Hollerbach, R, Kim, E-J and 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, 27. 102301. ISSN 1070-664X
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(2t∗−t) for t>t∗, linearly decreasing with time until t=2t∗. 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 ℒx(t) and ℒv(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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2020 Author(s). This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article will appear in Physics of Plasmas. Uploaded in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 03 Sep 2020 10:42 |
Last Modified: | 30 Nov 2020 15:53 |
Status: | Published |
Publisher: | American Institute of Physics |
Identification Number: | 10.1063/5.0011473 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:165073 |