Nonperturbative theory of the low-to-high confinement transition through stochastic simulations and information geometry: Correlation and causal analyses.

The low-to-high confinement (L-H) transition signifies one of the important plasma bifurcations occurring in magnetic confinement plasmas, with vital implications for exploring high-performance regimes in future fusion reactors. In particular, the accurate turbulence statistical description of self-regulation and causal relation among turbulence and shear flows is essential for accessing enhanced plasma performance and advanced operation scenarios. To address this, we provide a nonperturbative theory of the L-H transition by stochastic simulations of a reduced L-H transition model and detailed statistical analysis. By calculating time-dependent probability density functions (PDFs) of turbulence, zonal flows, and the mean pressure gradient, we elucidate how statistical properties change over time with the help of the information geometry theory (information rate, causal information rate), highlighting its utility in capturing self-regulation and causal relation among turbulence, zonal flow shears, and the mean flow shears. Furthermore, stochastic noises in turbulence, zonal flows, and/or input power are shown to induce uncertainty in the power threshold Q_{c} above which the L-H transition occurs while leading to a rather gradual L-H transition. A time-dependent PDF of power loss over the L-H transition is presented.