The effective csr forces for an energy-chirped bunch under magnetic compression

Following our earlier formulation of the coherent synchrotron radiation (CSR) effect on bunch dynamics in magnetic bends, here we investigate the behavior of the effective CSR forces for an energy-chirped Gaussian bunch in the bending plane around full compression, with special care being taken in the incorporation of the retardation relation. Our results show clearly a delayed response of the CSR forces to the compression or lengthening of the bunch length. In addition, around full compression, our results reveal sensitivity of the effective CSR forces on the particles´ transverse position, as a consequence of the geometry of particle interaction and retardation in this regime. These results can serve as benchmarks to the numerical simulation of the CSR effects.