Homoclinic tangle in tokamak divertors

Magnetic field lines are the trajectories of a 112 degree of freedom Hamiltonians. Plasmas in tokamaks are confined in regions where the magnetic field lines form closed toroidal surfaces. These surfaces are bounded by a separatrix, and outside the separatrix the magnetic field lines and the plasma flow to special regions of the walls called divertors. Both the confinement of the plasma and the feasibility of divertors are sensitive to the behavior of the magnetic field lines near the separatrix in the presence of non-axisymmetric magnetic perturbations. Separatrix manifold forms homoclinic tangle to preserve the symplectic invariant and topological neighborhood as the manifold evolves in canonical time. A scheme is developed based on these two invariants to calculate homoclinic tangle for actual tokamak equilibria that are subjected to non-axisymmetric perturbations. This scheme is used to study homoclinic tangles of a specific tokamak configuration. How non-ideal effects fill in the lobes formed by homoclinic tangles is demonstrated using a radial expansion operator to simulate plasma diffusion. It is found that for sufficiently rapid plasma diffusion the effects of the tangle on plasma footprint on collector plate are washed out.