Wave interaction and low-frequency magnetic field generation in planar free-electron lasers

In recent work by the present author the full dispersion relation for multi-dimensional perturbations propagating in saturated free-electron lasers was derived. A number of approximations were used in order to derive a simplified description of the unstable modes. Although this simplified analysis was shown to be appropriate for quasi-transverse modes, it was not possible to describe the generic case of non-transverse ones. In the present paper, via a numerical analysis of this dispersion relation, we argue that a considerable number of modes do indeed not satisfy the quasi-transversality condition. The generation of low-frequency maenetic fields is also analysed.