Case Study 1: FRIB — Inside the World's Most Powerful Rare Isotope Accelerator

The Machine That Maps Terra Incognita

On May 2, 2022, a beam of calcium-48 ions accelerated to nearly half the speed of light struck a beryllium target at Michigan State University, producing a spray of rare isotopes never before observed on Earth. The Facility for Rare Isotope Beams — FRIB — had begun operations, and nuclear physics entered a new era.

FRIB is the culmination of more than two decades of planning, design, and construction — a $730 million investment by the U.S. Department of Energy and Michigan State University to build the most powerful rare-isotope accelerator in the world. Its mission is to produce and study the thousands of exotic nuclei that exist between the valley of stability and the nuclear drip lines: the frontier of nuclear physics.

This case study takes you inside FRIB, from the ion source to the experimental halls, explaining the physics at every stage.

The Driver Linac: From Ions to 200 MeV/u

The Ion Source

FRIB's journey begins with an Electron Cyclotron Resonance (ECR) ion source — a plasma device that strips electrons from atoms using microwave-heated electrons spiraling in a magnetic field. The ECR source produces highly charged ions: for uranium, the workhorse charge state is ${}^{238}\text{U}^{33+}$ (33 of 92 electrons removed), which represents a compromise between high charge (for efficient acceleration) and high source output.

The source delivers a continuous (CW) beam of uranium ions at an energy of only $\sim 12$ keV per nucleon — barely above thermal energies on the nuclear scale. From this quiet beginning, the ions will be accelerated by a factor of more than 16,000 in energy.

The RFQ and DTL

The low-energy beam first enters a Radio-Frequency Quadrupole (RFQ), a 4-meter-long copper structure whose interior electrodes create a sinusoidal electric field pattern that simultaneously bunches the continuous beam into packets, focuses it transversely, and accelerates it from 12 keV/u to about 0.3 MeV/u.

A short Drift Tube Linac (DTL) section then boosts the energy to approximately 2 MeV/u, preparing the beam for the main accelerating section.

The Superconducting Linac

FRIB's main accelerator is a superconducting linac — 324 individually powered superconducting radiofrequency (SRF) cavities made of pure niobium, cooled to 2 K by a liquid helium cryogenic plant. The cavities operate at three different frequencies (80.5 MHz, 161 MHz, and 322 MHz) optimized for different velocity ranges.

The linac is folded into three segments connected by two 180-degree bending sections, fitting the 450-meter total acceleration path into a 150-meter-long tunnel. This "folded linac" design was a key engineering innovation — it reduces the building footprint and cost while maintaining the full accelerating length.

At the end of the linac, the ${}^{238}\text{U}^{33+}$ beam passes through a carbon stripper foil that removes the remaining electrons, producing fully stripped ${}^{238}\text{U}^{92+}$. A final linac section accelerates the stripped beam to the design energy of $\geq 200$ MeV per nucleon.

The Numbers

The beam power of 400 kW is the critical figure. Power = (energy per ion) $\times$ (ions per second). For uranium at 200 MeV/u:

$$P = (200 \times 238) \; \text{MeV} \times 5 \times 10^{13} \; \text{ions/s} \times 1.6 \times 10^{-13} \; \text{J/MeV} \approx 380 \; \text{kW}$$

This intense beam, slamming into a target at half the speed of light, produces the world's most copious source of rare isotopes.

The Production Target and Fragment Separator (ARIS)

Fragmentation at the Target

The 200 MeV/u ${}^{238}\text{U}$ beam strikes a production target — typically a rotating graphite disk, 1–2 cm thick, that distributes the enormous beam power (400 kW) over a large area to prevent melting. The target rotation is essential: a stationary target would vaporize in seconds.

In the target, peripheral nuclear collisions strip nucleons from the uranium projectile. A single ${}^{238}\text{U}$ nucleus can lose anywhere from 1 to 100+ nucleons, producing a vast spectrum of fragments spanning the chart of nuclides from the lightest to the heaviest elements. The fragments emerge from the downstream face of the target at nearly the beam velocity ($\beta \sim 0.5$), traveling forward in a narrow cone.

