NONLINEAR SELF-CONSISTENT 3-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 f ield 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 classe s only one has an arcade-like magnetic field topology. This solution c lass is investigated further and two examples are shown for specific c hoices of the free functions and parameters which the solution class h as.