Theory of an absolute instability of a finite-length free-electron laser

The long-wavelength, backward mode of the free-electron laser is shown theoretically to be absolutely unstable for sufficient system length and applied magnetic-field strength. Finite-length one-dimensional particle simulations also show the mode to be absolutely unstable when the theoretical criteria are satisfied. The broad parameter regime in which a free-electron laser can produce the desired forward-propagating short-wavelength radiation, yet be stable to the backward mode, is calculated.