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 x , l y , and l z . The ratio / of the particle Larmor radius over the turbulence correlation length is also varied. It is found that for l x ,l y ӷ l z , and for / Շ10 −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 x / l z , nearly Gaussian ͑normal͒ diffusion is obtained, showing that the transport regime depends on the turbulence anisotropy. Changing the particle Larmor radius, normal diffusion is found for 10 −2 Շ / Շ1 because of increased pitch angle diffusion. New anomalous superdiffusive regimes appear when / տ1 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.

Nonclassical Transport and Particle-Field Coupling: from Laboratory Plasmas to the Solar Wind

“…Interestingly, from Fig. 6 one can see that for ρ/ l ⊥ ∼ 1 parallel superdiffusion is obtained again: this is because in the turbulence model considered by Pommois et al (2007) most of the fluctuation energy is at scales smaller than l ⊥ . In such a case, most fluctuations are average out by the large Larmor radius, and pitch angle scattering is reduced.…”

“…On the other hand, the transport regime also depends on the particle energy, in particular through the ratio between the particle Larmor radius ρ in the background magnetic field and the turbulence correlation lengths. Pommois et al (2007) find that for ρ/ l ⊥ = 0.001-0.01, parallel superdiffusion and perpendicular subdiffusion can be found, while normal diffusion is obtained for ρ/ l ⊥ ∼ 0.1 (see Fig. 6).…”

“…In either weakly collisional or collisionless plasmas, the transport is influenced by electric and magnetic fluctuations and by wave-particle interactions, which cause pitch angle scattering and transverse particle drifts, and by low frequency magnetic fluctuations, which cause field lines to trace a random walk (Jokipii 1966). The strength of these effects varies with the particle species and energy, and with the properties of turbulence, so that a large number of different transport regimes can arise, as shown by independent numerical simulations (Zimbardo et al 2000a;Pommois et al 2007;Shalchi and Kourakis 2007;Gustafson et al 2012b). Detailed study of wave-particle interactions is necessary to understand transport.…”

The Cosmic‐Ray Diffusion Tensor in Nonaxisymmetric Turbulence

“…While being noted in the literature (see de Koning & Bieber 2003), the consequences of nonaxisymmetric turbulence have, so far, been subject of only a few studies that dealt with the transport of magnetic field lines (Pommois et al 1999(Pommois et al , 2001) rather than with the consequences for particle transport. The latter has been studied very recently by Pommois et al (2007).…”

Pitch-Angle Dependent Perpendicular Diffusion of Energetic Particles Interacting With Magnetic Turbulence

“…From these particle orbits one can obtain the diffusion parameters κ ∥ and κ ⊥ . This procedure can be seen as standard approach and it was performed by numerous authors (see, e.g., Michałek & Ostrowski, 1996;Mace et al, 2000;Qin et al, 2002aQin et al, , 2002bPommois et al, 2005;Zimbardo et al, 2006;Pommois et al, 2007;Ruffolo et al, 2008;Tautz, 2010;Qin & Shalchi, 2012;Tautz & Shalchi, 2013). However, one can also be interested in the pitch-angle dependence of the different transport parameters.…”