Time-dependent probability density functions and information diagnostics in forward and backward processes in a stochastic prey-predator model of fusion plasmas

Rainer Hollerbach, Eun-jin Kim, Lothar Schmitz

    Research output: Contribution to journalArticlepeer-review

    5 Citations (Scopus)
    13 Downloads (Pure)

    Abstract

    Forward and backward processes associated with the low-to-high (L-H) transition in magnetically confined fusion plasmas are investigated by using a time-dependent probability density function (PDF) approach and information length diagnostics. Our model is based on the extension of the deterministic prey-predator-type model [Kim and Diamond, Phys. Rev. Lett. 90, 185006 (2003)] to a stochastic model by including two independent, short-correlated Gaussian noises. The "forward"process consists of ramping up the input power linearly in time so that zonal flows self-regulate with turbulence after their initial growth from turbulence. The "backward"process ramps the power down again, by starting at time t = t∗ when the input power is switched to Q (t) = Q (2 t∗ - t) for t > t*, linearly decreasing with time until t = 2 t*. Using three choices for Q(t), with differing ramping rates, the time-dependent PDFs are calculated by numerically solving the appropriate Fokker-Planck equation, and several statistical measures including the information length for the forward and backward processes are investigated. The information lengths L x (t) and L v (t) for turbulence and zonal flows, respectively, are path-dependent dimensionless numbers, representing the total number of statistically different states that turbulence and zonal flows evolve through in time t. In particular, PDFs are shown to be strongly non-Gaussian with convoluted structures and multiple peaks, with intermittency in zonal flows playing a key role in turbulence regulation. The stark difference between the forward and backward processes is captured by time-dependent PDFs of turbulence and zonal flows and the corresponding information length diagnostics. The latter are shown to give us a useful insight into understanding the correlation and self-regulation, and transition to the self-regulatory dithering phase.

    Original languageEnglish
    Article number102301
    Number of pages27
    JournalPhysics of Plasmas
    Volume27
    Issue number10
    Early online date1 Oct 2020
    DOIs
    Publication statusPublished - 1 Oct 2020

    Bibliographical note

    Free via journal website.

    This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Hollerbach, R, Kim, E & Schmitz, L 2020, 'Time-dependent probability density functions and information diagnostics in forward and backward processes in a stochastic prey-predator model of fusion plasmas', Physics of Plasmas, vol. 27, no. 10, 102301. and may be found at https://doi.org/10.1063/5.0011473

    Copyright © and Moral Rights are retained by the author(s) and/ or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This item cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder(s). The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders.

    Funder

    the Leverhulme Trust Research Fellowship (RF- 2018-142-9).

    ASJC Scopus subject areas

    • Condensed Matter Physics

    Fingerprint

    Dive into the research topics of 'Time-dependent probability density functions and information diagnostics in forward and backward processes in a stochastic prey-predator model of fusion plasmas'. Together they form a unique fingerprint.

    Cite this