Development of an efficient algorithm for computing the magnetic field intensity in a plasma trap

When modeling the behavior of plasma in an open magnetic trap in the form of a cylinder, it is necessary to find the initial magnetic field strength. The paper deals with an algorithm to compute a two-dimensional (r,z) configuration of a magnetic field, which has the required intensity value in the center of the chamber and a given mirror ratio. The problem reduces to solving an elliptic equation. At the beginning of the computation, the location of the current coils and an arbitrary current value in them are specified. The equality to zero of the radial component of the magnetic field at the ends of the cylinder leads to zero boundary conditions for the normal derivatives of the vector potential. It allows one to replace the desired function with another, for which zero boundary conditions are specified at the ends of the chamber. The developed algorithm to find the vector potential combines two methods: the Fourier transform and the double-sweep method allowing to reduce the number of operations to solve the problem. In order to obtain the required values of the magnetic field strength in the center of the chamber and the mirror ratio, the solution is corrected.