Narrow-band radiation from long-pulse free-electron lasers

Abstract

A perturbative theoretical analysis of the operation of a long-pulse free-electron laser (FEL) is presented. This analysis was prompted by the remarkable property of the FEL at the University of California at Santa Barbara of generating radiation with a very small fractional bandwidth of the order of ${10}^{\mathrm{\ensuremath{-}}8}$. To third order in the radiation field, the transverse current driving the FEL contains large crossed-saturation terms between resonator modes. Through the strong crossed saturation the dominant mode depresses the effective gain of other modes to the point of extinction, resulting in single-mode operation. These conclusions hold as long as the long-pulse FEL is operating in a low-gain, homogeneously broadened regime, outside the deep saturation region. The perturbation expansion, nonlinear single-mode, and two-mode problems are discussed in detail.