Intermittency and hysteresis in a stochastic model of the Low-to-High confinement mode transition

The need for a proper statistical theory for understanding fusion plasmas has grown significantly, with experiments and simulations revealing ample evidence for non-Gaussian fluctuations, anomalous transport, or intermittency. The latter questions the validity of the mean-field-type theory based on small Gaussian fluctuations, necessitating the calculation of an entire probability density function (PDF). In this paper, we show the importance of intermittency and time-dependent PDF approach in the Low-to-High confinement mode (L-H) transition. In particular, PDFs are shown to be strongly non-Gaussian with convoluted structures and multiple peaks, and that intermittency (rare events of large amplitude) of zonal flows can play an important role in promoting the L-H transition.  We also propose a new information geometric method by using information length, dynamical time scale, and information phase portrait, and show their utility in forecasting transitions and self-regulation between turbulence and zonal flows. Implications for hysteresis in the L-H and H-L transition are discussed.