<title>Three-Dimensional Theory Of The Raman Free-Electron Laser</title>

Abstract

A fully self-consistent theory of the free -electron laser is derived in the collective regime which includes all transverse variations in the wiggler field as well as the effects of a finite waveguide geometry. A set of coupled differential equations is found which describes an arbitrary radial beam profile, and a dispersion equation is obtained under the assumption of a thin monoenergetic beam which is solved numerically for the growth rates of the TE11 and TM11 modes in a cylindrical waveguide. X = ±ir /2 + SX, and x = xo + 8X, where Xo = +vw /v11. To first order in the perturbed quantities, therefore, we find that ABSTRACT A fully self-consistent theory of the free-electron laser is derived in the collective regime which includes all transverse variations in the wiggler field as well as the effects of a finite waveguide geometry. A set of coupled differential equations is found which describes an arbitrary radial beam profile, and a dispersion equation is obtained under the assumption of a thin monoenergetic beam which is solved numerically for the growth rates of the TE n and TM n modes in a cylindrical waveguide.