CSR Interaction for a 2D Energy-Chirped Bunch on a General Orbit

When an electron bunch with initial linear energy chirp traverses a bunch compression chicane, the bunch interacts with itself via coherent synchrotron radiation (CSR) and space charge force. The effective longitudinal CSR force for such kind of 2D bunch on a circular orbit has been analyzed earlier (1). In this paper, we present the analytical results of the effective longitudinal CSR force for a 2D energy-chirped bunch going through a general orbit, which includes the entrance and exit of a circular orbit. In particular, we will show the behavior of the force in the last bend of a chicane when the bunch is under extreme compression. This is the condition when bifurcation of bunch phase space occurs in many CSR measurements. (1) R. Li, Phys. Rev. ST Accel. Beams 11, 024401 (2008)