Variational method for the 3-dimensional inverse-equilibrium problem in toroids

A variational method is developed for three dimensional magnetostatic equilibria in toroids. We represent equilibria in cylindrical inverse variables R (v, theta, zeta), phi (v, theta, zeta), and Z (v, theta, zeta), where v is a radial flux surface label, theta, a poloidal angle, and zeta, a toroidal angle. We Fourier-expand in theta and zeta and derive, from the variational principle, a set of ordinary differential equations for the amplitudes in v. Truncation of the infinite Fourier series leads to a reduced set of equations which we solve numerically by collocation to obtain two and three dimensional toroidal equilibria.