Fixed-field alternating gradient accelerator

The magnetic fields needed for an FFA are quite complex. The computation for the magnets used on the Michigan FFA Mark Ib, a radial sector 500 keV machine from 1956, were done by Frank Cole at the University of Illinois on a mechanical calculator built by Friden.[6] This was at the limit of what could be reasonably done without computers; the more complex magnet geometries of spiral sector and non-scaling FFAs require sophisticated computer modeling.

The MURA machines were scaling FFA synchrotrons meaning that orbits of any momentum are photographic enlargements of those of any other momentum. In such machines the betatron frequencies are constant, thus no resonances, that could lead to beam loss,[31] are crossed. A machine is scaling if the median plane magnetic field satisfies

${\displaystyle B_{r}=0,\quad B_{\theta }=0,\quad B_{z}=ar^{k}~f(\psi )}$,

where

• ${\displaystyle \psi =N~[\tan ~\zeta ~\ln(r/r_{0})~-~\theta ]}$,
• ${\displaystyle k}$ is the field index,
• ${\displaystyle N}$is the periodicity,
• ${\displaystyle \zeta }$ is the spiral angle (which equals zero for a radial machine),
• ${\displaystyle r}$ the average radius, and
• ${\displaystyle f(\psi )}$ is an arbitrary function that enables a stable orbit.

For ${\displaystyle k>>1}$ an FFA magnet is much smaller than that for a cyclotron of the same energy. The disadvantage is that these machines are highly nonlinear. These and other relationships are developed in the paper by Frank Cole.[32]

The idea of building a non-scaling FFA first occurred to Kent Terwilliger and Lawrence W. Jones in the late 1950s while thinking about how to increase the beam luminosity in the collision regions of the 2-way colliding beam FFA they were working on. This idea had immediate applications in designing better focusing magnets for conventional accelerators,[6] but was not applied to FFA design until several decades later.

If acceleration is fast enough, the particles can pass through the betatron resonances before they have time to build up to a damaging amplitude. In that case the dipole field can be linear with radius, making the magnets smaller and simpler to construct. A proof-of-principle linear, non-scaling FFA called (EMMA) (Electron Machine with Many Applications) has been successfully operated at Daresbury Laboratory, UK,.[33][34]

Vertical Orbit Excursion FFAs (VFFAs) are a special type of FFA arranged so that higher energy orbits occur above (or below) lower energy orbits, rather than radially outward. This is accomplished with skew-focusing fields that push particles with higher beam rigidity vertically into regions with a higher dipole field.[35]

The major advantage offered by a VFFA design over a FFA design is that the path-length is held constant between particles with different energies and therefore relativistic particles travel isochronously. Isochronicity of the revolution period enables continuous beam operation, therefore offering the same advantage in power that isochronous cyclotrons have over synchrocyclotrons. Isochronous accelerators have no longitudinal beam focusing, but this is not a strong limitation in accelerators with rapid ramp rates typically used in FFA designs.

The major disadvantages include the fact that VFFAs requires unusual magnet designs and currently VFFA designs have only been simulated rather than tested.

FFA accelerators have potential medical applications in proton therapy for cancer, as proton sources for high intensity neutron production, for non-invasive security inspections of closed cargo containers, for the rapid acceleration of muons to high energies before they have time to decay, and as "energy amplifiers", for Accelerator-Driven Sub-critical Reactors (ADSRs) / Sub-critical Reactors in which a neutron beam derived from a FFA drives a slightly sub-critical fission reactor. Such ADSRs would be inherently safe, having no danger of accidental exponential runaway, and relatively little production of transuranium waste, with its long life and potential for nuclear weapons proliferation.

Because of their quasi-continuous beam and the resulting minimal acceleration intervals for high energies, FFAs have also gained interest as possible parts of future muon collider facilities.

In the 1990s, researchers at the KEK particle physics laboratory near Tokyo began developing the FFA concept, culminating in a 150 MeV machine in 2003. A non-scaling machine, dubbed PAMELA, to accelerate both protons and carbon nuclei for cancer therapy has been designed.[36] Meanwhile, an ADSR operating at 100 MeV was demonstrated in Japan in March 2009 at the Kyoto University Critical Assembly (KUCA), achieving "sustainable nuclear reactions" with the critical assembly's control rods inserted into the reactor core to damp it below criticality.

• Energy amplifier a subcritical nuclear reactor which might use an FFA as a neutron source

• "The rebirth of the FFAG". CERN Courier. Jul 28, 2004. Retrieved Apr 11, 2012.