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We propose and discuss a numerical method to model electromagnetic emissionfrom the oscillating relativistic charged particles and its coherentamplification. The developed technique is well suited for free electron lasersimulations, but it may also be useful for a wider range of physical problemsinvolving resonant field-particles interactions. The algorithm integrates theunaveraged coupled equations for the particles and the electromagnetic fieldsin a discrete spectral domain. Using this algorithm, it is possible to performfull three-dimensional or axisymmetric simulations of short-wavelengthamplification. In this paper we describe the method, its implementation, and wepresent examples of free electron laser simulations comparing the results withthe ones provided by commonly known free electron laser codes.

A spectral unaveraged algorithm for free electron laser simulations