A fast method to estimate the gain of the microbunch instability in a bunch compressor

To reach high peak currents driving free-electron lasers an initial chirped electron bunch is compressed in a bunch compressor. The interaction of the electron beam with its radiation field can yield a collective instability, which amplifies any initial modulation in the current profile. We present a model, which allows one to derive an explicit analytical expression for the gain of the microbunch instability. The results are compared to those of the more complex analytical models