Fractional diffusion in plasma turbulence
- 1 August 2004
- journal article
- research article
- Published by AIP Publishing in Physics of Plasmas
- Vol. 11 (8), 3854-3864
- https://doi.org/10.1063/1.1767097
Abstract
Transport of tracer particles is studied in a model of three-dimensional, resistive, pressure-gradient-driven plasma turbulence. It is shown that in this system transport is anomalous and cannot be described in the context of the standard diffusion paradigm. In particular, the probability density function (pdf) of the radial displacements of tracers is strongly non-Gaussian with algebraic decaying tails, and the moments of the tracer displacements exhibit superdiffusive scaling. To model these results we present a transport model with fractional derivatives in space and time. The model incorporates in a unified way nonlocal effects in space (i.e., non-Fickian transport), memory effects (i.e., non-Markovian transport), and non-Gaussian scaling. There is quantitative agreement between the turbulence transport calculations and the fractional diffusion model. In particular, the model reproduces the shape and space-time scaling of the pdf, and the superdiffusive scaling of moments.Keywords
This publication has 26 references indexed in Scilit:
- Propagation of cold pulses and heat pulses in ASDEX UpgradeNuclear Fusion, 2000
- Large-scale behavior of the tokamak density fluctuationsPhysics of Plasmas, 2000
- Nonlocal Transient Transport and Thermal Barriers in Rijnhuizen Tokamak Project PlasmasPhysical Review Letters, 1999
- Long-Range Time Correlations in Plasma Edge TurbulencePhysical Review Letters, 1998
- Evidence and concepts for non-local transportPlasma Physics and Controlled Fusion, 1997
- Perturbative transport studies in fusion plasmasPlasma Physics and Controlled Fusion, 1995
- An experimental counter-example to the local transport paradigmPhysics of Plasmas, 1995
- A numerical simulation of the L-H transition in JET with local and global models of anomalous transportNuclear Fusion, 1995
- Scalings for tokamak energy confinementNuclear Fusion, 1990
- Energy confinement scaling in Tokamaks: some implications of recent experiments with Ohmic and strong auxiliary heatingPlasma Physics and Controlled Fusion, 1984