Turbulence-Level Dependence of Cosmic-Ray Parallel Diffusion

TL;DR

This paper investigates how the level of turbulence affects cosmic-ray parallel diffusion, revealing limitations of existing theories and proposing a turbulence-dependent diffusion model to improve cosmic-ray transport understanding.

Contribution

It provides a detailed numerical analysis of cosmic-ray diffusion dependence on turbulence levels, challenging quasi-linear theory predictions and establishing new regimes based on turbulence strength.

Findings

Quasi-linear theory overestimates diffusion at high turbulence levels.

Numerical simulations reveal five distinct rigidity regimes.

A turbulence-dependent diffusion coefficient improves cosmic-ray propagation models.

Abstract

Understanding the transport of energetic cosmic rays belongs to the most challenging topics in astrophysics. Diffusion due to scattering by electromagnetic fluctuations is a key process in cosmic-ray transport. The transition from a ballistic to a diffusive-propagation regime is presented in direct numerical calculations of diffusion coefficients for homogeneous magnetic field lines subject to turbulent perturbations. Simulation results are compared with theoretical derivations of the parallel diffusion coefficient's dependencies on the energy and the fluctuation amplitudes in the limit of weak turbulence. The present study shows that the widely-used extrapolation of the energy scaling for the parallel diffusion coefficient to high turbulence levels predicted by quasi-linear theory does not provide a universally accurate description in the resonant-scattering regime. It is highlighted here that the numerically calculated diffusion coefficients can be polluted for low energies due to missing resonant interaction possibilities of the particles with the turbulence. Five reduced-rigidity regimes are established, which are separated by analytical boundaries derived in the present work. Consequently, a proper description of cosmic-ray propagation can only be achieved by using a turbulence-level-dependent diffusion coefficient and can contribute to solving the Galactic cosmic-ray gradient problem.