Simulation of electron beam instabilities and nonlinear potential structures

This paper gives a tutorial for the electrostatic instabilities induced by electron and/or ion beams in space plasmas. After a brief review of the linear theory of the electron/ion beam instabilities, we describe various types of nonlinear processes reproduced by electrostatic particle simulations. We first study the basic nonlinear processes in a uniform system with periodic boundaries, and then we study the beam plasma interactions in a nonuniform system with open boundaries. Importance of ion dynamics in the nonlinear evolution of the electron beam instabilities are discussed based on the simulations with different distributions of ions.