Validity of 1D free electron laser sideband models

Abstract

Analytic 1D models have been used to estimate sideband growth in a free electron laser (FEL) with a constant-amplitude primary wave [1,2]. A simple 2D sideband model is used here to show that the 1D approximation is valid only when the beam radius rb is large compared with [2k8min(ω0, dφ0dz)]−12, where ks and φ0 are the wave number and phase of the primary wave and ω0 is the maximum synchrotron wave number of trapped electrons. For smaller rb values, sideband growth rates are reduced below 1D predictions, and both the growth rate scaling with beam density and the primary-wave amplitude are altered.