Analysis of anomalous transport based on radial fractional diffusion equation

Wu, Kaibang; Wei, Lai; Wang, Jialei

doi:10.1088/2058-6272/ac41bd

Cited by 3 publications

(3 citation statements)

References 32 publications

(59 reference statements)

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“…It should be pointed out that non-local effects are also important to transport in Markovian processes, as investigated in Refs. [35][36][37][38]. It would be interesting to consider both non-local and memory effects at the same time.…”

Section: Discussionmentioning

confidence: 99%

“…In early works, hollow temperature profiles were observed in steady states under off-axis heating, [34] and theories based on nonlocal transport by utilizing the spatial fractional transport equation in Markovian processes were developed. [35][36][37][38] In order to investigate memory effects on the formation of hollow temperature profiles under off-axis heating processes, we assume the heating source to be of the form H add = H e e −(r−r 0 ) 2 /a 2 , where r 0 = 0.75, a = 0.05, and H e is a constant, such that 2π 1 0…”

Section: Applications To Magnetically Confined Plasmasmentioning

confidence: 99%

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Analysis of anomalous transport with temporal fractional transport equations in a bounded domain

Wu 吴,

Liu 刘,

Liu 刘

et al. 2023

Chinese Phys. B

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In this work, 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 with respect 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 relates to the fact that the evolution of a physical quantity is affected by its past history, via what are termed memory effects. The magnitude of α is a measure of such memory effects. As 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 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 that hollow temperature profiles can be sustained for a longer time in sub-diffusion processes than in ordinary diffusion processes.

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Section: Discussionmentioning

confidence: 99%

Section: Applications To Magnetically Confined Plasmasmentioning

confidence: 99%

Analysis of anomalous transport with temporal fractional transport equations in a bounded domain

Wu 吴,

Liu 刘,

Liu 刘

et al. 2023

Chinese Phys. B

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“…Kaibang Wu et al analyzed anomalous transport based on the radial fractional diffusion equation. If the particles sit in strong turbulence with large fluctuation amplitude, the particles are trapped, and the average of their square of displacement is not proportional to time anymore, which can be described by the radial fractional transport model [26]. 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.…”

Section: Micro-turbulence and Transportmentioning

confidence: 99%

Summary of the 10th Conference on Magnetically Confined Fusion Theory and Simulation (CMCFTS)

Wang

Qiu

Wang

et al. 2023

Plasma Sci. Technol.

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This paper gives a summary of the organization and the presentations delivered at the 10th Conference on Magnetically Confined Fusion Theory and Simulation (CMCFTS) held in Zhuhai, China, from 28th to 31st October 2022. The conference focused on the latest progress in the research of the magnetic confined fusion plasma theory and simulations, as well as the large-scale numerical simulation techniques developed in recent years. This conference is held both online and offline, with about 110 domestic participants from 18 institutes participating in the live conference, and the statistical data from the live broadcast platform indicated that the online conference attracted over 20000 views per day. A summary of the conference is given, and the history of the CMCFTS is presented. A brief introduction to the poster section is also included in this paper.

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Exploration of anomalous transport based on the use of general conformable fractional derivative in tokamak plasmas

Wu,

Liu,

Wang

et al. 2024

AIP Advances

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This study investigates anomalous transport in tokamak plasmas by employing general conformable fractional derivatives (GCFDs) and utilizing general conformable fractional diffusion equations (GCFDEs). GCFDs, which are local derivatives utilizing fractional conformable functions, exhibit properties similar to those of ordinary derivatives. The action can be defined by employing the definition of the inverse operation of GCFDs, and the general conformable fractional equation of motion (GCFEM) is derived through the calculus of variations. Introducing a damping term to the GCFEM results in the general conformable fractional Langevin equation (GCFLE). Solutions of the GCFLE indicate a scaling law for the mean squared displacement (MSD) ⟨x2⟩∝tα/Γ1+α, linking MSD scaling to the order α of the GCFD if the conformable fractional function ψt,α=Γαt1−α, where Γx is the gamma function. Therefore, the general conformable fractional diffusion coefficient (GCFDC) Dψ,α is defined as the ratio of the classical diffusion coefficient to ψt,α. From the definition of the running diffusion coefficient, it is found that when the Kubo number is much greater than unity, indicating that the system is in a turbulent state, both the classical and the GCFDC are inversely proportional to α—the power of the magnitude of the background magnetic field. After constructing a GCFDE based on the scaling law of MSD, it is applied to investigate the formation of hollow temperature profiles during off-axis heating in magnetically confined plasmas. Simulation results reveal the crucial role of the fractional conformable function in sustaining the long-term existence of these hollow temperature profiles as it can impede thermal conduction.

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Analysis of anomalous transport based on radial fractional diffusion equation

Cited by 3 publications

References 32 publications

Analysis of anomalous transport with temporal fractional transport equations in a bounded domain

Analysis of anomalous transport with temporal fractional transport equations in a bounded domain

Summary of the 10th Conference on Magnetically Confined Fusion Theory and Simulation (CMCFTS)

Exploration of anomalous transport based on the use of general conformable fractional derivative in tokamak plasmas

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