Forward and backward processes associated with the Low-to-High (L-H) transition in mag- netically 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. 91, 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 in- formation length for the forward and backward processes are investigated. The information length 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, intermittency in zonal flows playing a key role in tur- bulence regulation. The stark difference between the forward and backward processes is captured by time-dependent PDFs of turbulence and zonal flows and corresponding information length di- agnostics. The latter are shown to give us a useful insight in understanding the correlation and self-regulation, and transitions to the self-regulatory dithering phase.
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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
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