Stimulated Raman scattering by a relativistic electron beam - Analysis of a free electron laser

A free electron laser is investigated using stimulated electromagnetic wave scattering, that is, stimulated Raman scattering by the electron-plasma (negative energy) wave excited in a relativistic electron beam. A rigorous analysis of its oscillation property is given. Particular attention is given to the output power saturation with decreasing pump power and the energy relations. For simplicity, a one-dimensional relativistic electron beam is considered, and a strong plane EM wave (pump wave) that impinges on the electron beam from the opposite direction is assumed. First, Maxwell's equations, the relativistic motion equation for the electron, and the continuum equation for the beam are applied. Consideration is given to oscillatory components up to the second order. The mode-coupling equations for the pump, scattered, and electron-plasma (negative energy) waves are derived and rigorous solutions are sought. Energy relations are formulated involving these three waves. Owing to the effect of the pump wave, energy is found to transfer from the electron beam to the scattered waves; the manner in which the scattered wave gradually grows is clarified quantitatively.