The blow-up rate of the envelope instability of a cold beam in a storage ring

Envelope instability is investigated in a storage ring using particle simulation. A typical distortion pattern of the instability is observed in transverse phase planes of cold ion beams considering the storage ring both with and without ring periodicity perturbations. The dependence of the blow-up rate of the instability on the single particle phase advance of the storage ring is calculated. Typical e-folding blow-up times of the envelope instability increase from 10-5s to 10-2s when the single particle phase advance is smaller than 90 degree. copyright 1996 American Institute of Physics