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

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...

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Bibliographic Details
Published in:Physics of plasmas 2020-10, Vol.27 (10)
Main Authors: Hollerbach, Rainer, Kim, Eun-jin, Schmitz, Lothar
Format: Article
Language:English
Subjects:
Computational fluid dynamics
Diamonds
Dimensionless numbers
Dithering
Fokker-Planck equation
Gaussian process
Plasma physics
Plasmas (physics)
Probability density functions
Probability theory
Ramps
Statistical analysis
Stochastic models
Time dependence
Turbulence
Zonal flow (meteorology)
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Summary: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.
ISSN:1070-664X
1089-7674
DOI:10.1063/5.0011473