Approximated expressions for the coherent synchrotron radiation effect in various accelerator scenarios

In this paper, we present analytic expressions for the coherent synchrotron radiation (CSR)-induced rms energy spread and the resulting emittance dilution due to three common scenarios in electron particle accelerators: An electron bunch transitioning into the steady-state regime while traversing a bending magnet with and without the effects of compression, and an electron bunch coasting into a subsequent drift section. The expressions are used to calculate the CSR-induced rms energy spread and emittance dilution for real bunch compressor systems: the first and second bunch compressors of the LCLS-II CuRF and LCLS-II-HE. The expressions are compared with simulations using elegant for various parameter scans.