Synchrobetatron Oscillation Driving Mechanism

Any cavity-like structure which supports modes that have both a finite accelerating field at the location of a particle beam passing through the structure and a transverse gradient in that accelerating field is capable of driving synchrobetatron oscillations. Such oscillations are incoherent, are substantially independent of the chromaticity, and do not depend explicitly on the ¿-function. Methods of computing the amplitudes of such oscillations, which can be quite significant under some circumstances, are presented.