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.
Highlights
A fundamental problem in the sciences of the 20th and 21st centuries is to understand the physics of cosmic rays
The situation is different in the theory of field line random walk and energetic particle transport where the position vectors are stochastic quantities somehow related to the magnetic fields
In the theory of field line random walk (FLRW) we study the statistics of magnetic field lines by computing the mean square displacement of different field line realizations
Summary
A fundamental problem in the sciences of the 20th and 21st centuries is to understand the physics of cosmic rays. To study the stochastic behavior of magnetic field lines in turbulence is done in the theory of field line random walk (FLRW) Energetic particles such as protons, electrons, and heavy ions are electrically charged. They interact with turbulent magnetic fields as described by the Newton-Lorentz equation. If particles follow random walking magnetic field lines, this would either lead to an energy independent perpendicular mean free path (if the parallel motion is assumed to be unperturbed) or to sub-diffusive transport (if the parallel motion is assumed to be diffusive). In the theoretical investigation of the acceleration of particles at shock waves one usually solves a diffusive transport equation in order to compute the cosmic ray spectrum Such transport equations contain diffusion coefficients in the different directions of space. ∂f ∂p leads to a slightly different form of the transport equation which can often be found in the literature
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have