Longitudinal wake of a bunch of suddenly accelerated electrons within the radiation formation zone

The longitudinal wake is considered for a bunch of electrons that are suddenly accelerated to an ultrarelativistic velocity. This wake describes the wake of forward transition radiation, and it approximates the edge-radiation wake of a bunch exiting a bending magnet. The wake is large within the radiation formation zone, where it provides resistive impedance. A comparison with the computed wake downstream of a bending magnet yields good agreement, indicating that our wake expressions may be used to approximate the wake without numerical computation. For schemes in which a bunch produced by laser-plasma acceleration exits the plasma and then drives a free electron laser (FEL), the transition-radiation wake causes energy losses of many MeV that may affect the FEL process.