Role of stochastic anisotropy and shear on magnetic field lines diffusion

Negrea, Marian; Petrișor, Iulian; Weyssow, Boris

doi:10.1088/0741-3335/49/11/002

Cited by 16 publications

(24 citation statements)

References 25 publications

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“…Given that both RBD and DD provide inaccurate descriptions of the evolution, and that the ODE provides a transition from RBD to DD behavior, we conclude that all three theories are probably failing due to trapping effects. Some previous studies already concluded that trapping behavior implies that Corrsin's hypothesis does not work properly (Vlad et al 1998;Neuer & Spatschek 2006;Negrea et al 2007), which is a possible explanation for why all these theories are inaccurate for this case.…”

Section: Discussionmentioning

confidence: 86%

“…Previous work has often used a closure in terms of Corrsin's independence hypothesis, as described below. (For cases where trapping along flux surfaces is important, an alternative to Corrsin's hypothesis is the decorrelation trajectory method (e.g., Vlad et al 1998;Neuer & Spatschek 2006;Negrea et al 2007). An alternative approach, based on the direct interaction approximation (Kraichnan 1959), has been shown by Vanden Eijnden & Balescu (1995) to be consistent with the present approach.)…”

Section: General Formmentioning

confidence: 99%

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Model of the Field Line Random Walk Evolution and Approach to Asymptotic Diffusion in Magnetic Turbulence

Snodin

Ruffolo

Matthaeus

2012

ApJ

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The turbulent random walk of magnetic field lines plays an important role in the transport of plasmas and energetic particles in a wide variety of astrophysical situations, but most theoretical work has concentrated on determination of the asymptotic field line diffusion coefficient. Here we consider the evolution with distance of the field line random walk using a general ordinary differential equation (ODE), which for most cases of interest in astrophysics describes a transition from free streaming to asymptotic diffusion. By challenging theories of asymptotic diffusion to also describe the evolution, one gains insight on how accurately they describe the random walk process. Previous theoretical work has effectively involved closure of the ODE, often by assuming Corrsin's hypothesis and a Gaussian displacement distribution. Approaches that use quasilinear theory and prescribe the mean squared displacement Δx 2 according to free streaming (random ballistic decorrelation, RBD) or asymptotic diffusion (diffusive decorrelation, DD) can match computer simulation results, but only over specific parameter ranges, with no obvious "marker" of the range of validity. Here we make use of a unified description in which the ODE determines Δx 2 self-consistently, providing a natural transition between the assumptions of RBD and DD. We find that the minimum kurtosis of the displacement distribution provides a good indicator of whether the self-consistent ODE is applicable, i.e., inaccuracy of the self-consistent ODE is associated with non-Gaussian displacement distributions.

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Section: Discussionmentioning

confidence: 86%

Section: General Formmentioning

confidence: 99%

Model of the Field Line Random Walk Evolution and Approach to Asymptotic Diffusion in Magnetic Turbulence

Snodin

Ruffolo

Matthaeus

2012

ApJ

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“…The simulations and the DCT method yield diffusion coefficients that differ by 50% or less, they can thus be considered to be in good qualitative agreement. Another instance where the results obtained by the DCT method were compared with numerical test-particle simulation, and where also relatively good agreement was found, is given in [33,34].…”

Section: Test-particle Simulationsmentioning

confidence: 96%

“…Note that we can define the vector potential with different normalization factors, such as λ x λ y , λ 2 x or λ 2 y . We have chosen the second case in order to keep the analysis close to the one in [33]. The qualitative results are not changed by the particular choice of the normalization factor.…”

