Probabilistic theory of the L-H transition and causality

The low-to-high confinement (L-H) transition is critical for understanding plasma bifurcations and self-organization in high-temperature fusion plasmas. This paper reports a probabilistic theory of the L-H transition, in particular, a probability density function of power threshold Qc for the first time. Specifically, by utilizing a stochastic prey-predator model with energy-conserving zonal flow-turbulence interactions and extensive GPU computing, we investigate the effects of stochastic noises, external perturbations, time-dependent input power ramping, and initial conditions on the power threshold uncertainty. The information geometry theory (information rate, causal information rate) is employed to highlight how statistical properties of turbulence, zonal flows, and mean pressure gradient change over the transition, clarifying self-regulation and causal relations among them.