Three-dimensional Structures of Magnetostatic Atmospheres. V. Coupled Electric Current Systems

The magnetostatic equations describing equilibrium among the Lorentz, pressure, and gravitational forces are transformed to a statement of Ampere's law incorporating the condition of equilibrium. The pressure as a function of space is expressed in terms of the gravitational potential, a component of the magnetic field, and an arbitrary third variable to complete a set of local curvilinear coordinates. The coupling of the two current systems is shown to be manifest in the need for the third variable to describe the pressure structure. A discussion relating the derived equations to other known forms of the magnetostatic equations is presented.