Abstract
The equations of ideal magnetohydrodynamic equilibria in the presence of gravitational forcing and in the absence of pressure gradient are relevant for large-scale, extremely cold plasmas. Its 2D formulation possesses a highly symmetrical form that allows a complete analysis of its solvability. It turns out that when the boundary condition is given by the vanishing of the normal component of the magnetic field, in the absence of vacuum, solutions exist precisely for doubly connected domains, and in that case there exists an infinity of solutions.
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