Nonlinear theory of electron neutralization waves in ion beams with dissipation

Abstract

An analytical theory of nonlinear neutralization waves generated by injection of electrons from a grid in the direction of a homogeneous ion beam of uniform velocity and infinite extension is presented. The electrons are assumed to interact with the ions through the self-consistent space charge field and by strong collective interactions, while diffusion in the pressure gradient is disregarded (zero-temperature approximation). The associated nonlinear boundary-value problem is solved in closed form by means of a von Mises transformation. It is shown that the electron gas moves into the ion space in the form of a discontinuous neutralization wave, which exhibits a periodic field structure (incomplete neutralization). This periodic wave structure is damped out by intercomponent momentum transfer, i.e., after a few relaxation lengths a quasineutral plasma results. The relaxation scale in space agrees with neutralization experiments of rarefied ion beams if the collective momentum transfer between the electron and ion streams is assumed to be of the Buneman type.