Flow of electrons in weak stationary magnetic field
The wide spread plasma conductivity models as applied to certain types electric rocket thrusters give results inconsistent with the experiment data on local and integral parameters of plasma in magnetic field. The goal of this article was development of a mathematical model of electrons flow through the magnetic field, which may be used for parameters computation of such kind of thrusters. Analysis of gas discharges in ion thrusters, such as stationary plasma thrusters (SPT) and thrusters with anode layer (TAL), revealed two specific features of magnetic fields used in them. Firstly, the width of the area with magnetic field is comparable to Larmor radius of electron. Secondly, due to plasma sparsity the electron collision with heavy particles are quite seldom, i. e. wt>> 1. Thus, one of the assumptions included into basis of the “classical” plasma conductivity model is not complying. Moreover, the electron drift in the thrusters under consideration is closed. It allows simplify the mathematical model. Analytical study revealed that an extra electrons velocity component is formed in plasma in the specified conditions. This component, in its turn, due to the Lorentz force results in forming the force, impeding the electron flow through the magnetic field. The magnitude of this force appears proportional to the square of vector magnetic potential gradient. Thus, the author managed to obtain analytical equation for energy consumption associated with electron flow through the weak magnetic field. To evaluate the obtained model error and define the area of its implementation the more complex problem with account for electrons dissipation on heavy particles was considered. Analytical solution for a special case was obtained. It allowed define limitations on application of the suggested model more precisely. The developed model's application to SPT and TAL discharge voltage computation revealed close agreement with the experimental data.