Statistical approaches to self-organization and uncertainty quantification in magnetic confinement fusion plasmas

Astrophysical and fusion plasmas share significant similarities, particularly in their ubiquitous turbulence, coherent structures, and self-organization. This paper focuses on magnetic confinement fusion plasmas, emphasizing their inherently non-equilibrium nature and the use of non-perturbative statistical approaches to quantify them. The statistical properties of fusion plasmas often deviate from Gaussian distributions, rendering low-order moments—such as means and standard deviations—inadequate for fully characterizing turbulence and its impact. The low-to-high confinement (L-H) transition, a key plasma bifurcation leading to improved confinement, is examined as a stochastic bifurcation, where the transition occurs probabilistically for a given input power. Probability density function methods help reveal how hidden variables influence the power threshold. Additionally, information theory is employed to uncover nonlinear plasma interactions, including self-regulation and causality.