Collective Phenomena

Abstract

Transverse and longitudinal beam dynamics as discussed in earlier chapters is governed by purely single particle effects where the results do not depend on the presence of the other particles in the beam. We specifically excluded space charge effects to allow the detailed discussion of single particle dynamics. In many cases this assumption may not be appropriate and collective effects must be taken into account. Similar to the treatment of errors, we try to include collective effects as perturbations although a number of such effects cause serious beam instability which can hardly be considered a perturbation. However, the strength of collective beam instability depends on the beam intensity and we can always reduce the beam current such that the instability indeed is only a perturbation. Once the mechanism of instability is understood, corrective measures can be introduced allowing the increase of the beam current.