Two-Dimensional Theory Of Coherent Synchrotron Radiation With Transient Effects

A two-dimensional theory of coherent synchrotron radiation for a bending magnet with finite length is developed as an extension to the one-dimensional theory. On axis, the transient longitudinal wakes agree exactly to those in the one-dimensional theory. Off axis, the deviations are small but noticeable. The theory includes the transient centrifugal and centripetal forces after electron bunch enters and then exits the magnet. However, the transverse wakes are an order of magnitude smaller than the longitudinal ones.