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.

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.

Linear Force-free (or Beltrami) fields are three-components divergence-free fields solutions of the equation curlB = α B, where α is a real number.Such fields appear in many branches of physics like astrophysics, fluid mechanics, electromagnetics and plasma physics. In this paper,we deal with some related boundary value problems in multiply-connected bounded domains, in half-cylindrical domains and in exterior domains.