Matter Dynamics in Helical Magnetic Fields: A Mathematical Model with Infinite Boundaries

Abstract

This paper develops a mathematical model of plasma transfer in an open magnetic trap, incorporating the boundary condition of zero plasma concentration at infinity. Experimental data from the SMOLA trap at the Budker Institute of Nuclear Physics SB RAS serve as validation for the model. Plasma confinement is achieved by transferring momentum from a helical-symmetric magnetic field to a rotating plasma. The model is formulated using a stationary plasma transfer equation in an axially symmetric configuration, incorporating second-order spatial derivatives. An optimal numerical template for approximating mixed derivatives is determined through a benchmark test problem. The numerical implementation of the model is evaluated by comparing the establishment method and the successive over-relaxation method. The findings demonstrate the model’s capability to accurately describe plasma dynamics in helical magnetic fields and its effectiveness in optimizing plasma confinement.