Theory of the cerenkov free electron laser

Abstract

Using the fluid-Maxwell equations the theory of the Cerenkov maser operating in the high gain collective regime is presented. Also studied are the characteristics of the beam-wave system in the dielectric loaded cylindrical waveguide using the particle simulation. For the linear regime, in a dielectric loaded waveguid we investigate in a self consistent way a slow rotating equilibrium of a relativistic electron beam which interracts with the electromagnetic waves. General dispersion relations for the fundamental transverse magnetic modes ($TM_{0n}$) in the presence of the external magnetic field are derived using the cold fluidMaxwell equations and the appropriate boundary conditions. For slow space-charge and slow cyclotron modes algebraic equations are obtained from the dispersion relation by using a tenuous beam approximation. Solutions of the resulting equations are obtained for variations of several parameters, such as the external magnetic field, the dielectric constant, the thickness of the dielectric material, and the gap between the beam and dielectric material. With the beam-dielectric gap satisfying the stability condition, the growth rate of the space-charge and the slow cyclotron instabilities show the same behavior as previous results for the no gap case [IEEE Trans. Plasma Sci. PS-17, 576(1989)]. Finally, emphasis in the analysis is given to the effect of the finite gap between the beam and dielectric and the comparison to the previous study of no gap case. From this analysis we also show that as the gap width increases, the growth rate decreases due to the finite geometric effect related to the gap width. For the nonlinear regime, using the Maxwell and relativistic fluid equations, the nonlinesr equilibrium state composed of the wave and beam in a dielectric-loaded cylindrical waveguide is analyzed. For the case of strongly magnetized plasma, where the beam may be treated as one dimensional, the TM modes are the dominant ones which interact with...