Model and simulation of wide-band interaction in free-electron lasers
  A three-dimensional, space-frequency model for simulation of interaction in free-electron lasers (FELs) is presented. The model utilizes an expansion of the total electromagnetic field (radiation and space-charge waves) in terms of transverse eigenmodes of the waveguide, in which the field is excited and propagates. The mutual interaction between the electron beam and the electromagnetic field is fully described by coupled equations, expressing the evolution of mode amplitudes and electron beam dynamics.   Based on the three-dimensional model, a numerical particle simulation code was developed. A set of coupled-mode excitation equations, expressed in the frequency domain, are solved self-consistently with the equations of particles motion. Variational numerical methods were used to simulate excitation of backward modes. At present, the code can simulate free-electron lasers operation in various modes: spontaneous (shot-noise) and self-amplified spontaneous emission (SASE), super-radiance and stimulated emission, all in the non-linear Compton or Raman regimes. 
Yosef Pinhasi, Yuri Lurie and Asher Yahalom