Cyclotrons and fixed-field alternating-gradient accelerators

This article describes particle accelerators using magnets whose field strengths are fixed in time to steer and focus ion beams in a spiral orbit so that they pass between (and can be accelerated by) the same electrodes many times. The first example of such a device, Lawrence's cyclotron, revolutionized nuclear physics in the 1930s, but was limited in energy by relativistic effects. To overcome these limits two approaches were taken, enabling energies of many hundreds of MeV/u to be reached: either frequency-modulating the rf accelerating field (the synchrocyclotron) or introducing an azimuthal variation in the magnetic field (the isochronous or sector-focused cyclotron). Both techniques are applied in fixed-field alternating-gradient accelerators (FFAGs), which were intensively studied in the 1950s and '60s with electron models. Technological advances have made possible the recent construction of several proton FFAGs, and a wide variety of designs is being studied for diverse applications with electrons,...