| Citation: |
Kaibang WU, Lai WEI, Zhengxiong WANG. Analysis of anomalous transport based on radial fractional diffusion equation[J]. Plasma Science and Technology, 2022, 24(4): 045101. DOI: 10.1088/2058-6272/ac41bd
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Anomalous transport in magnetically confined plasmas is investigated by radial fractional transport equations. It is shown that for fractional transport models, hollow density profiles are formed and uphill transports can be observed regardless of whether the fractional diffusion coefficients (FDCs) are radially dependent or not. When a radially dependent FDC Dα(r) < 1 is imposed, compared with the case under Dα(r) = 1.0, it is observed that the position of the peak of the density profile is closer to the core. Further, it is found that when FDCs at the positions of source injections increase, the peak values of density profiles decrease. The non-local effect becomes significant as the order of fractional derivative α → 1 and causes the uphill transport. However, as α → 2, the fractional diffusion model returns to the standard model governed by Fick's law.
The authors thank Dr Patrick Diamond for his comments on this work. This work is supported by the National MCF Energy R & D Program of China (No. 2019YFE03090300), National Natural Science Foundation of China (No. 11925501), and Fundamental Research Funds for the Central Universities (No. DUT21GJ204).
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