Mathematical Model of Plasma Equilibrium in the Multi-Connected Region of a Magnetic Trap

In the paper, the numerical model and the results of calculations of equilibrium plasma configurations in the magnetic trap “Belt” from the class of Galatea traps proposed by A.I. Morozov have been clarified. The confining magnetic field is created by current-carrying conductors immersed in the plasma, but not in contact with it. In a series of previous studies, the geometry and basic patterns of configurations in a toroidal trap “Belt” straightened into a cylinder with two conductors parallel to its axis were studied. The two-dimensional plasmastatic model of the configuration is based on the numerical solution of a boundary value problem with the well-known Grad–Shafranov equation for the magnetic flux function in the cross section of a cylinder. It contained a significant simplifying assumption that makes it possible to deal with a simply connected domain of the problem solution: the conductors were not excluded from the domain, and the currents in them were represented by additional terms in the equation. In the proposed study, this simplification is absent, and the problem is posed in a non-singly connected domain outside the conductors of square cross section. The role of the electric current in the formation and maintenance of the equilibrium magnetoplasma configuration is played by the boundary condition containing the circulation of the magnetic field along the boundary of each conductor. In a series of calculations with different values of the dimensionless parameters of the problem in a non-singly connected domain, it has been found that the main properties of the configuration and the patterns of their dependence on the parameters qualitatively coincide with those obtained earlier in a simply connected domain. This indicates the legitimacy of the previous version of the model and at the same time clarifies its result. The dependence of the geometry and quantitative characteristics of the configurations on the dimensionless parameters of the problem has been clarified.