  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.
