A stochastic model of edge-localized modes in magnetically confined plasmas

Eun-jin Kim, Rainer Hollerbach

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
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Magnetically confined plasmas are far from equilibrium and pose considerable challenges in statistical analysis. We discuss a non-perturbative statistical method, namely a time-dependent probability density function (PDF) approach that is potentially useful for analysing time-varying, large, or non-Gaussian fluctuations and bursty events associated with instabilities in the low-to-high confinement transition and the H-mode. Specifically, we present a stochastic Langevin model of edge-localized modes (ELMs) by including stochastic noise terms in a previous ODE ELM model. We calculate exact time-dependent PDFs by numerically solving the Fokker–Planck equation and characterize time-varying statistical properties of ELMs for different energy fluxes and noise amplitudes. The stochastic noise is shown to introduce phase-mixing and plays a significant role in mitigating extreme bursts of large ELMs. Furthermore, based on time-dependent PDFs, we provide a path-dependent information geometric theory of the ELM dynamics and demonstrate its utility in capturing self-regulatory relaxation oscillations, bursts and a sudden change in the system.
Original languageEnglish
Article number20210226
Number of pages16
JournalPhilosophical transactions. Series A, Mathematical, physical, and engineering sciences
Issue number2242
Early online date2 Jan 2023
Publication statusPublished - 20 Feb 2023


  • High-confinement mode
  • statistical theory
  • self-regulation
  • Langevin model
  • Fokker-Planck equation
  • time-dependent probability density function
  • information geometry


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