Application of the Modified Drift-Diffusion Theory to Study of the Two-Dimensional Structure of the Penning Discharge

Abstract

Theory and computational model of the Penning discharge at pressure ~1 mTorr in cylindrical configuration with axial magnetic field is presented. This kind of glow discharges is used for acceleration of protons in various kinds of plasma accelerators. Electro-dynamic model of such kind of a low-pressure discharge is formulated. The model consists of continuity equations for electron and ion fluids, and the Poisson equation for the selfconsistent electric field. Numerical simulation algorithm developed in the author's computer code is described and discussed. The general idea of the work is the introduction of the non-linear dependences electrons and ions mobilities from the electric field intensity, and modification of dependencies for ionization coefficient, which can be used in rare weakly ionized gas at low pressure with axial magnetic field. Numerical simulation results are presented for two-dimensional Penning discharge at various initial conditions. The results are obtained for atomic hydrogen at pressure 1÷4 mTorr, Emf of power supply 2.5 kV, and magnetic field induction of B = 0÷0.1 Tl. It is shown that in axial magnetic field an azimuthal oppositely directed gyration of ions and electrons in the glow discharge are observed. The objective of this work is to study the two-dimensional structure of the Penning discharge in an axial magnetic field, and patterns of counter-rotating ions (protons) and electrons fluids in imposing the axial magnetic field. It allows study also the structure of accelerated beam of protons which is of great practical interest for aerospace applications.