An iterative method is used to solve the magnetohydrodynamic equations of free-boundary, axially symmetric equilibria with arbitrary cross section. The method is applied numerically to the study of the plasma equilibrium. The limiter creates a vacuum region outside the plasma. It is shown that the current density profile has a strong effect on the equilibrium. Topologically different equilibria may be obtained by changes in the parameters which determine the current profile. The method is also applied to generate elliptic, D-shape, doublet, and other shapes of equilibria maintained by coil systems.
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Chu et al. (1974) studied this question.