Stochastic Dynamics of Fusion Low-to-High Confinement Mode (L-H) Transition: Correlation and Causal Analyses Using Information Geometry

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We investigate the stochastic dynamics of the prey–predator model of the Low-to-High confinement mode (L-H) transition in magnetically confined fusion plasmas. By considering stochas- tic noise in the turbulence and zonal flows as well as constant and time-varying input power Q, we perform multiple stochastic simulations of over a million trajectories using GPU computing. Due to stochastic noise, some trajectories undergo the L-H transition while others do not, leading to a mixture of H-mode and dithering at a given time and/or input power. One of the consequences of this is that H-mode characteristics appear at a smaller input power Q < Qc (where Qc is the critical value for the L-H transition in the deterministic system) as a secondary peak of a probability density function (PDF) while dithering characteristics persists beyond the power threshold for Q > Qc as a second peak. The coexisting H-mode and dithering near Q = Qc leads to a prominent bimodal PDF with a gradual L-H transition rather than a sudden transition at Q = Qc and uncertainty in the input power. Also, a time-dependent input power leads to increased variability (dispersion) in stochastic trajectories and a more prominent bimodal PDF. We provide an interpretation of the results using information geometry to elucidate self-regulation between zonal flows, turbulence, and information causality rate to unravel causal relations involved in the L-H transition.
Original languageEnglish
Article number17
Pages (from-to)1-23
Number of pages23
Issue number1
Publication statusPublished - 22 Dec 2023

Bibliographical note

This is an Open Access article distributed under the terms of the Creative
Commons Attribution License (,
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provided the original work is properly cited.


  • magnetic fusion plasma
  • non-equilibrium statistics
  • L-H transition
  • bifurcation
  • information geometry
  • non-perturbative analysis
  • causality

ASJC Scopus subject areas

  • Mathematics(all)
  • Energy(all)


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