Almost - invariant surfaces for magnetic field - line flows

Two approaches to defining almost-invariant surfaces for magnetic-fields with imperfect magnetic surfaces are compared. Both methods are based on treating magnetic field-line flow as a 1 :-dimensional Hamiltonian (or Lagrangian) dynamical system. In the quadratic-flux minimizing surface approach. the integral of the square of the action gradient over the toroidal and poloidal angles is minimized, while in the ghoul M a c e approach a gradient flow between a minimax and an action-minimizing orbit is used. In both cases the almost-invariant surface is eon-structed as a family of periodic pseudo-orbits. and consequently it has a rational rotational transform. The construction of quadratic-flux minimizing surfaces is simple, and easily implemented using a new magnetic field-line tracing method. The construction of ghost surfaces requires the representation of a pseudo field line as an (in principle) infinite-dimensional vector and also is inherently slow for systems near integrability. As a test problem the magnetic field-line Hamiltonian is constructed analytically for a topologically toroidal. non-integrable ABC-flow model. and both tvpes of almost-invariant surface are constructed nun~erically.