A spectral unaveraged algorithm for free electron laser simulations
  We propose and discuss a numerical method to model electromagnetic emission from the oscillating relativistic charged particles and its coherent amplification. The developed technique is well suited for free electron laser simulations, but it may also be useful for a wider range of physical problems involving resonant field-particles interactions. The algorithm integrates the unaveraged coupled equations for the particles and the electromagnetic fields in a discrete spectral domain. Using this algorithm, it is possible to perform full three-dimensional or axisymmetric simulations of short-wavelength amplification. In this paper we describe the method, its implementation, and we present examples of free electron laser simulations comparing the results with the ones provided by commonly known free electron laser codes. 
Igor A. Andriyash, Remi Lehe, Victor Malka
physics.comp-ph