Effective coupling impedance and the microwave instability

Recent observations on the growth of beam density fluctuations have demonstrated the existence of longitudinal instabilities of individual bunches at very high frequencies. A single bunch could develop an unstable condition in spite of the damping character for unstable waves propagating along the top of a bunch. The main results of a theory for the fast bunch blow-up are presented. The predictions of this theory are consistent with both computational and experimental observations