Instability of wave modes in a free-electron laser with a helical wiggler and ion-channel guiding

The dispersion relation for a free-electron laser (FEL) with a one-dimensional helical wiggler and an ion channel, in the collective regime, is found with all relativistic effects on the space-charge wave and radiation included. This dispersion relation is solved numerically to study the unstable interaction among all wave modes. In group I orbits, coupling between the positive-energy space-charge wave and the left circularly polarized electromagnetic wave is found. This instability and the coupling between the negative and positive-energy space-charge wave are found in the group II orbits in the negative mass regime. In group II orbits, there is a coupling between the right and left circularly polarized electromagnetic waves, in the positive mass regime. These instabilities are found to be distinct from the main FEL resonance. Contrary to the main FEL resonance, the additional instabilities have a nonrelativistic nature and are made of strongly coupled modes.