Abstract
Magnetohydrodynamic equilibria for a plasma in a gravitational field are investigated analytically. For equilibria with one ignorable spatial coordinate, the equations reduce to a single nonlinear elliptic partial differential equation for the magnetic potential A, known as the Grad-Shafranov equation. Specifying the arbitrary functions in the latter equation, one gets a nonlinear elliptic partial differential equation (the sinh Poisson equation). Analytical solutions of this equation are obtained for the case of an isothermal atmosphere in a uniform gravitational field. The solutions are obtained by using the tanh method, and are adequate for describing parallel filaments of diffuse, magnetized plasma suspended horizontally in equilibrium in a uniform gravitational field.
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