Self consistent monte Carlo method to study CSR effects in bunch compressors

In this paper we report on the results of a self-consistent calculation of CSR effects on a particle bunch moving through the benchmark Zeuthen bunch compressors. The theoretical framework is based on a 4D Vlasov-Maxwell approach including shielding from the vacuum chamber. We calculate the fields in the lab frame, where time is the independent variable, and evolve the phase space density/points in the beam frame, where arc length along a reference orbit is the independent variable. We also discuss three approaches, the unperturbed source model (UPS), the self consistent Monte Carlo (SCMC) method and the method of local characteristics.