Theory of free electron laser instability forrelativistic election beam propagating in dielectric loaded waveguide

Abstract

A feee electron laser (FEL) with a dielectric loaded waveguide operating in undulator(multi-mirror) field is analyzed. The stability properties are investigated self-consistently on the basis of the linealized Vlasov-Maxwell equations for an electron distribution functions, in which all electrons conditions a dispersion relation is derived in the low density approximation $v/\gamma_b\ll 1$, and the growth rates of several types of mode couplings are computed. Even for a mildly relativistic electron beam ($\gamma\leqslant 1.5$) the typical maximum growth rate of instability is a few percent of c/Rw. As the axial momentum spread increases, the growth rate reduces 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 on the free electron laser instability. In the case of the short wiggler wavelength (SWW) mode, the frequency of free electron laser is greatly enhanced in mildly relativistic electron beam with the appropriate choices of physical parameter values. Therefore, the intense submillimeter micriwave can easily be produced by making use of a mildly relativistic electron beam with $\gamma \cong 1.1$. A wide band free electron laser amplifier can also be operated by the proper choice of the external parameters, such as wiggler wavenumber, dielectric constant and beam energy, etc.