Development of coherence from noise in the free-electron laser

Abstract

A classical theory of the development of coherence in the free-electron laser is presented, which depends on the assumptions of a small signal, low gain and long pulses. The method is to take the Fourier transform of the linearized Maxwell-pendulum equation for the field, separate the transverse driving current into spontaneous and stimulated parts and integrate both parts analytically. The rate of development of coherence thus predicted is compared with the results of a one-dimensional numerical simulation of the laser oscillator.