Global scaling of the heat transport in fusion plasmas

Abstract

A global heat flux model based on a fractional derivative of plasma pressure is proposed for the heat transport in fusion plasmas. The degree of the fractional derivative of the heat flux, α, is defined through the power balance analysis of the steady state. The model was used to obtain the experimental values of α for a large database of the JET Carbon-wall as well as ITER Like-wall plasmas. The findings show that the average fractional degree of the heat flux over the database for electrons is α ∼ 0.8, suggesting a global scaling between the net heating and the pressure profile in the JET plasmas. The model is expected to provide an accurate and a simple description of heat transport that can be used in transport studies of fusion plasmas.

Information Geometric Investigation of Solutions to the Fractional Fokker–Planck Equation

“…The current work opens up for new research on the statistical characterization of anomalous transport, in particular continuing the analysis of the experimental data obtained in the JET Tokamak, see [38], as was started with an estimation of a global scaling of heat flux where the fractional α∼0.8 was found. Further characterization of transport events and modes causing the anomalous transport in Tokamaks using the current results employing a fractional model would be of great interest.…”

“…Phenomenological models pertinent for anomalous plasma transport including a fractional derivative have recently been studied [4,39,40] and in particular the properties of fractional derivatives in velocity space [35,36,38]. Fractional kinetics is a powerful tool in modeling anomalous transport processes exhibiting Lévy statistics.…”

“…Here a smaller fractional index α yield a longer relaxation time. Note that estimating the parameters D, ν, and α have to be done for the situation at hand often by experimental means such as the global scaling properties found for heat flux in the JET Tokamak [38].…”

“…the present work is based on previous efforts reported in and may provide new insights on the recent developments in the understanding of the anomalous transport and turbulent processes. One particular example is the turbulently driven transport of charged particles in plasmas such as the super-diffusive heat transport found in JET plasmas [38] and numerically generated data of the Hasegawa-Wakatani model where the fractionality is induced by the generation of large-scale events such as zonal flows and streamer-like structures [37]. the information length may give an opportunity to identify large-scale events by a sudden change in the statistical state described by the PDFs, yielding a sudden change in information, i.e., a sharp peak in the dynamic time.…”

Inverse Problem for a Two-Dimensional Anomalous Diffusion Equation with a Fractional Derivative of the Riemann–Liouville Type

“…One of the main problems with using models with the fractional derivative is determining the order of the derivative. There are papers in which the authors determined it based on physical experiments [37]. To determine the order of the derivative, it may be useful to solve the inverse problem, which the authors present in this paper.…”