The main-wave one-dimensional modulational instability due to the dispersive terms of the wave equation in a free-electron laser is introduced and analyzed. We derive the appropriate dispersion relation and compare its associated growth rate with one due to wave-particle energy exchange alone, as obtained by Davidson and Wurtele under the deep trapping assumption [Phys. Fluids 30, 557 (1987)]. It is found that, depending basically on the relation between some characteristic parameters, the modulational instability may be governed by wave dispersion. We also discuss the effects of waveguides on these instabilities and the behavior of the unstable modes as a function of the mentioned characteristic parameters.

• Received 1 September 1989

DOI:https://doi.org/10.1103/PhysRevA.41.1629