Investigation of charged particle beam stability: Numerical method and physical results (Q1339523)

The general scheme of the method of parameter evolution, a way of treating ordinary second order differential equations and their spectral theory for boundary value problems, is used in the study of high current electron beams in gases and plasmas. An evolution operator is derived for the case of smoothly varying coefficients, and a numerical algorithm is proposed. In the process of evolution, the prediction of possible bifurcations and the method of finding the evolution across such points are outlined. The mathematical method is shown to work for: 1) a non- vortex tube electron beam in longitudinal homogeneous magnetic and radial electric fields, and 2) an isorotational vortex charged particle beam without the drift approximation. The paper summarizes the previous results of the authors published earlier in the form of preprints of the Keldysh Institute (Moscow) and in other Russian publications.