Cyclotrons: Magnetic Design and Beam Dynamics

Abstract: Classical, isochronous, and synchro-cyclotrons are introduced. Transverse and longitudinal beam dynamics in these accelerators are covered. The problem of vertical focusing and iscochronism in compact isochronous cyclotrons is treated in some detail. Different methods for isochronization of the cyclotron magnetic field are discussed. The limits of the classical cyclotron are explained. Typical features of the synchro-cyclotron, such as the beam capture problem, stable phase motion, and the extraction problem are discussed. The main design goals for beam injection are explained and special problems related to a central region with an internal ion source are considered. The principle of a Penning ion gauge source is addressed. The issue of vertical focusing in the cyclotron centre is briefly discussed. Several examples of numerical simulations are given. Different methods of (axial) injection are briefly outlined. Different solutions for beam extraction are described. These include the internal target, extraction by stripping, resonant extraction using a deflector, regenerative extraction, and self-extraction. Different methods of creating a turn separation are explained. Different types of extraction device, such as harmonic coils, deflectors, and gradient corrector channels, are outlined. Some general considerations for cyclotron magnetic design are given and the use of modern magnetic modelling tools is discussed, with a few illustrative examples. An approach is chosen where the accent is less on completeness and rigorousness (because this has already been done) and more on explaining and illustrating the main principles that are used in medical cyclotrons. Sometimes a more industrial viewpoint is taken. The use of complicated formulae is limited.