Theory of free-electron laser instability for a relativistic electron beam propagating in a dielectric-loaded waveguide

Abstract

A free-electron laser (FEL) with a dielectric-loaded waveguide operating in an undulator (multiple mirror) field is analyzed. The stability properties are investigated self-consistently on the basis of the linearized Vlasov–Maxwell equations for an electron distribution function, in which all electrons have a Lorentzian distribution in the axial canonical momentum. Using appropriate boundary conditions, a dispersion relation is derived in the low density approximation; νb/γb≪1, and the growth rates of several types of mode couplings are computed. Even for a mildly relativistic electron beam (γb≤1.5), the typical maximum growth rate of instability is a few percent of c/Rw. As the axial momentum spread increases, the growth rate decreases substantially while the instability bandwidth increases. For the long-wiggler wavelength (LWW) mode, which only occurs in the dielectric-loaded waveguide, Cerenkov interaction plays an important role in the free-electron laser instability. In the case of the short-wiggler wavelength (SWW) mode, the frequency of the free-electron laser is greatly enhanced in mildly relativistic electron beams with appropriate choices of physical parameter values. Therefore, intense submillimeter microwaves might be produced by making use of a mildly relativistic electron beam with γ≊1.1. A wide band free-electron laser amplifier is also possible with a proper choice of external parameters, such as wiggler wavenumber k0, dielectric constant, and beam energy γb.