An overview of collective effects in circular and linear accelerators

The purpose of both linear and circular accelerator is, of course, to accelerate beams of charged particles. In order to do this it is necessary not only to accelerate particles but also to confine them transversely so that they remain in the vacuum environment. Originally, as accelerators were developed, the intensity of the beams was rather low and so the external fields could be applied without regard to the effects of the space-charge forces of the beams. However, as the demand for high intensity increased, collective effects that are due to the space-charge forces became increasingly important. In order to control a beam of particles we apply external fields. These focus the beam transversely and accelerate it and focus it longitudinally. In addition to these externally applied fields a particle within the beam feels a field due to the charge and current of all the other particles in the beam. By collective effects, we mean all those modifications to the beam behavior which are due to these beam-induced forces. The first two major topics discussed are linear and circular accelerators. In the linear accelerator case, we will consider as examples only electron linacs that have relatively high energy and so particles will have {nu} {approx equal} c. For circular accelerators we'll consider both protons and electrons or their anti-particles. The next two topics are single bunches and multi-bunches. In both linear accelerators and circular accelerators the particles have a bunched character because they are accelerated by an RF system, and the RF has a natural wavelength. The next two topics arise from the natural separation of longitudinal and transverse effects. 40 refs., 30 figs., 1 tab