An Efficient Algorithm for Calculating the Magnetic Field in a Cylindrical Plasma Trap

In this work, we propose a numerical algorithm for calculating the magnetic field in an open magnetic trap, which is an axisymmetric chamber filled with plasma. The plasma is held in the trap by a special configuration of the magnetic field generated by current coils located at the ends of the chamber. The problem consists in developing an efficient algorithm for calculating the configuration of the magnetic field, which is determined by a given distribution of the external azimuthal current in the coils. The task is solved in two steps. First, the magnetic field distribution is found from the known arrangement of coils, and then this distribution is scaled so that the magnitude of the field in the center of the chamber and the mirror ratio are equal to the given values. The proposed algorithm can be easily generalized to solve the Poisson equation with Neumann boundary conditions on two opposing boundaries of the computational domain. This allows us to apply the developed method to calculate the potential in nonstationary problems.