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 50s 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, muons, protons and heavier ions. All fixed-field accelerators offer high beam intensity: classical and isochronous cyclotrons operate in cw mode and in some cases deliver beams of 2 mA; synchrocyclotrons and most FFAGs operate in pulsed mode, but are capable of much higher pulse repetition rates (≤ kHz) than synchrotrons.