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, $\alpha$, is defined through the power balance analysis of the steady state. The model was used to obtain the experimental values of $\alpha$ 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 $\alpha \sim 0.8$, 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.
Highlights
Fusion plasmas are open systems with continuous energy input, inherently having a continuous drive of turbulence at many scales, i.e., similar to or approaching a scale-free process, leading to a behavior that is much more complex than standard diffusion
A global heat flux model based on a fractional derivative of plasma pressure is proposed for the heat transport in the fusion plasmas
The degree of the globality of the heat transport is defined through the power balance analysis
Summary
Fusion plasmas are open systems with continuous energy input, inherently having a continuous drive of turbulence at many scales, i.e., similar to or approaching a scale-free process, leading to a behavior that is much more complex than standard diffusion. Similar results were witnessed at the Large Plasma Device facility at UCLA [26], where vorticity probes (VP) were used to directly measurement the vorticity associated with E × B flow shear. These regimes possess complex dynamics and self-organization properties that display unimodal nonGaussian features, which is one of the signatures of intermittent turbulence with patchy spatial structure that is bursty in time [27,28,29]. The model depends on a single fractional index α that describe the degree of the global heat transport; i.e., the flux of the transported scalar at a point depends on the gradient of the scalar throughout the entire domain. Note that we have employed the methodology for heat flux in magnetically confined plasmas, it is a general methodology that could be applied in any instance where a fractional model of dynamics is used
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