A minimal dynamical model of edge localized mode phenomena

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Abstract
A simple, low-dimensional model of edge localized mode (ELM) phenomena is presented. ELM dynamics are determined by the interaction of few basic processes at the edge of tokamak plasma; these include the evolution of magnetohydrodynamic (MHD) pressure gradient driven instabilities, the low–high (L–H) transition (mediated by electric field shear induced suppression and generation), the fueling of the edge by neutral particles, and edge heating by thermal flux from the core plasma. In the parameter regime characteristic of an H-mode plasma, the model exhibits a transition to stationary relaxation oscillations (i.e., stable limit cycle behavior) corresponding to ELMs. The dependence of ELM frequency, amplitude, etc. on the heating power Pin and other control parameters is studied. The transition from giant to grassy ELM behavior appears as a consequence of increasingly marginal stability to ideal ballooning as Pin increases. Several details of the dynamics of the ELM onset and behavior close to the L–H transition threshold are revealed, as well.