MATHEMATICAL MODEL OF PLASMA EQUILIBRIUM IN THE MULTIPLY CONNECTED DOMAIN OF A MAGNETIC TRAP

The article clarifies 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. 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 works, the geometry and basic regularities of configurations in the toroidal trap «Belt» straightened into a cylinder with two conductors parallel to its axis were researched. The two-dimensional plasmostatic model of the configuration is based on the numerical solution of the boundary value problem with the known Grad-Shafranov equation for the magnetic flux function in the cross-section of the cylinder. It contained an essential simplifying assumption, that makes it possible to deal with a single-connected domain of the problem solution: conductors were not excluded from the domain, and currents in them were represented by additional summands in equation. In the proposed work this simplification is absent, and the problem is posed in a multiply connected domain of out of conductors of square cross section. The role of the electric current in the formation and maintenance of the equilibrium magnetoplasma configuration is played by a boundary condition containing the circulation of the magnetic field along the boundary of each conductor. In a series of calculations with different values of dimensionless parameters of the problem in the multiply connected domain, it was found that the main properties of the configuration and the regularities of their dependence on the parameters qualitatively coincide with those obtained earlier in the single-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 configurations on the dimensionless parameters of the problem has been clarified

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