  In this paper we present a novel approach to FEL simulations based on the
decomposition of the electromagnetic field in a finite number of radiation
modes. The evolution of each mode amplitude is simply determined by energy
conservation. The code is developed as an expansion of the General Particle
Tracer framework and adds important capabilities to the suite of
well-established numerical simulations already available to the FEL community.
The approach is not based on the period average approximation and can handle
long-wavelength waveguide FELs as it is possible to include the dispersion
effects of the boundaries. Futhermore, it correctly simulates lower charge
systems where both transverse and longitudinal space charge forces still play a
significant role in the dynamics. For free-space FEL interactions, a source
dependent expansion approximation can be used to limit the number of transverse
modes required to model the field profile and speed up the calculation of the
system evolution. Three examples are studied in detail including a single pass
FEL amplifier, the high efficiency TESSA266 scenario and a THz waveguide FEL
operating in the zero-slippage regime.
