Perpendicular Transport of Energetic Particles in Magnetic Turbulence

Abstract

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.

Regimes of cosmic-ray diffusion in Galactic turbulence

“…Good agreement between analytical models such as QLT (in some regimes), nonlinear guiding center theory and unified nonlinear theory with test particle simulations was found for two-dimensional, slab, or composite (two-dimensional & slab) turbulence (see e.g. [ 44 ] for a review). Despite these advances, for isotropic three-dimensional turbulence, tension with these theories was found at small reduced rigidities [ 12 , 32 ].…”

The Transport and Evolution of MHD Turbulence throughout the Heliosphere: Models and Observations

“…It is generally believed that the magnetic field line wandering is the main physical mechanism that controls Ωτ. There are two ways to model the magnetic field line wandering: quasi-linear theory (QLT) [147][148][149][150][151], and a nonperturbative approach [152][153][154][155][156].…”

“…Shalchi [166] introduced an important extensions of NLGC theory, namely the unified nonlinear theory (UNLT), which addresses the weaknesses of NLGC theory. Turbulence responsible for the scattering of charged particles can be described as the superposition of a dominant 2D component and a minority slab component [41,43,44,[154][155][156], in which case UNLT theory and NLGC theory give very similar results. If the turbulence models do not contain a dominant 2D component, the UNLT theory should be used instead of NLGC theory.…”

Effect of Ergodic and Non-Ergodic Fluctuations on a Charge Diffusing in a Stochastic Magnetic Field

“…We focus on the diffusion of the particles caused by the magnetic field fluctuations, which can destroy the plasma confinement. The fluctuations of physical quantities are an almost inevitable occurrence and generate diffusion processes of the related quantity [ 10 , 11 , 12 ]. It is important, therefore, to have an adequate theoretical framework to model their effect.…”