Pulse shapes for absolute and convective free-electron-laser instabilities

This paper contains an analysis of pulse shapes produced by a delta-function disturbance of the equilibrium state of a relativistic electron beam propagating through a constant-amplitude, helical magnetic wiggler field. Pulse shapes are determined by using the relativistic pinch-point techniques developed by Bers, Ram and Francis. Two pulses are produced corresponding to a convective upshifted pulse (representing the production of the high-frequency radiation desired in a free electron laser) and a downshifted pulse. Parameter regimes in which the downshifted instability is convective are investigated. It is found that momentum spreads sufficiently large to suppress the absolute instability reduce the growth rate of the upshifted pulse to negligible values. Pulse shapes computed by using the Raman and Compton approximations are compared with exact pulse shapes. It is found that the Raman approximation should be applied to the downshifted regime for most systems of practical interest.