A new method for calculating a special class of self-consistent three-dimensional magnetohydrostatic equilibria

A new mathematical formulation for calculating a special class of self-cons istent three-dimensional magnetohydrostatic equilibria in Cartesian and sph erical coordinates is presented. The method uses a representation of the ma gnetic field in terms of poloidal and toroidal field components which autom atically guarantees the solenoidal character of the magnetic field. This re presentation is commonly used in the theory of linear force-free magnetic f ields. One advantage of this representation of the magnetic field is that t he calculation involves only one scalar function whereas in previous treatm ents one was forced to operate with all three components of the magnetic fi eld independently.