A closer look at turbulence spreading: how bistability admits intermittent, propagating turbulence fronts

In magnetic fusion plasmas, the observation of hysteresis in the turbulence intensity level (Inagaki et al. 2013) strongly suggests bistability. Commonly employed reduced models for turbulence spreading are unistable. In this work, a minimal phenomenological model for \emph{bistable} turbulence spreading is introduced and analyzed. The model is related to the FitzHugh-Nagumo system. In addition to to being able to account for hysteresis, we show that, in contrast to previous models of turbulence spreading, this model predicts stronger penetration of turbulence into the stable core as well as the existence of avalanche-like, intermittent turbulence pulses. We also derive a novel spatial size threshold for the spreading of a localized slug of turbulence. This lays a groundwork for future models, which should include couplings to zonal flow and profiles.