Abstract Anomalous transport in magnetically confined plasmas is investigated using temporal fractional transport equations. The use of temporal fractional transport equations means that the order of the partial derivative with respect to time is a fraction. In this case, the Caputo fractional derivative relative to time is utilized, because it preserves the form of the initial conditions. A numerical calculation reveals that the fractional order of the temporal derivative α (α ∈ (0,1), sub-diffusive regime) controls the diffusion rate. The temporal fractional derivative is related to the fact that the evolution of a physical quantity is affected by its past history, depending on what are termed memory effects. The magnitude of α is a measure of such memory effects. When α decreases, so does the rate of particle diffusion due to memory effects. As a result, if a system initially has a density profile without a source, then the smaller the α is, the more slowly the density profile approaches zero. When a source is added, due to the balance of the diffusion and fueling processes, the system reaches a steady state and the density profile does not evolve. As α decreases, the time required for the system to reach a steady state increases. In magnetically confined plasmas, the temporal fractional transport model can be applied to off-axis heating processes. Moreover, it is found that the memory effects reduce the rate of energy conduction and hollow temperature profiles can be sustained for a longer time in sub-diffusion processes than in ordinary diffusion processes.

Fund: This work was supported by the National Key R&D Program of China (Grant No. 2022YFE03090000), the National Natural Science Foundation of China (Grant No. 11925501), and the Fundamental Research Fund for the Central Universities (Grant No. DUT22ZD215).

Corresponding Authors:
Zheng-Xiong Wang
E-mail: zxwang@dlut.edu.cn

Cite this article:

Kaibang Wu(吴凯邦), Jiayan Liu(刘嘉言), Shijie Liu(刘仕洁), Feng Wang(王丰), Lai Wei(魏来), Qibin Luan(栾其斌), and Zheng-Xiong Wang(王正汹) Analysis of anomalous transport with temporal fractional transport equations in a bounded domain 2023 Chin. Phys. B 32 110502

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