Remarks on the Poukey‐Rostoker‐model of relativistic electron beam propagation

Abstract

Some properties of an analytic electrostatic model of relativistic electron beam propagation in vacuum, developed by POUKEY and ROSTOKER [l] Introductory remarksThe propagation of relativistic electron beams depends on the geometric conditions, on their own electric and magnetic fields, on the degree of charge neutralisation, on external fields and on the gas resp. plasma, which they penetrate. Several models have been developed to solve this complicated task at least partly and approximately, e.g. I n one of the simplest cases, the purely electrostatic, onedimensional movement of electrons in field-free vacuum , a self-consistent analytic solution has been given by POUKEY and ROSTOKER [ 11 who use a single-particle model with Lagrangian description of the motion. Because of the great simplicity and transparency of this model a more careful and detailed study of its characteristics and its limits may be of interest.After a description of the equations and main results of the model -this is largely a repetition from [l] -we discuss the most important "events" in the beam: the reflection, the mixing and backflow of electrons, as well as the distribution of potential and space charge. In this way the limits of validity of the model are exactly determined, and the procedures to overcome this limitation is indicated. Equations of the modelWe assume: The cathode may be located at z = 0, where the electrons at the time T = To enter the half-space X > 0 with the velocity V = Vo and the density N = No.There is no dependence of physical quantities on the other coordinates (fig. 1) ; magnetic fields are not taken into account. 12*

Kinetics of ultrashort relativistic electron pulses emitted from solid targets

“…3 the results of Eqs. (15) and (17), viz., the fractions of electrons bridging a vacuum gap behind the target, are plotted for kT e = 200, 500, and 1000 keV (exponential energy distribution) and for E el = 200, 500, and 1000 keV (monoenergetic beam). To make the results better applicable to a real situation an areal density of N a =10 15 cm −2 is chosen and the distance scale is in micrometers.…”

“…In previous work, analytical theories were developed for the case of a monoenergetic electron beam which is constant in time [14] or rises with a power law [15]. Furthermore, the case of an infinitely short electron pulse with a flat distribution of energies [16] and with an energy spectrum [17] was developed.…”