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In this paper we present a novel approach to FEL simulations based on thedecomposition of the electromagnetic field in a finite number of radiationmodes. The evolution of each mode amplitude is simply determined by energyconservation. The code is developed as an expansion of the General ParticleTracer framework and adds important capabilities to the suite ofwell-established numerical simulations already available to the FEL community.The approach is not based on the period average approximation and can handlelong-wavelength waveguide FELs as it is possible to include the dispersioneffects of the boundaries. Futhermore, it correctly simulates lower chargesystems where both transverse and longitudinal space charge forces still play asignificant role in the dynamics. For free-space FEL interactions, a sourcedependent expansion approximation can be used to limit the number of transversemodes required to model the field profile and speed up the calculation of thesystem evolution. Three examples are studied in detail including a single passFEL amplifier, the high efficiency TESSA266 scenario and a THz waveguide FELoperating in the zero-slippage regime.

A self-consistent numerical approach to track particles in FEL interaction with electromagnetic field modes