Parallel and Perpendicular Diffusion Coefficients of Energetic Charged Particles with Adiabatic Focusing

Wang, J. F.; Qin, Gang

doi:10.3847/1538-4357/aae927

Cited by 9 publications

(14 citation statements)

References 40 publications

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“…Diffusive UNLT with plasma wave propagation effects was derived in Hussein and Shalchi (2014b). Furthermore, the theory was extended in Wang and Qin (2018) by including the effect of adiabatic focusing, which occurs if the mean magnetic field is curved. We also note that Eq.…”

Section: Derivation From the Fokker-planck Equationmentioning

confidence: 99%

Perpendicular Transport of Energetic Particles in Magnetic Turbulence

Shalchi

2020

Space Sci Rev

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Scientists have explored how energetic particles such as solar energetic particles and cosmic rays move through a magnetized plasma such as the interplanetary and interstellar medium since more than five decades. From a theoretical point of view, this topic is difficult because the particles experience complicated interactions with turbulent magnetic fields. Besides turbulent fields, there are also large scale or mean magnetic fields breaking the symmetry in such systems and one has to distinguish between transport of particles parallel and perpendicular with respect to such mean fields. In standard descriptions of transport phenomena, one often assumes that the transport in both directions is normal diffusive but non-diffusive transport was found in more recent work. This is in particular true for early and intermediate times where the diffusive regime is not yet reached. In recent years researchers employed advanced numerical tools in order to simulate the motion of those particles through the aforementioned systems. Nevertheless, the analytical description of the problem discussed here is of utmost importance since analytical forms of particle transport parameters need to be known in several applications such as solar modulation studies or investigations of shock acceleration. The latter process is directly linked to the question of what the sources of high energy cosmic rays are, a problem which is considered to be one of the most important problems of the sciences of the 21st century. The present review article discusses analytical theories developed for describing particle transport across a large scale magnetic field as well as field line random walk. A heuristic approach explaining the basic physics of perpendicular transport is also presented. Simple analytical forms for the perpendicular diffusion coefficient are proposed which can easily be incorporated in numerical codes for solar modulation or shock acceleration studies. Test-particle simulations are also discussed together with a comparison with analytical results. Several applications such as cosmic ray propagation and diffusive shock acceleration are also part of this review.

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Section: Derivation From the Fokker-planck Equationmentioning

confidence: 99%

Perpendicular Transport of Energetic Particles in Magnetic Turbulence

Shalchi

2020

Space Sci Rev

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“…2.1. The variable coefficient differential equation of the isotropic distribution function F (z, t) In this subsection, by employing the method in Wang & Qin (2018) we derive the formula of the variable coefficient differential equation of the isotropic distribution function F(z, t), and the derivation are similar to Equation (22) in Wang & Qin (2018).…”

Section: Equation Of Isotropic Distribution Functionmentioning

confidence: 99%

“…This equation determines the transport regimes by the specific forms of its coefficient. For example, as shown in Wang & Qin (2018), κ z (t) is the coefficient of the convection term…”

Section: The Specific Form Of the Variable Coefficient Differential Ementioning

confidence: 99%

“…The interaction process between particles and turbulent magnetic fields is very complicated, and particles and magnetic field lines have the stochastic properties. Therefore, one has to employ methods of statistics to describe the complicated transport of energetic particles (Earl 1974(Earl , 1976Beeck & Wibberenz 1986;Shalchi 2011;Litvinenko 2012a,b;Shalchi & Danos 2013;He & Schlickeiser 2014;Wang et al 2017a,b;Wang & Qin 2018) and field line random walk (Matthaeus et al 1995;Shalchi & Kourakis 2007;Shalchi & Qin 2010). Because the background magnetic field B 0 breaks the symmetry of the magnetized plasma, one has to distinguish particle diffusion along and across the largescale magnetic field.…”

Section: Introductionmentioning

confidence: 99%

“…Because the background magnetic field B 0 breaks the symmetry of the magnetized plasma, one has to distinguish particle diffusion along and across the largescale magnetic field. One may only consider the parallel diffusion in many cases, when it is much greater than the perpendicular one (see, e.g., Earl 1974Earl , 1976Beeck & Wibberenz 1986;Shalchi 2009bShalchi , 2011Litvinenko 2012a,b;Shalchi & Danos 2013;He & Schlickeiser 2014;Wang & Qin 2018).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Diffusion Coefficient with Displacement Variance of Energetic Particles Caused by Adiabatic Focusing

Wang

Qin

2019

ApJ

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The equation κ zz = dσ 2 /(2dt) (hereafter DCDV) is a well-known formula of energetic particles describing the relation of parallel diffusion coefficient κ zz with the parallel displacement variance σ 2 . In this study, we find that DCDV is only applicable to two kinds of transport equations of isotropic distribution function, one is without cross terms, the other is without convection term. Here, by employing the more general transport equation, i.e., the variable coefficient differential equation derived from the Fokker-Planck equation, a new equation of κ zz as a function of σ 2 is obtained. We find that DCDV is the special case of the new equation. In addition, another equation of κ zz as a function of σ 2 corresponding to the telegraph equation is also investigated preliminarily.

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A Primer on Focused Solar Energetic Particle Transport

2020

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The basics of focused transport as applied to solar energetic particles are reviewed, paying special attention to areas of common misconception. The micro-physics of charged particles interacting with slab turbulence are investigated to illustrate the concept of pitch-angle scattering, where after the distribution function and focused transport equation are introduced as theoretical tools to describe the transport processes and it is discussed how observable quantities can be calculated from the distribution function. In particular, two approximations, the diffusion-advection and the telegraph equation, are compared in simplified situations to the full solution of the focused transport equation describing particle motion along a magnetic field line. It is shown that these approximations are insufficient to capture the complexity of the physical processes involved. To overcome such limitations, a finite-difference model, which is open for use by the public, is introduced to solve the focused transport equation. The use of the model is briefly discussed and it is shown how the model can be applied to reproduce an observed solar energetic electron event, providing insights into the acceleration and transport processes involved. Past work and literature on the application of these concepts are also reviewed, starting with the most basic models and building up to more complex models.

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Parallel and Perpendicular Diffusion Coefficients of Energetic Charged Particles with Adiabatic Focusing

Cited by 9 publications

References 40 publications

Perpendicular Transport of Energetic Particles in Magnetic Turbulence

Perpendicular Transport of Energetic Particles in Magnetic Turbulence

The Diffusion Coefficient with Displacement Variance of Energetic Particles Caused by Adiabatic Focusing

A Primer on Focused Solar Energetic Particle Transport

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