ExB flow-induced shearing-merging of filaments: a Ginzburg-Landau model of Edge-Localized Mode cycles

Abstract

We derive and study a simple 1D nonlinear model for Edge Localized Mode (ELM) cycles. The nonlinear dynamics of a resistive ballooning mode is modeled via a single nonlinear equation of the Ginzburg-Landau type with a radial frequency gradient due to a prescribed ExB shear layer of finite extent. The nonlinearity is due to the feedback of the mode on the profile. We identify a novel mechanism, whereby the ELM only crosses the linear stability boundary once, and subsequently stays in the nonlinear regime for the full duration of the cycles. This is made possible by the shearing and merging of filaments by the ExB flow, which forces the system to oscillate between a radially-uniform solution and a non-uniform solitary - wave like solution. The model predicts a 'phase-jump' correlated with the ELM bursts.