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Accelerators

How a heavy-ion beam is made, using FRIB at Michigan State as the worked example: a superconducting linac folded twice, a charge stripper, a production target and the ARIS fragment separator. Pick an ion, a charge state and an energy; every panel is computed from them. Click a part of the complex to open its physics.

Ion

E/AMeV

This beam

Facility

Physics

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Rendering

Scene scale & rendering notes

Schematic, after FRIB. The order of the sections is FRIB's, and so are the front end (47 m long; drawn as 47 m from the ion sources to the linac entrance along the linac axis, so the beam's path through it, with the 10 m drop, is about 53 m), the total length of the folded superconducting linac (472 m), the 80 m transport and 70° bend to the target, the ion sources about 10 m above the tunnel, and the cryomodule count of each segment (15, 24, 7). Not to scale: how the 472 m divide between the segments and the two 180° folds, the fold radius, ARIS, and the positions and sizes of the experimental areas (their arrangement follows the published layout, see the end-stations panel). Only FRIB's own facilities are drawn; the HRS hall holds a planned instrument whose beam line is in construction, drawn schematically. Bunches move at a display speed. Buildings are drawn open at the top from outside; the tunnel ceiling appears when the camera goes inside. The cryomodule green and black cable bundles follow published FRIB tunnel photographs (CNRS, photo credit FRIB), with silver services and a neutral concrete interior. Paint shades are visual approximations under the scene lighting. Equipment, racks, cables and people are generic in shape; magnet colours remain schematic (cryomodule vessels, couplers, dipoles, quadrupoles, shielding), not FRIB's drawings, and the walls between segments are illustrative; the people are 1.7 m tall, for scale. Walking speed is 3 m/s. With the focusing panel open, the tube along the linac is the beam envelope of its periodic channel, magnified about 400 times; FRIB's real focusing changes from segment to segment.

The superconducting linacFRIB

Voltage a cavity gives this ionV_eff·T(β)/T(β_opt) vs β

80.5 MHz QWR322 MHz HWRthis beam

A cavity has a fixed gap spacing, matched to one velocity β_opt: an ion that is too slow or too fast arrives at the second gap with the field already turned. So the linac is a relay of four cavity families, each used where T(β) is high. The energy gained per nucleon is (Q/A) times the voltage: a uranium ion carrying 33 charges gains 2.4 times less than one carrying 78, which is why the beam is stripped at 17 MeV/u.

Drift-tube cell lengthβλ/2 vs E/A

f_RF

this ionproton5 cm

The ion leaves the source at 12 keV/u. Uranium then moves at β = 0.005, and half an RF period at 80.5 MHz is a flight of under 1 cm: no room for drift tubes with focusing magnets. FRIB's first accelerator is therefore a radio-frequency quadrupole, which bunches, focuses and accelerates with shaped electrode vanes and has no drift tubes, from 12 keV/u to 0.5 MeV/u. Once the ions are faster, the frequency can be raised fourfold, to 322 MHz, for the half-wave resonators.

How it is computed

two gaps, β_optλ/2 apart, opposite fields: T(β) = |sin(πβ_opt/(2β))|
gain at crest per nucleon: ΔW/A = (Q/A) V_eff T(β)/T(β_opt)
cell length L = βλ/2, λ = c/f

Thin gaps; the finite-gap factor sin(πg/βλ)/(πg/βλ) is left out, and the real FRIB cavities differ in detail from an ideal two-gap structure. The gain is shown at the crest: the linac runs at a negative synchronous phase φ_s for longitudinal focusing, which multiplies it by cos φ_s (FRIB's phase is not quoted here). V_eff is the effective voltage at β_opt from FRIB's resonator table.

ARIS: Bρ–ΔE–Bρ

want

Δp/p

d/R

madepasses Bρ₁passes Bρ₁, ΔE, Bρ₂wanted

ARIS, FRIB's fragment separator, takes up to 8 T m within ±5% in momentum and ±40 mrad in angle^[19], in three stages: a pre-separator that removes the unreacted beam, then two stages with wedge degraders. Here one Bρ–ΔE–Bρ stage is modelled. The primary beam is the ion chosen on the left, at its energy. Its fragments fly on at nearly the beam velocity, so the first dipole stage selects Bρ ∝ (A/Z)βγ: a whole diagonal of nuclei with the same A/Z survives. A degrader then takes energy ∝ Z²/v² from each, so the second stage, set for the wanted nucleus, rejects neighbours with a different Z.

How it is computed, and what is left out

fragment: γ_f = γ_beam, Q = Z ⇒ Bρ₁
degrader: dE/dx (Bethe, Bloch term, effective charge) integrated through t = (d/R)·R(wanted)
keep |Bρ/Bρ_ref − 1| < Δp/p at both stages

−dE/dx = K z² (Z_t/A_t) β⁻² [½ ln(2m_ec²β²γ²W_max/I²) − β² − y² Σ_n 1/(n(n² + y²))]
K = 0.307075 MeV cm²/mol, y = zα/β, z = Z[1 − exp(−0.95 v/(v₀Z^2/3))]
I = 63.7 eV (Be), 166 eV (Al)

Checked against NIST PSTAR and ASTAR in Be and Al and against measured Ar, Kr and Xe stopping (IAEA stopping database): . The shortfall for heavy ions is the missing Lindhard–Sørensen and Barkas terms, so for Xe-like fragments the wedge loss is a few per cent low and Bρ₂ 1 to 3% high. Because every fragment is shifted alike, it hardly moves the selection relative to the wanted ion, but it does move the absolute setting. Recomputing stage 2 with a full stopping-power calculation that includes those terms and shell corrections: . So the panel shows which neighbours a stage tuned on the wanted ion lets through; the Bρ₂ it prints is good to a few per cent, coarser than the acceptance, and a real separator is set on the measured beam.

