Extended definitions of wake fields and their influence on beam dynamics

Based on experience gained from present machines, a new generation of accelerators with high intensities and low losses is being designed. For example, the design for the Spallation Neutron Source storage ring specifies fractional beam losses of the order of 10^-4, so that even small instabilities or resonances can lead to the violation of this number. The purpose of this paper is to show that there exist potentially important beam fields, missing from standard analyses, that can lead either to instabilities or to large deviations of instability thresholds from their conventional values. Some of these fields and related effects, e.g., “fast damping,” were discovered earlier and are presented here in more standard form as an extension of the wake field's definition. In addition, nonrelativistic collective phenomena are analyzed. It is shown that the nonrelativistic case could be significantly different from the relativistic case.