Numerical simulation of magnetic field in stationary plasma thruster

The key parameter determining operation of stationary plasma thruster (SPT) is the magnetic field. It is necessary to have information about its local properties in the accelerating channel and in sufficiently wide region near the channel cut. In this paper it is presented a combined method of magnetic field characteristics determination in which magnetic field induction is measured on the boundary of the studied region and then magnetic field characteristics are calculated in the whole region. To describe magnetic field in SPT a magnetic potential $\Phi_m$ is introduced, magnetic field is then defined as $B(0)=B(2\pi)$. For determination of $\Phi_m$ a 3-dimensional Laplace equation is solved in cylindrical coordinates $r$, $z$ and $\varphi$. Magnetic induction $B$ values measured on the surfaces – boundaries of calculating region are used as the boundary conditions. To ensure periodical solution on angular coordinate it is assumed $B(0)=B(2\pi)$. The calculating region is confined by coaxial cylindrical surfaces and 2 butt end surfaces.
Laplace equation is solved with the one of the modifications of the upper relaxation method. While solving finite-difference equation iterations converge steadily and given accuracy is reached. With the use of this technique the magnetic field in SPT model was investigated. In this model it is essentially 3-dimensional. Impact of the boundary conditions is shown. The problem of “interfacing” of calculated values on the boundary of adjacent calculating regions is considered.