Homoclinic tangles in the DIII-D tokamak from the map equations in natural canonical coordinates*

Abstract

ABSTRACTTrajectories of magnetic field lines are a 1½ degree of freedom Hamiltonian system. The unperturbed separatrix and the perturbed separatrix in a divertor tokamak are fundamentally different. Magnetic asymmetries cause the separatrix to form extremely complicated structures known as homoclinic tangles. After each toroidal circuit, the perturbed separatrix manifolds meet in a fixed poloidal plane and intersect to form homoclinic tangle in order to preserve the topological invariants. This tangle becomes extremely complicated as the magnetic field lines take more and more toroidal turns. This effect is most pronounced near the X-point. The homoclinic tangles of the DIII-D tokamak separatrix from the magnetic perturbation representing the peeling-ballooning modes are studied. The homoclinic tangles can have important implications for the edge physics in divertor tokamaks.