Evolution of the fastest-growing relativistic mixed mode instability driven by a tenuous plasma beam in one and two dimensions

Abstract

Particle-in-cell simulations confirm here that a mixed plasma mode is the fastest growing when a highly relativistic tenuous electron-proton beam interacts with an unmagnetized plasma. The mixed modes grow faster than the filamentation and two-stream modes in simulations with beam Lorentz factors Γ of 4, 16, and 256, and are responsible for thermalizing the electrons. The mixed modes are followed to their saturation for the case of Γ=4 and electron phase space holes are shown to form in the bulk plasma, while the electron beam becomes filamentary. The initial saturation is electrostatic in nature in the considered one- and two-dimensional geometries. Simulations performed with two different particle-in-cell simulation codes evidence that a finite grid instability couples energy into high-frequency electromagnetic waves, imposing simulation constraints.