Investigation of Charged Particle Beam Stability: Numerical Method and Physical Results

Abstract

Experiments on generation and transport of high current electron beams in gases and plasmas excite interest in studying their stability, which is reduced to solving a spectral boundary value problem for an ordinary second-order differential equation for some equilibrium beam configuration. The numerical technique which best satisfies the objectives of studying the beam stability and specific mathematical features of the correspondent spectral problem is the method of parameter evolution (MPE). In this paper a general scheme of the MPE is given, the evolution operator is derived for problems with smooth coefficients and the numerical algorithm is discussed. The problem of the bifurcations arising in the space of physical parameters is considered. An algorithm for predicting the point of bifurcation of a finite order and two algorithms for evolution across such a point are proposed. The following configurations of charged particle beams are studied on stability: a nonvortex tube electron beam in a longitudinal homogeneous magnetic field and radial electric field; and an isorotational vortex charged particle beam without the drift approximation.