Intrinsic corrections to optical guiding in a freeelectron laser: Beam Research Program
Abstract
The effect on optical guiding of the undulations of an electron beam in a free electron laser (FEL) is investigated. A model for a fully saturated FEL amplifier with no remaining gain is developed. The density of the electron beam includes the effects of both transverse and longitudinal undulation. The longitudinal density modulation is expressed in terms of the Bessel functions of zeta, where zeta = a(sub w)/2(1 + a(sub w)) is the shift of the electron phase in the electron bucket caused by its longitudinal undulation. The transverse density modulation is evaluated to second order in the ratio of undulation amplitude delta r to beam radial scale length r(sub b). The radiation field is calculated in terms of spatial modes proportional to exp(i(k + delta k + lk(sub w)z  iwt)), where l is an arbitrary integer. Here, delta k is the change of the wavenumber of the radiation caused by the electron bunches. Radially radiating modes with intensity on the order of (delta k/k(sub w))zeta sup 2 are found. Optical guiding is modified by the transverse undulations of the beam at second order in delta r(sub b), and by the longitudinal undulations to first order in delta k/k (sub w). For the usual FEL parameters, the correction is quite small.
 Publication:

Presented at the 9th International FreeElectron Laser Conference
 Pub Date:
 1987
 Bibcode:
 1987ifel.confR....C
 Keywords:

 Correction;
 Electron Beams;
 Free Electron Lasers;
 Bessel Functions;
 Optical Properties;
 Wave Equations;
 Lasers and Masers