Abstract
The mathematical apparatus of plasmastatics, which includes the MHD equilibrium equation and steady-state Maxwell equations, is reduced, in two-dimensional problems arising due to symmetry, to a single scalar second-order elliptic equation with a nonlinear right-hand side known as the Grad-Shafranov equation. In this paper, we numerically solve a series of boundary value problems for this equation that model equilibrium plasma configurations in the magnetic field of the belt-like galathea trap in a cylinder with two plasma embedded conductors. The mathematical model is outlined, the results of calculations of the magnetic field and plasma pressure in the cylinder depending on the parameters of the problem are presented, and the main integral characteristics of the trap are calculated. The existence and uniqueness of the solution is discussed; the limiting values of the maximal pressure at which there exists a solution of the equilibrium problem are found.
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Dedicated to Academician A.A. Dorodnicyn on the Occasion of the Centenary of His Birth
Original Russian Text © K.V. Brushlinskii, P.A. Ignatov, 2010, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2010, Vol. 50, No. 12, pp. 2184–2194.
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Brushlinskii, K.V., Ignatov, P.A. A plasmastatic model of the galathea-belt magnetic trap. Comput. Math. and Math. Phys. 50, 2071–2081 (2010). https://doi.org/10.1134/S0965542510120092
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DOI: https://doi.org/10.1134/S0965542510120092