Parametric instabilities in density modulated relativistic electron beam plasma interaction

Abstract

Parametric coupling between negative energy beam synchronous modes and positive energy plasma oscillation modes of a uniform beam‐plasma system, due to the presence of sinusoidal density modulation in the monoenergetic, relativistic electron beam, have been theoretically investigated on the basis of linearized Vlasov–Poisson equations using a multiple‐time‐scale perturbation theoretical approach. It has been found that, for a given beam‐to‐plasma density ratio, there exists an upper limit to the initial beam energy for which the instabilities can be excited. Within the allowed range, maximum linear growth rate exhibits a minimum as the beam energy increases from its nonrelativistic value. To determine the effectiveness of the parametric interaction process, feedback effects of the instabilities on the beam‐plasma distribution functions have also been considered and estimates of energy transfers have been made. For typical parameters, the beam is found to lose about 15% of its initial kinetic energy during the ’’hydrodynamic’’ stage and the time required is about 4.72 nsec.