Hamiltonian approach to magnetic fields with toroidal surfaces

The equivalence of magnetic field line equations to a one-dimensional time-dependent Hamiltonian system is used to construct magnetic fields with arbitrary toroidal magnetic surfaces I = const. For this purpose Hamiltonians H which together with their invariants satisfy periodicity constraints have to be known. The choice of H fixes the rotational transform eta(I). Arbitrary axisymmetric fields, and nonaxisymmetric fields with constant eta(I) are considered in detail. Configurations with coinciding magnetic and current density surfaces are obtained. The particular approach used is not well suited, however, to satisfying the additional MHD equilibrium condition of constant pressure on magnetic surfaces. (orig.)