Spectral Properties and Length Scales of Two‐dimensional Magnetic Field Models

Matthaeus, W. H.; Bieber, J. W.; Ruffolo, D.; Chuychai, P.; Minnie, J.

doi:10.1086/520924

Cited by 133 publications

(148 citation statements)

References 26 publications

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“…The two spectra (4) and (6) are also in agreement with the forms discussed in Matthaeus et al (2007).…”

Section: The Shalchi and Weinhorst Model Spectrumsupporting

confidence: 86%

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

Qin¹,

Shalchi²

2013

APR

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We employ a test-particle code to explore diffusion of energetic particles interacting with the solar wind plasma. The first time we investigate the pitch-angle dependence of perpendicular diffusion for different parameter regimes. These results are important for numerical solutions of the pitch-angle dependent Cosmic Ray Fokker-Planck equation. We compare our finding also with predictions made by analytical theory.

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“…The two spectra (4) and (6) are also in agreement with the forms discussed in Matthaeus et al (2007).…”

Section: The Shalchi and Weinhorst Model Spectrumsupporting

confidence: 86%

“…According to Equation (11) of Shalchi (2011a), the latter integral corresponds to the square of the field line diffusion coefficient for pure two-dimensional turbulence (see also Matthaeus et al, 1995Matthaeus et al, , 2007 …”

Section: Dominant Perpendicular Diffusionmentioning

confidence: 99%

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

Qin¹,

Shalchi²

2013

APR

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“…where we use a slightly different definition of the "ultrascale"λ (see also Ruffolo et al 2004;Matthaeus et al 2007):…”

Section: Analytic Theorymentioning

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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“…This spectrum has three ranges: an inertial range, an energy-containing range, and an "inner" range that decreases as a function of wavenumber. This last range is included due to physical and theoretical considerations, discussed in detail by Matthaeus et al (2007). In this study, the inertial range spectral index is assumed to equal the Kolmogorov value, so that n = 5 3, and the inner range spectral index is set to q=3 (see, e.g., Matthaeus et al 2007).…”

Section: Relevance For Cosmic-ray Transport Coefficientsmentioning

confidence: 99%

“…This last range is included due to physical and theoretical considerations, discussed in detail by Matthaeus et al (2007). In this study, the inertial range spectral index is assumed to equal the Kolmogorov value, so that n = 5 3, and the inner range spectral index is set to q=3 (see, e.g., Matthaeus et al 2007). This leads, due to the piecewise definition of Equation (26), to an expression for the perpendicular mean-free path of the form …”

Section: Relevance For Cosmic-ray Transport Coefficientsmentioning

confidence: 99%

A Generalized Two-Component Model of Solar Wind Turbulence and Ab Initio Diffusion Mean-Free Paths and Drift Lengthscales of Cosmic Rays

Wiengarten

Oughton

Engelbrecht

et al. 2016

ApJ

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We extend a two-component model for the evolution of fluctuations in the solar wind plasma so that it is fully three-dimensional (3D) and also coupled self-consistently to the large-scale magnetohydrodynamic equations describing the background solar wind. The two classes of fluctuations considered are a high-frequency parallelpropagating wave-like piece and a low-frequency quasi-two-dimensional component. For both components, the nonlinear dynamics is dominanted by quasi-perpendicular spectral cascades of energy. Driving of the fluctuationsby, for example, velocity shear and pickup ionsis included. Numerical solutions to the new model are obtained using the CRONOS framework, and validated against previous simpler models. Comparing results from the new model with spacecraft measurements, we find improved agreement relative to earlier models that employ prescribed background solar wind fields. Finally, the new results for the wave-like and quasi-twodimensional fluctuations are used to calculate ab initio diffusion mean-free paths and drift lengthscales for the transport of cosmic rays in the turbulent solar wind.

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Spectral Properties and Length Scales of Two‐dimensional Magnetic Field Models

Cited by 133 publications

References 26 publications

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

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

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

A Generalized Two-Component Model of Solar Wind Turbulence and Ab Initio Diffusion Mean-Free Paths and Drift Lengthscales of Cosmic Rays

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