A Conceptual Model for the Nonlinear Dynamics of Edge-localized Modes in Tokamak Plasmas

Abstract

High performance magnetically confined toroidal plasmas, such as those required for the operation of a tokamak based fusion power plant, suffer from a troubling type of repetitive edge instability known as edge-localized modes (ELMs). Magnetohydrodynamic (MHD), peeling-ballooning, theory predicts that these instabilities are driven by a large current density and pressure gradient that forms at the plasma edge as a consequence of the enhanced confinement levels achieved in high performance H-mode plasmas. Although ELMs are a common feature of high confinement tokamak plasmas, there are significant gaps in our understanding of how these instabilities scale with the geometry of the plasma and operating conditions expected in large tokamaks that are required for the generation of fusion power. Thus, there is an urgent need for a model that can be validated with experimental data from existing smaller tokamaks. Here, we present a conceptual model describing the topological evolution of the magnetic separatrix, in a tokamak plasma with a dominate lower hyperbolic point. Subsequently, the nonlinear dynamics of the ELM instability, prescribed by the evolving separatrix topology, is discussed. The model invokes a feedback amplification mechanism that causes the stable and unstable invariant manifolds of the separatrix, comprising a “homoclinic tangle“ (Guckenheimer & Holmes, 1983), to grow explosively as the topology of the separatrix manifolds unfold. The amplification process is driven by the rapid growth of helical, fieldaligned, thermoelectric currents that flow through relatively short edge plasma flux tubes connecting high heat flux wall structures, known as divertor target plates, on both sides of the plasma. These thermoelectric currents produce magnetic fields that couple to the separatrix and modify its 3D (topological) structure. As the lobes of the separatrix tangle grow, their area of intersection with the divertor target plates increases along with the size of the flux tubes connecting target plates on both sides of the plasma. This increases the thermoelectric current flow and completes the feedback loop. Numerical simulations have shown that our model is consistent with measurements of the currents flowing between the target plates and with camera images of the heat flux patterns on the divertor target plates