Comparison of a modal-decomposition and a grid based field solver for free-electron laser simulations

We present a comparison of the modal-decomposition based field solver MINERVA to the grid-based solver GENESIS. The modal decomposition used employs a set of fixed-width, zero-curvature Gaussian modes, as opposed to the more-commonly used basis of vacuum-diffraction eigenmodes. Besides providing the dynamical equations for the field modal amplitudes, we give first-principle estimates of the number of modes required to achieve completeness in terms of field and source modal representation as a function of the electron-current and mode size. As a practical application of this new framework, we present steady-state numerical results for several configurations. The numerical results show a good agreement between the modal expansion and the grid-based solver, not only in terms of the total energy produced, but also in terms of the transverse radiation profile.