read it before designing an enclosure.

Sources

• AD-755510, Martin (ed.), Accelerator Radiation Protection, US Army Natick Laboratories, 1972 — added after this page was written, and the closest thing in the collection to a radiation-protection manual for small machines: it is scoped to accelerators below 40–50 MeV and covers X-ray and neutron shielding, induced radioactivity, exposure limits, measurement and interlocks. Hosted here.
  Read one limit of it before reaching for its numbers. Its X-ray shielding curves (Fig. II-11) run from 1.0 to 40 MeV, so a machine with a dee at a few kilovolts sits off the bottom of every chart in the chapter. What it offers that range instead is a way to bound the source: assume the ion current I drives a reverse electron current of about 0.2 I through roughly a third of the terminal voltage. The report is candid that these assumptions are unreliable estimates, and its conclusion is the useful part — that the shielding a heavy-ion machine needs may not be so much less than that for a comparable electron accelerator. For actual output at dee voltages you need X-ray tube data, not this chapter.
• AECD-2149, Moyer, Hildebrand, Knable, Parmley & York, Character of the Radiation Field and Shielding at the 184-Inch Cyclotron, UC Radiation Laboratory, 1947 — the collection’s first measured shielding source rather than a method: concrete and water attenuation taken with the machine as the source, front-face transition effects, the composite-layer result above, and a dose map normalised to beam current. Its numbers are for a 190 MeV deuteron beam and do not transfer; the measurement design does. B. J. Moyer later gave his name to the Moyer model, the standard analytic method for accelerator shield design. Read it at the Internet Archive.
• ORNL-3540, A Proposal for the Mc² Isochronous Cyclotron, Oak Ridge National Laboratory, 1963, ch. 11 (pp. 184–242) — the estimate chain, the duct and maze method with its worked table (pp. 200–204, Fig. 11.8), stepped joints, cost per attenuation, and the instruction to assume the estimate is low. Hosted here.
• ORNL-3158, Boom, Toth & Zucker, Residual Radiation of the LRL 184-Inch Cyclotron, 1961 — measured line energies and lead half-thickness, the collimated-detector method, alloy-dependent inventories, witness foils. Hosted here.
• UCRL-8276, McWalters et al., Radiation Exposures of Personnel at the 60-Inch Cyclotron, 1958 — handling time as dose control, extremity dose, the hottest objects in the building. Hosted here.
• NYO-780 (pp. 43–44) — staggered removable shielding and access interlocks. Hosted here. · ORNL-1884 (p. 21) — below-grade siting. Hosted here. · NYO-3823 — the beam-defining slit inside the shield wall. Hosted here.
• ⁷Li(p,n)⁷Be threshold 1.881 MeV and its near-threshold ~100 keV neutron spectrum — verified August 2026 against IAEA INIS and OSTI, and consistent with the NNDC Q-value calculator figures used on Experiments by Energy Band.
• NCRP Report No. 144, Radiation Protection for Particle Accelerator Facilities (2003), verified current August 2026; a free executive summary is published by NCRP. The report itself is copyrighted and is not hosted here.
• Amateur-scale onsets: dg-559 (X-rays from ~18–20 kV), dg-543 and dg-560 (D–D onset and the ~6 × 10⁵ n/s shielding threshold). All shielding-domain rules.