Linear theory of optical guiding in a free electron laser with an annular electron beam

Abstract

With decreasing wavelength of a free electron laser a canalization of the radiation comes into play, when the electron beam concentrates growing waves inside its volume like an optical fiber. This is accompanied by an improvement of the interaction between electrons and radiation field due to an enhancement of the transverse intersection of electron and electromagnetic beams. In this article, the linear theory of induced scattering of axisymmetric electromagnetic waves on an annular electron beam is developed. Analytic solutions of the dispersion equation are obtained. They show the existence of growing waves which are concentrated near the beam surface. This case is similar to that of a plane ribbon electron beam in the limit of large beam radius when the radiation fields are concentrated near the beam surface at a distance which is much smaller than the beam radius. New results are obtained in the opposite limit when the beam is thin and the instability acquires the character of a “negative mass” instability with stronger dependence of the growth rate upon beam current (directly proportional to the square root of the current). Under these conditions a decrease of the beam radius results in a fall off of the growth rate, and the beam loses its optical guiding properties.