Pitch-Angle Diffusion and Bohm-type Approximations in Diffusive Shock Acceleration

TL;DR

This paper develops a comprehensive model for cosmic ray acceleration via diffusive shock acceleration, bridging weak and strong turbulence regimes, and providing analytical insights into diffusion behavior and Bohm-type approximations.

Contribution

The authors introduce a new model that unifies weak and strong turbulence regimes in diffusive shock acceleration, with analytical descriptions of the Bohm exponent and diffusion limitations.

Findings

Model converges to quasi-linear theory in weak turbulence

Quantifies limitations of Bohm-type models in strong turbulence

Accounts for anomalous diffusive behavior

Abstract

The problem of accelerating cosmic rays is one of fundamental importance, particularly given the uncertainty in the conditions inside the acceleration sites. Here we examine Diffusive Shock Acceleration in arbitrary turbulent magnetic fields, constructing a new model that is capable of bridging the gap between the very weak ($\delta B/B_0 \ll 1$) and the strong turbulence regimes. To describe the diffusion we provide quantitative analytical description of the "Bohm exponent" in each regime. We show that our results converge to the well known quasi-linear theory in the weak turbulence regime. In the strong regime, we quantify the limitations of the Bohm-type models. Furthermore, our results account for the anomalous diffusive behaviour which has been noted previously. Finally, we discuss the implications of our model in the study of possible acceleration sites in different astronomical objects.