Analysis of a class of free electron laser using a periodic static magnetic field

With the aid of coupled mode theory, this paper clarifies quantitatively the oscillation mechanism of the free electron laser in the submillimeter and far infrared wave region which is composed of a relativistic electron beam and periodic static magnetic field. First, on the basis of Maxwell's equations, the relativistic equation of motion for the electron and the equation of continuity for electrons, the coupled mode equations are derived which couple the electromagnetic wave mode (positive‐energy wave) and electron plasma wave mode (negative‐energy wave) propagated along a relativistic electron beam. Also, the spatial growth rate for these wave modes is obtained from these equations. Next, the energy relations for the electromagnetic and electron plasma wave modes are formulated, together with the discussion on the mechanism for energy exchange between these two modes. Finally, this paper considers the saturation in the laser output produced by trapped electrons in the electron plasma wave, and the efficiency of energy transfer from the kinetic energy of the electron beam to the laser output.