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Title: Anomalous, non-Gaussian transport of charged particles in anisotropic magnetic turbulence

Abstract

The transport of energetic particles in a mean magnetic field and in the presence of anisotropic magnetic turbulence is studied numerically, for parameter values relevant to astrophysical plasmas. A numerical realization of magnetic turbulence is set up, in which the degree of anisotropy is varied by changing the correlation lengths l{sub x}, l{sub y}, and l{sub z}. The ratio {rho}/{lambda} of the particle Larmor radius {rho} over the turbulence correlation length {lambda} is also varied. It is found that for l{sub x},l{sub y}>>l{sub z}, and for {rho}/{lambda} < or approx. 10{sup -2} transport can be non-Gaussian, with superdiffusion along the average magnetic field and subdiffusion perpendicular to it. In addition, the spatial distribution of particles is clearly non-Gaussian. Such regimes are characterized by a Levy statistics, with diverging second-order moments. Decreasing the ratio l{sub x}/l{sub z}, nearly Gaussian (normal) diffusion is obtained, showing that the transport regime depends on the turbulence anisotropy. Changing the particle Larmor radius, normal diffusion is found for 10{sup -2} < or approx. {rho}/{lambda} < or approx. 1 because of increased pitch angle diffusion. New anomalous superdiffusive regimes appear when {rho}/{lambda} > or approx. 1 showing that the interaction between particles and turbulence decreases in thesemore » cases. A new regime, called generalized double diffusion, is proposed for the cases when particles are able to trace back field lines. A summary of the physical conditions which lead to non-Gaussian transport is given.« less

Authors:
; ;  [1]
  1. Physics Department, University of Calabria, Arcavacata di Rende, 87036 Rende (Italy)
Publication Date:
OSTI Identifier:
20960099
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 14; Journal Issue: 1; Other Information: DOI: 10.1063/1.2434795; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ANISOTROPY; CHARGED PARTICLES; CORRELATIONS; DIFFUSION; LARMOR RADIUS; LENGTH; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; NUMERICAL ANALYSIS; PARTICLES; PLASMA; SPATIAL DISTRIBUTION; STATISTICS; TURBULENCE

Citation Formats

Pommois, P., Zimbardo, G., and Veltri, P. Anomalous, non-Gaussian transport of charged particles in anisotropic magnetic turbulence. United States: N. p., 2007. Web. doi:10.1063/1.2434795.
Pommois, P., Zimbardo, G., & Veltri, P. Anomalous, non-Gaussian transport of charged particles in anisotropic magnetic turbulence. United States. doi:10.1063/1.2434795.
Pommois, P., Zimbardo, G., and Veltri, P. Mon . "Anomalous, non-Gaussian transport of charged particles in anisotropic magnetic turbulence". United States. doi:10.1063/1.2434795.
@article{osti_20960099,
title = {Anomalous, non-Gaussian transport of charged particles in anisotropic magnetic turbulence},
author = {Pommois, P. and Zimbardo, G. and Veltri, P.},
abstractNote = {The transport of energetic particles in a mean magnetic field and in the presence of anisotropic magnetic turbulence is studied numerically, for parameter values relevant to astrophysical plasmas. A numerical realization of magnetic turbulence is set up, in which the degree of anisotropy is varied by changing the correlation lengths l{sub x}, l{sub y}, and l{sub z}. The ratio {rho}/{lambda} of the particle Larmor radius {rho} over the turbulence correlation length {lambda} is also varied. It is found that for l{sub x},l{sub y}>>l{sub z}, and for {rho}/{lambda} < or approx. 10{sup -2} transport can be non-Gaussian, with superdiffusion along the average magnetic field and subdiffusion perpendicular to it. In addition, the spatial distribution of particles is clearly non-Gaussian. Such regimes are characterized by a Levy statistics, with diverging second-order moments. Decreasing the ratio l{sub x}/l{sub z}, nearly Gaussian (normal) diffusion is obtained, showing that the transport regime depends on the turbulence anisotropy. Changing the particle Larmor radius, normal diffusion is found for 10{sup -2} < or approx. {rho}/{lambda} < or approx. 1 because of increased pitch angle diffusion. New anomalous superdiffusive regimes appear when {rho}/{lambda} > or approx. 1 showing that the interaction between particles and turbulence decreases in these cases. A new regime, called generalized double diffusion, is proposed for the cases when particles are able to trace back field lines. A summary of the physical conditions which lead to non-Gaussian transport is given.},
doi = {10.1063/1.2434795},
journal = {Physics of Plasmas},
number = 1,
volume = 14,
place = {United States},
year = {Mon Jan 15 00:00:00 EST 2007},
month = {Mon Jan 15 00:00:00 EST 2007}
}
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  • We investigate the transport of charged particles across magnetic discontinuities, focusing specifically on stream interfaces associated with co-rotating interaction regions in the solar wind. We argue that the magnetic field fluctuations perpendicular to the magnetic discontinuity, and usually also perpendicular to the mean magnetic field, are strongly damped in the vicinity of such a magnetic structure, leading to anisotropic perpendicular diffusion. Assuming that perpendicular diffusion arises from drifts in a turbulent magnetic field, we adopt a simplified approach to derive the relevant perpendicular diffusion coefficient. This approach, which we believe gives the correct principal dependences as expected from more elaboratemore » calculations, allows us to investigate transport in different turbulent geometries, such as longitudinal compressional turbulence that may be present near the heliopause. Although highly dependent on the (possibly anisotropic) perpendicular length scales and turbulence levels, we generally find perpendicular diffusion to be strongly damped at magnetic discontinuities, which may in turn provide an explanation for the large particle gradients associated with these structures.« less
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  • The transport of magnetic field lines is studied numerically in the case where strong three-dimensional magnetic fluctuations are superimposed to a uniform average magnetic field. The magnetic percolation of field lines between magnetic islands is found, as well as a non-Gaussian regime where the field lines exhibit Levy random walks, changing from Levy flights to trapped motion. Anomalous diffusion laws [l angle][Delta][ital x][sub [ital i]][sup 2][r angle][proportional to][ital s][sup [alpha]] with [alpha][gt]1 and [alpha][lt]1 are found for low fluctuation levels, while normal diffusion and Gaussian random walks are recovered for sufficiently high fluctuation levels.
  • Transport in a toroidal system with broken flux surfaces is considered. Flux surfaces with rational field line winding number can degenerate and form magnetic islands. The experimental evidence for the existence of magnetic structures is reviewed. If neighboring chains of islands overlap, a region of stochastic field is formed. In a stochastic field, a field line fills up a region of space and thus makes significant radial excursions. Particles following a stochastic field line may experience rapid radial transport. The problem of computing transport in a stochastic field has two stages: what is the behavior of field lines in amore » stochastic region? and what is the implication for particle transport? The much used formula due to Rechester & Rosenbluth for collisionless transport in a fully ergodic field is treated. It is shown that the conditions for the validity of this formula are normally not met in a tokamak. 16 refs.« less