A New Cosmic Ray Transport Theory in Partially Turbulent Space Plasmas: Extending the Quasilinear Approach

Abstract

A new transport theory of cosmic rays in magnetized space plasmas with axisymmetric incompressible magnetic turbulence is developed extending the quasilinear approximation to the particle orbit. Arbitrary gyrophase deviations from the unperturbed spiral orbits in the uniform magnetic field are allowed. For quasi-stationary and spatially homogeneous magnetic turbulence, we derive the small Larmor radius approximation gyrophaseaveraged cosmic ray Fokker-Planck coefficients. The generalized Fokker-Planck coefficients correctly reduce to their known quasilinear values in the corresponding limit. New forms of the quasilinear Fokker-Planck coefficients in axisymmetric turbulence are derived which no longer involve infinite sums of products of Bessel functions, which facilitate their numerical computation for specified turbulence field correlation tensors. The Fokker-Planck coefficients for arbitrary phase orbits of the cosmic ray particles provide strict upper limits for the perpendicular and pitch-angle Fokker-Planck coefficients, which in turn yield strict upper and lower limits for the perpendicular and parallel spatial diffusion coefficients, respectively, describing the spatial diffusion of the isotropic part of the cosmic ray phase space density. For the associated mean free paths, we find for this general case that the product of the minimum parallel mean free path with the sum of the maximum perpendicular mean free paths equals R 2 L , where R L denotes the cosmic ray gyroradius.

The Diffusion Approximation Versus the Telegraph Equation for Modeling Solar Energetic Particle Transport With Adiabatic Focusing. I. Isotropic Pitch-Angle Scattering

“…The Fokker-Planck equation is typically used in the description of the evolution of the particle distribution function (see, e.g. Schlickeiser 2011, for a recent derivation). The Fokker-Planck description of the SEP transport incorporates various important effects, such as turbulent pitch-angle scattering and adiabatic focusing due to large-scale gradients in a background magnetic field, for instance in the Parker spiral field.…”

Comparison of the telegraph and hyperdiffusion approximations in cosmic-ray transport

“…The Fokker-Planck equation for the particle distribution function plays a central role in the theory of cosmic-ray transport in turbulent astrophysical plasmas (see, e.g., Schlickeiser 1 for a systematic derivation of the equation and Schlickeiser 2 for a recent review of its history and applications). It is well known, however, that the complicated evolution of the particle distribution often can be described as a simpler diffusive process.…”

Amplification of Collective Magnetic Fluctuations in Magnetized Bi-Maxwellian Plasmas for Parallel Wave Vectors. I. Electron–proton Plasma

“…Indeed, it has implications for many relevant problems, such as the acceleration and transport of charged particles in turbulent electromagnetic fields (Schlickeiser 2011(Schlickeiser , 2015, turbulent magnetic reconnection (Lazarian & Vishniac 1999), the dynamics of collisional shock waves (Blandford & Eichler 1987;Medevedev & Loeb 1999;Balogh & Treumann 2013;Bret et al 2013), and the generation and amplification of the seed magnetic field in the early intergalactic medium (Schlickeiser 2012).…”