Nonlinear self-consistent three-dimensional arcade-like solutions of the magnetohydrostatic equations

Exact self-consistent solutions of the magnetohydrostatic equations in three dimensions with a nonlinear relationship between the magnetic field and the current density are presented. The derivation is carried out in Cartesian coordinates including a constant gravitational force pointing into the negative z-direction. Out of several solution classes only one has an arcade-like magnetic field topology. This solution class is investigated further and two examples are shown for specific choices of the free functions and parameters which the solution class has.