Magnet Error Driven Resonances

Abstract

This chapter considers space charge effects in connection with externally excited resonances in circular accelerators. The main focus is on coherent phenomena, which are evident in second order gradient as well as skew error driven resonances, and in particular for coasting beams. A direct consequence are coherent shifts of resonance conditions beyond the incoherent space charge tune shifts as well as the phenomenon of “coherent advantage” suggesting that the shifts allow higher intensity than would result from an incoherent resonance condition. These externally excited second order resonances are described by coherent integer resonance conditions – in contrast with the half-integer resonance conditions of the parametric instabilities. In the field of higher order magnet error driven resonances, in particular when applied to bunched beams with Gaussian distributions, the current understanding is that of dominance of incoherent space charge effects, which is briefly discussed in connection with an experimental observation.