Transient resistive-wall effects of a bunched electron beam in a wiggler

Abstract

The effects of transverse resistive-wall instability on the operation of a free-electron laser(FEL) are analysed. The equation of motion for a bunched beam was previously solved analytically and a steady-state solution shown to exist. The possibility that the transient state could dominate this steady state is now considered. The maximum transient amplitude is obtained for the case where the focussing force dominates the resistive-wall force. An analytic expression for this amplitude when the bunches come in with random initial displacements is also derived. Results are compared with numerical simulations and are applied to various FEL's to determine if the transverse resistive-wall instability could pose a problem in their operations.