Tutorial: Statistical approaches to self-organization and variability in magnetic confinement fusion plasmas*

A key challenge in magnetically confined fusion of high-temperature plasmas is that plasmas tend to be unstable and become turbulent, causing anomalous transport and confinement degradation. However, novel plasma self-organization can emerge spontaneously and play a vital role in plasma confinement. For instance, when an input power exceeds a critical power threshold, the transition from a low-confinement mode (L-mode) to a high-confinement mode (H-mode) occurs spontaneously, where plasmas organize themselves into an ‘ordered’, high-confinement state. Despite over 40 years of research on the L-H transition, its triggering mechanisms and causality relations are not fully understood. Furthermore, turbulence characteristics in the L and H modes are highly variable. On the other hand, the H-mode is subject to quasi-periodic edge-localized modes (ELMs), which can potentially cause significant damage to wall-facing materials. What is necessary for successful ELM control is not fully understood.

To address these issues, I will present new statistical approaches to quantify turbulence statistics accurately, especially with time-varying, large fluctuations. Often-used plasma parameters given by mean values and a few low-order moments will be shown to be insufficient to characterize details of plasma turbulence -- plasmas with similar parameters can significantly differ in their statistical properties and evolve into different states over time. In particular, stochastic noises produce random trajectories and phase mixing, leading to uncertainty in power threshold and ELM suppression. I elucidate self-regulation and causal relations by information geometry that works better than other popular entropy-based methods (e.g., transfer entropy). The theoretical prediction will be tested against experimental data analysis of the L-H transition. The statistical analysis of ELM control by RMPs and other advanced operation scenarios will also be discussed. The presented methods can also be applied to other systems.