Magnetic X-points, edge localized modes, and stochasticity

Abstract

Edge localized modes (ELMs) near the boundary of a high temperature, magnetically confined toroidal plasma represent a new type of nonlinear magnetohydrodynamic (MHD) plasma instability that grows through a coherent plasma interaction with part of a chaotic magnetic field. Under perturbation, the freely moving magnetic boundary surface with an X-point splits into two different limiting asymptotic surfaces (manifolds), similar to the behavior of a hyperbolic saddle point in Hamiltonian dynamics. Numerical simulation using the extended MHD code M3D shows that field-aligned plasma instabilities, such as ballooning modes, can couple to the “unstable” manifold that forms helical, field-following lobes around the original surface. Large type I ELMs proceed in stages. Initially, a rapidly growing ballooning outburst involves the entire outboard side. Large plasma fingers grow well off the midplane, while low density regions penetrate deeply into the plasma. The magnetic field becomes superficially stochastic. A secondary inboard edge instability causes inboard plasma loss. The plasma gradually relaxes back toward axisymmetry, with diminishing cycles of edge instability. Poloidal rotation of the interior and edge plasma may be driven. The magnetic tangle constrains the early nonlinear ballooning, but may encourage the later inward penetration. Equilibrium toroidal rotation and two-fluid diamagnetic drifts have relatively small effects on a strong MHD instability. Intrinsic magnetic stochasticity may help explain the wide range of experimentally observed ELMs and ELM-free behavior in fusion plasmas, as well as properties of the H-mode and plasma edge.