Statistical analysis and modeling of intermittent transport events in the tokamak scrape-off layer

Abstract

The turbulence observed in the scrape-off-layer of a tokamak is often characterized by intermittent events of bursty nature, a feature which raises concerns about the prediction of heat loads on the physical boundaries of the device. It appears thus necessary to delve into the statistical properties of turbulent physical fields such as density, electrostatic potential, and temperature, focusing on the mathematical expression of tails of the probability distribution functions. The method followed here is to generate statistical information from time-traces of the plasma density stemming from Braginskii-type fluid simulations and check this against a first-principles theoretical model. The analysis of the numerical simulations indicates that the probability distribution function of the intermittent process contains strong exponential tails, as predicted by the analytical theory.

Statistical analysis of Hasegawa-Wakatani turbulence

“…We find in the regions with strong nonlinear characteristics an emergent universal scaling of the PDF tails of exponential form ∼ exp − const |φ| as suggested by recent theoretical work in Ref. [32][33][34] relevant for the direct cascade dynamics.…”

“…Thus it is of great importance to be able to minimize large scale transport events. Previously we have seen the strong exponential character (χ = 1.0) in coherent transport events at the edge in the form of meso-scale blob structures 34 . In order to achieve this we have performed statistical analysis of the produced time traces, averaged in the poloidal (y) -direction, at ten radial positions.…”

Statistical properties of Charney-Hasegawa-Mima zonal flows

“…(4) in the following cases: Laplacian distribution denotes the analytical model for χ = 1.0, whereas a Gaussian PDF is represented by χ = 2.0. The appearance of a Laplacian distribution at the stream ( Figure 11) is suggestive of a vorticity conserving nonlinear system 38,40 , whereas a Gaussian distribution is likely for a weakly nonlinear system In Figure 9(b) the kurtosis of the time series generated by the fast-flowing anti-parallel streams corresponding to the simulation presented in Figure 8 Initial pairs of bipolar vortices merge to form monopolar vortices. In the case of two parallel flowing streams, all the vortices move in the flow direction of the two streams ( Figure 13).…”

“…In this situation it has been predicted 38,40 that the system has exponential tails in the direct cascade, exp We focus on the time traces (averaged in the y-direction) at five equidistant radial points located at x = −18.9, −9.5, 0.0, 9.5, 18.9 (in units of ρ s ). Each set of data describes the time evolution of the potential and vorticity to which we apply a standard Box-Jenkins modeling 30 .…”

Statistical description of turbulent transport for flux driven toroidal plasmas

“…A key finding of this work is that the intermittent process in the context of drift-wave turbulence appears to be PDP-13 independent of the specific modelling framework, opening the way to the prediction of its salient features. The methodology has been validated using various different modelling strategies and simulation softwares [17,18]. Specifically, we were able to quantitatively confirm the exponential form of the PDFs, therefore adding the important element of predictive strength to the existing phenomenological approaches.…”