Adiabatic Collapse of a Relativistic Electron Beam

Abstract

Differential equations are derived and two computer solutions presented for the case of a relativistic electron beam injected into neutral gas. Processes included are ionization, scattering of electrons on atoms and ions, charge exchange, supply of neutrals to the beam by diffusion, and incoherent radiation by the electrons. A longitudinal electric field is assumed. The main restrictive assumptions are those of uniform densities and hydrodynamic stability. Solutions are given for an 1100-amp, 0.77-Mev, externally-focused beam injected into H2 at pressures of 10−6 and 2×10−5 mm Hg. The beam contracts from an initial radius of 1.73 cm to an equilibrium radius of 7×10−4 cm in 3 and 0.5 msec, respectively. It is found in these cases that neutrality of the beam does not occur until after the radiation-scattering equilibrium, which was first studied by Budker, has occurred. Several difficulties connected with a neutralized beam are discussed. It is shown that a space-charge-limited beam of high phase-space density is the type most suitable for obtaining a small beam diameter in the shortest time. An approximate solution is derived which applies after a specified time near equilibrium and allows calculation of several parameters of interest without the necessity of computer integration.

Transport of moderately relativistic electron beam in dense plasma

“…Moreover, as a result of Coulomb collisions in the dense plasma, the magnetic field spreads (diffuses) rapidly in the transverse direction. The rapid diffusion limits the magnetic strength and thus the pinching at the beam boundary, preventing its collapse [48]. Although in the figure we have only shown the region 2<x<10, the pinching and relaxation of the remaining REB in fact continues in a quasi-periodic manner, although the beam becomes rapidly weakened as it losses its electrons and energy to the background plasma.…”