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 Joint European Torus (JET) carbon-wall as well as ITER like-wall plasmas. The fractional degrees of the electron heat flux are found to be $\alpha <2$, for all the selected pulses in the database, suggesting a deviation from the diffusive paradigm. Moreover, the results show that as the volume integrated input power is increased, the fractional degree of the electron heat flux converges to $\alpha \sim 0.8$, indicating a global scaling between the net heating and the pressure profile in the high-power JET plasmas. The model is expected to provide insight into the proper kinetic description for the fusion plasmas and improve the accuracy of the heat transport predictions.

• Received 4 July 2019

DOI:https://doi.org/10.1103/PhysRevResearch.2.013027

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Published by the American Physical Society