The Longitudinal Effective CSR Force at Mild Compression

In the scheme of magnetic bunch compression, an electron bunch with linear energy chirp (energy-bunch length correlation), imposed by an upstream RF cavity, is sent to a magnetic chicane. The bunch length at the exit of the chicane can thus be manipulated via the pathlength-energy dependence due to chicane dispersion. As a linear energy-chirped bunch ((delta)-z correlation) being transported through a dispersive region (x-(delta) correlation), the bunch will have a linear horizontal-longitudinal (x-z) correlation in the configuration space (bunch tilt). Comparing to the case of a nontilted bunch, this x-z correlation modifies the geometry of particle interaction with respect to the direction of particle motion, which consequently modifies the retardation solution and the effective CSR forces. The simulation result of the CSR field for a tilted thin beam was presented earlier by Dohlus [1]. In this paper, we first give an example of the bunch x-z correlation, or bunch tilt, in a bunch compression chicane. The effect of this x-z correlation on the retardation solution and the longitudinal effective force are then analyzed for a line bunch with linear energy chirp transported by design optics