Nonlinear theory of the free-electron laser with an axial magnetic field

A nonlinear, one-dimensional formulation of the free-electron laser with an axial magnetic field is presented. The problem is formulated in the cold-fluid approximation for the electron beam, and is reduced to a system of the first-order, nonlinear, coupled, ordinary differential equations. Nonlinear effects due to the departure of the electrons in the beam from the conventional helical orbits are considered and illustrated in numerical examples. The formalism also allows the study of the initial phase of saturation in the laser. In the presence of the axial magnetic field the saturation is shown to be mainly due to the development of undesirable large radial excursion of the electron trajectories.