The Advanced Rare Isotope Separator (ARIS)

The fragment soup entering ARIS contains thousands of different isotopes. ARIS must select the one species of interest from this mixture — often one isotope among millions of contaminants.

ARIS is a two-stage magnetic separator with the following specifications:

First stage: A set of large superconducting dipole and quadrupole magnets bends and focuses the fragment beam, selecting ions within a window of magnetic rigidity $B\rho = p/q$. At the beam velocity, this selects ions with similar $A/Z$ ratios.

Wedge degrader: At the mid-focal point, a wedge-shaped aluminum or beryllium degrader introduces differential energy loss. Heavier elements ($Z$-dependent stopping power: $\Delta E \propto Z^2$) lose more energy, shifting their $B\rho$ relative to lighter elements with the same $A/Z$.

Second stage: A second set of dipoles selects on the new $B\rho$, completing the two-dimensional ($A$, $Z$) separation. The desired isotope emerges from ARIS as a relatively pure secondary beam.

Particle identification: Every ion passing through ARIS is identified event-by-event using the $B\rho$–$\Delta E$–TOF method (Section 30.9). Silicon detectors and timing detectors at the focal planes measure the energy loss and time of flight, allowing the atomic number and mass number of each fragment to be determined.

The Experimental Areas

FRIB delivers rare-isotope beams to multiple experimental areas, each optimized for different physics:

Fast-Beam Area

The fragments arrive at full velocity ($\beta \sim 0.3$–$0.5$) for: - In-beam gamma-ray spectroscopy with GRETINA/GRETA: Coulomb excitation, knockout reactions, inelastic scattering to map nuclear level schemes. - Invariant mass spectroscopy with the MoNA-LISA neutron array: Measuring the decay of unbound states beyond the neutron drip line. - Reaction cross-section measurements with the $S800$ spectrograph: Total reaction and interaction cross sections that probe nuclear sizes.

Stopped-Beam Area

A gas stopping cell (a large helium-filled chamber at $\sim 100$ mbar) thermalizes the fast fragments. The stopped ions are extracted, purified by a multiple-reflection time-of-flight (MR-TOF) device, and delivered to: - LEBIT Penning trap: Precision mass measurements ($\delta m / m \sim 10^{-8}$). - BEam COoler and LAser Spectroscopy (BECOLA): Charge radii, moments, and spins of exotic nuclei. - Decay stations: Beta-delayed neutron emission, beta-delayed gamma spectroscopy.

ReA Reaccelerator

The stopped and purified ions can be re-ionized and re-accelerated by the ReA linac to energies of 3–12 MeV/u — providing ISOL-quality beams with the species reach of fragmentation. This enables: - Coulomb excitation and transfer reactions with clean, well-defined beams. - Astrophysical reaction studies at the energies relevant to stellar burning (Chapter 22).

Scientific Highlights: The First Years

FRIB's early science program has already produced landmark results:

New isotope discovery. In its first experimental campaigns, FRIB produced and identified dozens of previously unobserved isotopes, including ${}^{28}\text{O}$ ($Z = 8$, $N = 20$) — a nucleus predicted to be doubly magic. The observation that ${}^{28}\text{O}$ is unbound (it exists only as a resonance) provides a stringent test of nuclear shell models in the oxygen isotope chain.

Masses of r-process nuclei. The LEBIT Penning trap and the MR-TOF mass spectrograph have measured masses of neutron-rich nuclei in the $A \sim 60$–$140$ region that are critical for r-process abundance predictions (Chapter 23). Several of these masses deviated significantly from theoretical predictions, requiring revisions to nucleosynthesis models.

First measurement with GRETA modules. The deployment of additional GRETA detector modules at FRIB has enabled gamma-ray spectroscopy of nuclei produced at rates of only a few per second — experiments that would have been impossible with any previous array.

The Human Scale

FRIB is operated by a staff of approximately 600 people — accelerator physicists, nuclear physicists, engineers, technicians, and administrative staff — at Michigan State University. The user community comprises over 1,600 scientists from more than 200 institutions worldwide. A typical beam time involves a collaboration of 20–50 physicists from 5–15 institutions, spending 7–14 days at the facility.

