Self-fields in a free-electron laser with helical wiggler and axial magnetic field

An analysis of self-fields associated with charge and current densities of the electron beam in a free-electron laser with helical wiggler and axial magnetic field is presented. The self-electric field is derived from Poisson's equation. A more detailed analytical model for the self-magnetic field is determined from Ampere's law. Mutual influence of the electron velocity and self-magnetic field is considered to account for the total self-magnetic field. It is shown that for group I orbits, the self-magnetic field acts as a diamagnetic correction to the wiggler magnetic field; for group II orbits, it acts as a paramagnetic correction. Both diamagnetic and paramagnetic effects become stronger near the transverse velocity resonance. An important effect of the self-fields on the electron trajectories is the creation of unstable orbits for group II, which are not found in the absence of self-fields.