Klystron instability of a relativistic electron beam in a bunch compressor

In this paper, we consider a klystron-like mechanism of amplification of parasitic density modulations in an electron bunch passing a magnetic bunch compressor. Analytical expressions are derived for the small-signal gain. The effect of wakefields in front of the bunch compressor is analyzed by using a model of linear compression which assumes linear correlated energy chirp and linear dependence of a path length on energy deviation. Analysis of the density modulation growth due to coherent synchrotron radiation inside bends of the magnetic bunch compressor is done for the simplified case of no correlated energy chirp (no compression). Analytical results of this paper can be used for benchmarking numerical simulation codes.