Influence of space charge wave on quasilinear theory of the free-electron laser saturation

摘要

A quasilinear theory is presented that describes the self-consistent evolution of the electron beam distribution function and fields in a free-electron laser when the space charge wave is present. In the Raman regime, a high-density electron beam has an appreciable space charge potential. A broad spectrum of waves is assumed in order to have a relatively wide range of resonant particles. A one-dimensional helical magnetic field is considered and the analysis is based on the Vlasov-Maxwell equations. Two coupled differential equations are derived, which, in conjunction with conservation laws, describe the quasilinear development by the diffusion of electrons in the momentum space. This leads to the saturation of the free-electron laser instability by the plateau formation. Analytical expressions for the growth rate and for the diffusion coefficient are derived, which reduced to those in the Compton regime under appropriate conditions. By use of the linear growth rate and diffusion coefficient, an analytical expression for efficiency in Raman regime was derived. A numerical analysis is conducted to study the effects of the spectral width of radiation and the thermal spread of the electron beam on the efficiency.