ALMOST-INVARIANT SURFACES FOR MAGNETIC FIELD-LINE FLOWS

Two approaches to defining almost-invariant surfaces for magnetic fiel ds with imperfect magnetic surfaces are compared. Both methods are bas ed on treating magnetic field-line flow as a 1 1/2-dimensional Hamilto nian (or Lagrangian) dynamical system. In the quadratic-flux minimizin g surface approach, the integral of the square of the action gradient over the toroidal and poloidal angles is minimized, while in the ghost surface approach a gradient flow between a minimax and an action-mini mizing orbit is used. In both cases the almost-invariant surface is co nstructed as a family of periodic pseudo-orbits, and consequently it h as a rational rotational transform. The construction of quadratic-flux minimizing surfaces is simple, and easily implemented using a new mag netic field-line tracing method. The construction of ghost surfaces re quires the representation of a pseudo field line as an (in principle) infinite-dimensional vector and also is inherently slow for systems ne ar integrability. As a test problem the magnetic field-line Hamiltonia n is constructed analytically for a topologically toroidal, non-integr able ABC-flow model, and both types of almost-invariant surface are co nstructed numerically.