Analysis of anomalous transport based on radial fractional diffusion equation

Kaibang WU; Lai WEI; Zhengxiong WANG

doi:10.1088/2058-6272/ac41bd

Plasma Science and Technology > 2022 > 24(4): 045101. > DOI: 10.1088/2058-6272/ac41bd

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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Analysis of anomalous transport based on radial fractional diffusion equation

Key Laboratory of Materials Modification by Beams of the Ministry of Education, School of Physics, Dalian University of Technology, Dalian 116024, People's Republic of China

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Author Bio:
Zhengxiong WANG, E-mail: zxwang@dlut.edu.cn
Received Date: August 07, 2021
Revised Date: November 28, 2021
Accepted Date: December 08, 2021
Available Online: December 15, 2023
Published Date: April 05, 2022

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Abstract

Abstract

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 D_α(r) < 1 is imposed, compared with the case under D_α(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.
- anomalous transport,
- hollow profile,
- non-locality,
- fractional diffusion equation

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Acknowledgments

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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Analysis of anomalous transport based on radial fractional diffusion equation

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