Non-local transport based on the fractional Fokker–Planck Equation model
Paper in proceedings, 2018

Recently a non-local (non-diffusive) heat flux model based on a fractional derivative of plasma pressure was proposed for the heat transport in the JET tokamak plasmas [1], where the degree $\alpha$ of the fractional derivative i.e. non-locality (non-diffusivity), of the heat flux was defined though a simple power balance analysis of the steady state. The findings showed that the fractional degree in all of the analysed plasmas was $\alpha < 2$ for both ion and electron channels, suggesting that the heat transport in these plasmas is likely to be of a non-local (non-diffusive) nature. Thus, a study of anomalous diffusion of heat transport using a Fokker-Planck description with fractional velocity derivatives while keeping the non-linear terms is strongly called for. The distribution functions are found using numerical means for varying degree of fractionality of the stable L\'{e}vy distribution. The statistical properties of the distribution functions are assessed by a generalized normalized expectation measure and entropy. We find that the ratio of the generalized entropy and expectation is increasing with decreasing fractionality towards the well known so-called sub-diffusive domain, indicating a self-organising behavior. Here it is pertinent to keep in mind that the success of a fractional or non-local diffusion model indicates that there is lack of physics in current transport models, namely the super-diffusive character of heat transport, as such it is not only a simplified transport model. When the experimentally found values of the fractional derivatives are used in the model, within a good agreement the experimental heat fluxes were reproduced.

Non-diffussive transport

Fokker-Planck Equation


Johan Anderson

Chalmers, Space, Earth and Environment, Astronomy and Plasmaphysics, Plasma Physics and Fusion Energy

Sara Moradi

Royal Military Academy

Bulletin of the American Physical Society

Vol. 60 DPP18-001063

APS Division of Plasma Physics
Portland, ,


Basic sciences

Subject Categories

Fusion, Plasma and Space Physics

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