The Poukey‐Rostoker‐Model of Relativistic Electron Beam Propagation: Further Comments

Abstract

Several properties of the analytic one-dimensional model of relativistic electron beam prop;igation published by POUKEY and ROSTOKER [l] are discussed in the more realistic case of a time-dependent current. The general beam behaviour is similar to thet in the case of constant current; the tirue that is necessary to build up the space charge wall and the potential well (typically w 1 ns) and the sheath thickness (typically a few.cm) are evaluated in the case of constant current growth rate. Inhaltsiibersicht Description of the model1. A simple model of the space-charge controlled propagation of relativistic electron beams in vacuum has been published by POUHEY and ROSTOKER [l]. The assumptions are: An electron emitting cathode (resp. the anode foil) is located a t X = 0; a t times T > 0 a parallel beam of electrons enters a field-free drift space X > 0 (e.g. a tube with a large diameter); current density i and initialvelocity V , = Vx,o are independent of time ( Fig. 1). Magnetic fields, radial electric fields and radial velocity components axe not taken into account: the model is strictly one-dimensional. The electrons are retarded by their own space charge fields which are treated as image forces'). The initial stage of the beam development is completely and exactly describable in an analytic form. The properties of this solution are discussed in [Z]. l) However, the interaction of an electron with its own image charge is omitted in the model.