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Transport equation describing fractional Lévy motion of suprathermal ions in TORPEX

Bovet, A; Gamarino, M; Furno, I; Ricci, P; Fasoli, A; Gustafson, K; Newman, D E; Sánchez, R (2014). Transport equation describing fractional Lévy motion of suprathermal ions in TORPEX. Nuclear Fusion, 54(10):104009.

Abstract

Suprathermal ions, created by fusion reactions or by additional heating, will play an important role in burning plasmas such as the ones in ITER or DEMO. Basic plasma experiments, with easy access for diagnostics and well-controlled plasma scenarios, are particularly suitable to investigate the transport of suprathermal ions in plasma waves and turbulence. Experimental measurements and numerical simulations have revealed that the transport of fast ions in the presence of electrostatic turbulence in the basic plasma toroidal experiment TORPEX is generally non-classical. Namely, the mean-squared radial displacement of the ions does not scale linearly with time, but 〈r2(t)〉∼tγ , with γ �= 1 generally, γ>1 corresponding to superdiffusion and γ<1 to subdiffusion. A generalization of the classical model of diffusion, the so-called fractional L ́ evy motion, which encompasses power-law (L ́ evy) statistics for the displacements and correlated temporal increments, leads to non-classical dynamics such as that observed in the experiments. On a macroscopic scale, this results in fractional differential operators, which are used to model non-Gaussian, non-local anomalous transport in a growing number of applied fields, including plasma physics. In this paper, we show that asymmetric fractional L ́ evy motion can be described by a diffusion equation using spacefractional differential operator with skewness. Numerical simulations of tracers in TORPEX turbulence are performed. The time evolution of the radial particle position distribution is shown to be described by solutions of the fractional diffusion equation corresponding to asymmetric fractional L ́ evy motion in sub- and superdiffusive cases.

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > Nuclear and High Energy Physics
Physical Sciences > Condensed Matter Physics
Uncontrolled Keywords:Condensed Matter Physics, Nuclear and High Energy Physics
Language:English
Date:1 October 2014
Deposited On:16 Aug 2022 15:01
Last Modified:28 Oct 2024 02:35
Publisher:IOP Publishing
ISSN:0029-5515
OA Status:Green
Publisher DOI:https://doi.org/10.1088/0029-5515/54/10/104009
Project Information:
  • Funder: Swiss National Science Foundation
  • Grant ID:
  • Project Title:
  • Funder: MICINN
  • Grant ID: ENE2009-12213-C03-03
  • Project Title:
  • Funder: MINECO
  • Grant ID: ENE2012-33219
  • Project Title:
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  • Content: Accepted Version
  • Language: English
  • Licence: Creative Commons: Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)

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