We derive a new nonlinear criterion for the occurrence of fast relaxation (crash) events at the edge of high-confinement-mode plasmas. These fast relaxation events called ELMs (edge-localized modes) evolve from ideal magnetohydrodynamics (MHD) instabilities, but the crash is not due only to linear physics. We show that for an ELM crash to occur, the coherence time of the relative phase between potential and pressure perturbations must be long enough to allow growth to large amplitude. This phase coherence time is determined by both linear and nonlinear dynamics. An ELM crash requires that the instability growth rate exceed a critical value, i.e., $\gamma >{\gamma }_c$, where ${\gamma }_c$ is set by $1/{\tau }_c$ and ${\tau }_c$ is the phase coherence time. For $0<\gamma <{\gamma }_c$, MHD turbulence develops and drives enhanced turbulent transport. The results indicate that the shape of the growth rate spectrum $\gamma (n)$ is important to whether the result is a crash or turbulence. We demonstrate that ELMs can be mitigated by reducing the phase coherence time without changing linear instability. These findings also offer an explanation of the occurrence of ELM-free H-mode regimes.

• Received 28 August 2013

DOI:https://doi.org/10.1103/PhysRevLett.112.085001