The investment in FRIB represents a societal commitment to understanding the nuclear world. Each isotope produced, each mass measured, each level scheme extended adds a brick to the edifice of nuclear physics — a structure built not by any one person but by a global community of scientists working with the most powerful tools they can build.

Discussion Questions

1. Why is beam power (watts), rather than beam energy (MeV/u) or beam current (ions/s) alone, the figure of merit for rare-isotope production? What happens if you increase energy but decrease current (or vice versa)?

2. FRIB uses a linac rather than a cyclotron (like RIKEN-RIBF) or a synchrotron (like GSI). What are the advantages and disadvantages of the linac design? Why was it chosen for a 400 kW machine?

3. The gas stopping cell is a critical link between the fast-beam and stopped-beam programs. What are the physics challenges of stopping a 200 MeV/u ion in helium gas and extracting it as a thermal, singly charged ion? What limits the efficiency?

4. Compare FRIB's first-year scientific output to what was possible with the previous NSCL coupled cyclotron facility. What experiments does the higher beam power make possible that were previously unfeasible?

Quantitative Exercises Based on This Case Study

CS30.1.1 The FRIB beam power is 400 kW with ${}^{238}\text{U}$ at 200 MeV/u. Calculate the beam current in particle-microamperes ($p\mu$A) and in ions per second.

CS30.1.2 The rotating graphite target has a diameter of 15 cm and rotates at 5000 RPM. The beam spot is 1 mm wide. Estimate the fraction of the target circumference illuminated at any instant, and hence the instantaneous power density (W/cm$^2$) on the target. Why is rotation essential?

CS30.1.3 ARIS has an angular acceptance of $\pm 40$ mrad. If the fragmentation cone half-angle for light fragments ($A \sim 50$) at 200 MeV/u is approximately $\Delta\theta \approx (p_F / p_{\text{beam}}) \sim 100$ mrad (where $p_F \sim 200$ MeV/c is the Fermi momentum), what fraction of the fragments falls within the ARIS acceptance? How does this fraction change for heavy fragments ($A \sim 200$)?

CS30.1.4 A new isotope is identified at FRIB by observing 3 events in the PID plot over 48 hours of beam time. Estimate the production rate. If the gas stopper efficiency is 30% and the transport efficiency to a Penning trap is 50%, how many ions per hour reach the trap? Is a mass measurement feasible?

The Broader Context: Why FRIB Matters

FRIB is not merely a faster, more powerful version of its predecessor (the NSCL Coupled Cyclotron Facility). The jump in beam power — from approximately 1 kW at the NSCL to 400 kW at FRIB — is qualitative, not just quantitative. Many rare isotopes that were produced at rates of one per day at the NSCL will be produced at rates of thousands per second at FRIB. This transforms the experimental program from discovery (seeing an isotope for the first time) to detailed spectroscopy (measuring its properties precisely).

The physics questions that FRIB was designed to answer span the breadth of nuclear science:

• Where are the drip lines? For elements heavier than oxygen ($Z = 8$), the neutron drip line has never been reached experimentally. FRIB will push the drip line to at least $Z \sim 30$–$40$, mapping the boundary of nuclear existence.

• What are the masses of r-process nuclei? The rapid neutron capture process (Chapter 23) synthesizes roughly half the elements heavier than iron. The nuclear masses along the r-process path — particularly at the waiting points near $N = 50$, $82$, and $126$ — determine the final abundance pattern. FRIB will measure hundreds of these masses for the first time.

• How does nuclear structure evolve far from stability? Shell closures, deformation onsets, and shape coexistence may behave differently in extremely neutron-rich nuclei. The shell model predictions tested by the ${}^{54}\text{Ca}$ measurement (Case Study 2) are just the beginning.

• What is the nuclear equation of state? Heavy-ion collisions at FRIB energies, analyzed with the S$\pi$RIT time projection chamber and other detectors, constrain the pressure-density relationship of neutron-rich matter — the same physics that determines neutron star radii (Chapter 25).

FRIB represents a $\$730$ million investment in pure science — a bet by the United States that understanding the nucleus is worth the cost. The experiments described in this chapter are the return on that investment.