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-consistent three-dimensional magnetohydrostatic equilibria in Cartesian and spherical coordinates is presented. The method uses a representation of the magnetic field in terms of poloidal and toroidal field components which automatically guarantees the solenoidal character of the magnetic field. This representation is commonly used in the theory of linear force-free magnetic fields. One advantage of this representation of the magnetic field is that the calculation involves only one scalar function whereas in previous treatments one was forced to operate with all three components of the magnetic field independently.