Short wavelength free electron laser operation in a periodic dielectric

Abstract

A layered dielectric with periodic permittivity profile, /spl epsiv/=/spl epsiv//sub 0/+/spl epsiv//sub 2/ cos(k/sub 0x/x+k/sub 0z/z), is suitable for the generation of coherent radiation at short wavelengths with moderate energy electron beams. When an electron beam is passed through the dielectric with velocity v/sub b/z/spl circ/, along with a copropagating electromagnetic wave perturbation, E/spl I.oarr//spl sim/A/spl I.oarr/ exp[-i(/spl omega/t-kz)], the displacement vector acquires a (/spl omega/,k/spl I.oarr/+k/spl I.oarr//sub 0/) component, driving a space charge field E/spl I.oarr//sub +/ when /spl omega/=(k+k/sub 0z/)v/sub b/. The space charge field couples with the periodic permittivity to produce displacement vector at (/spl omega/,k/spl I.oarr/), driving the original electromagnetic perturbation. The frequency of radiation /spl omega//spl sime/k/sub 0z/v/sub b//(1-v/sub b//spl epsiv//sup 1/2//sub 0//c) and the growth rate /spl Gamma//spl ap/[(k/sub 0x//sup 2//spl omega//sub pb//sup 2//spl omega//spl epsiv//sub 2//sup 2/)/(8/spl gamma//sub 0//sup 3//spl epsiv//sub 0//sup 3/k/sub 0z//sup 2/)]/sup 1/3/ where /spl omega//sub p/b is the beam plasma frequency and /spl gamma//sub 0/ is the relativistic gamma factor. The geometrical effects, however, limit full exploitation of the resonant enhancement of /spl omega/ and /spl Gamma/ around v/sub b/=c//spl epsiv//sup 1/2//sub 0/.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>