Nonlinear transient neutralization theory of 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 selfconsistent space charge field and by strong collective interactions. The associated nonlinear boundaryvalue 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. This periodic wave structure is damped out by intercomponent momentum transfer, i.e., after a few relaxation lengths a quasineutral beam 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.
 Publication:

American Institute of Aeronautics and Astronautics
 Pub Date:
 March 1975
 Bibcode:
 1975elpr.confR....W
 Keywords:

 Electron Gas;
 ElectronIon Recombination;
 Ion Beams;
 Particle Interactions;
 Rarefied Plasmas;
 Boundary Value Problems;
 Injection;
 Nonlinear Equations;
 Partial Differential Equations;
 Space Charge;
 Transient Response;
 Wave Propagation;
 Plasma Physics