Left out, on purpose: production cross sections (the chart says which nuclides pass, not how many arrive), the momentum spread of the fragments (comparable to the acceptance in reality, so real purity is worse), energy loss in the production target, angular acceptance, charge states other than bare, energy-loss straggling, and the wedge shape (a flat slab at the dispersive focus; the wedge angle restores achromatism without changing the mean selection). Nuclides with T_1/2 < 100 ns are dropped as they decay before the focal plane.

Magnetic rigidityBρ (T m) vs E/A (MeV)

this ion, charge Qsame ion baremachine limits

A dipole of field B bends a particle of momentum p and charge q on a circle of radius ρ = p/(qB). A ring or a separator is built for a maximum Bρ; an ion fits if its rigidity is below it. Stripping more electrons (larger Q) lowers Bρ in proportion, which is why rings take ions after a stripper and why the bare-ion curve lies lowest.

How it is computed

M_atom = Z M(¹H) + N m_n − A (B/A)
M_ion = M_atom − Q m_e (+ B_e, neglected)
T = A·(E/A), γ = 1 + T/M_ionc², βγ = √(T(T + 2M c²))/(M c²)
p c = βγ M c², Bρ [T m] = p c [MeV] / (299.792458 Q)
Eρ = p v/q [MV]

B/A from NUBASE2020 (Kondev et al., Chin. Phys. C 45, 030001 (2021)), which uses the atomic-mass convention B = Z M(¹H) + N m_n − M_atom. CODATA 2018 constants. The removed electrons' binding B_e is neglected: 0.76 MeV for bare uranium, 3×10⁻⁶ of the mass. E/A is kinetic energy per nucleon (mass number A); per atomic mass unit would differ by M/(Au) − 1, 2.1×10⁻⁴ for the ²³⁸U atom (1.4×10⁻⁴ for the U³³⁺ ion).

Checked against an independent 30-digit calculation that takes atomic masses from the AME2020 mass table instead of NUBASE: largest relative difference in Bρ .

Against quoted machine pairs, Bρ in T m computed here vs quoted: .

FRIB's experimental areasclick one in the scene

After ARIS the rare-isotope beam goes three ways: fast beams at near production energy to the south vaults and the HRS hall; beams stopped in gas in N4 for precision work; and stopped beams reaccelerated in ReA. The arrangement follows the published layout; positions and room sizes in the scene are schematic, the instruments generic shapes at roughly their size.

S1: FRIB Decay Station initiator (FDSi): implantation detector surrounded by germanium detectors, for β decay of fast-beam fragments. [a]
S2: Sweeper magnet and the MoNA-LISA neutron array (walls of plastic-scintillator bars): unbound states seen through their neutrons. [a]
S3: S800 spectrograph: superconducting, high resolution, bends vertically. The spectrograph takes up to 4 Tm with a momentum acceptance of about ±3 % and 20 msr; its analysis line up to about 4.9 Tm, within ±0.5 % (dispersion-matched mode) or ±2 % (focused mode). GRETINA ran here in FRIB's first S800 experiment (2022). [b, d, h]
N4: Gas stopping: fast fragments slowed and stopped in helium gas (linear gas cell, cyclotron stopper, cryogenic gas stopper) and extracted at about 60 keV. [b]
stopped beams: LEBIT: Penning-trap mass measurements in a 9.4 T magnet. BECOLA: collinear laser spectroscopy. [b]
ReA3: Reaccelerated beams at astrophysical energies: SECAR (a recoil separator about 40 m long) on its own beam line, with the JENSA gas-jet target at its entrance as its main target; the AT-TPC active target. [b, c, j, k]
ReA6: SOLARIS solenoidal spectrometer (up to 4 T) on its own beam line. GRETA, the γ-ray tracking array, is to serve experiments at ReA and at the S800, where it uses a modified GRETINA frame; the scene shows the fall 2025 configuration, with its frame in this vault. [c, e, i, j]
HRS: High Rigidity Spectrometer (Bρ up to 8 Tm), in two segments: the high-transmission beam line (HRS-HTBL) from ARIS to the reaction target, and the spectrometer section (HRS-SPS). In February 2025 DOE approved CD-2/3 and the start of execution for HRS-HTBL; the instrument as a whole is still under development, so the magnets in the scene are a planned layout, drawn schematically. [f, g]

[a] FRIB, second call for proposals (2022) and FDSi pages. [b] A. Gade and B. M. Sherrill, Phys. Scr. 91, 053003 (2016), Fig. 2 and Secs. 2.3, 2.8, 2.9. [c] FRIB instrument pages (JENSA, SECAR, SOLARIS, GIRAFFE). [d] P. Fallon, GRETINA/GRETA status (2024). [e] FRIB Laboratory Update, Fall 2025. [f] FRIB HRS fact sheet, March 2025. [g] FRIB, High Rigidity Spectrometer instrument page (as archived 12 June 2026), Status. [h] FRIB, S800 Spectrograph Service Level Description, FRIB-S30206-RC-007221-R003 (19 December 2023), Sec. 4. [i] FRIB, GRETA instrument page (as archived 21 May 2025). [j] FRIB, ReA Experiments Service Level Description, FRIB-S30206-RC-008645-R001 (31 July 2023), Sec. 3. [k] K. Schmidt et al., Status of the JENSA gas-jet target for experiments with rare isotope beams, Nucl. Instrum. Methods A (2018), arXiv:1804.06842.

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