Section: B(x; Z)mentioning

confidence: 99%

Ion and impurity transport in turbulent, anisotropic magnetic fields

Negrea

Petrișor

Isliker

et al. 2011

Plasma Phys. Control. Fusion

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We investigate ion and impurity transport in turbulent, possibly anisotropic, magnetic fields. The turbulent magnetic field is modeled as a correlated stochastic field, with Gaussian distribution function and prescribed spatial auto-correlation function, superimposed onto a strong background field. The (running) diffusion coefficients of ions are determined in the three-dimensional environment, using two alternative methods, the semi-analytical decorrelation trajectory (DCT) method, and test-particle simulations. In a first step, the results of the test-particle simulations are compared with and used to validate the results obtained from the DCT method. For this purpose, a drift approximation was made in slab geometry, and relatively good qualitative agreement between the DCT method and the test-particle simulations was found. In a second step, the ion species He, Be, Ne and W, all assumed to be fully ionized, are considered under ITER-like conditions, and the scaling of their diffusivities is determined with respect to varying levels of turbulence (varying Kubo number), varying degrees of anisotropy of the turbulent structures and atomic number. In a third step, the test-particle simulations are repeated without drift approximation, directly using the Lorentz force, first in slab geometry, in order to assess the finite Larmor radius effects, and second in toroidal geometry, to account for the geometric effects. It is found that both effects are important, most prominently the effects due to toroidal geometry and the diffusivities are overestimated in slab geometry by an order of magnitude.

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“…There is some computational confirmation for the FLRW and analogous problems (e.g., Ottaviani 1992;Reuss & Misguich 1996;Hauff et al 2010). Considerations related to percolation have also been referred to as trapping effects (e.g., Ottaviani 1992;Vlad et al 1998;Neuer & Spatschek 2006;Negrea et al 2007), a term that is broader than percolation. Additional theoretical techniques include the decorrelation trajectory method and A-Langevin equations (Vlad et al 1998;Neuer & Spatschek 2006).…”

Section: Introductionmentioning

confidence: 99%

Magnetic Field Line Random Walk for Disturbed Flux Surfaces: Trapping Effects and Multiple Routes to Bohm Diffusion

Ghilea

Ruffolo

Chuychai

et al. 2011

ApJ

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The magnetic field line random walk (FLRW) is important for the transport of energetic particles in many astrophysical situations. While all authors agree on the quasilinear diffusion of field lines for fluctuations that mainly vary parallel to a large-scale field, for the opposite case of fluctuations that mainly vary in the perpendicular directions, there has been an apparent conflict between concepts of Bohm diffusion and percolation/trapping effects. Here computer simulation and non-perturbative analytic techniques are used to re-examine the FLRW in magnetic turbulence with slab and two-dimensional (2D) components, in which 2D flux surfaces are disturbed by the slab fluctuations. Previous non-perturbative theories for D ⊥ , based on Corrsin's hypothesis, have identified a slab contribution with quasilinear behavior and a 2D contribution due to Bohm diffusion with diffusive decorrelation (DD), combined in a quadratic formula. Here we present analytic theories for other routes to Bohm diffusion, with random ballistic decorrelation (RBD) either due to the 2D component itself (for a weak slab contribution) or the total fluctuation field (for a strong slab contribution), combined in a direct sum with the slab contribution. Computer simulations confirm the applicability of RBD routes for weak or strong slab contributions, while the DD route applies for a moderate slab contribution. For a very low slab contribution, interesting trapping effects are found, including a depressed diffusion coefficient and subdiffusive behavior. Thus quasilinear, Bohm, and trapping behaviors are all found in the same system, together with an overall viewpoint to explain these behaviors.

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Role of stochastic anisotropy and shear on magnetic field lines diffusion

Cited by 16 publications

References 25 publications

Model of the Field Line Random Walk Evolution and Approach to Asymptotic Diffusion in Magnetic Turbulence

Model of the Field Line Random Walk Evolution and Approach to Asymptotic Diffusion in Magnetic Turbulence

Ion and impurity transport in turbulent, anisotropic magnetic fields

Magnetic Field Line Random Walk for Disturbed Flux Surfaces: Trapping Effects and Multiple Routes to Bohm Diffusion

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