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 (δB/B 0 ≪ 1) and the strong turbulence regimes. To describe the diffusion we provide a 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 behavior which has been noted previously. Finally, we discuss the implications of our model in the study of possible acceleration sites in different astronomical objects.
|State||Published - 2019|
Bibliographical noteFunding Information:
This research was partially supported by the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement no 618499. The authors also wish to acknowledge the DJEI/DES/SFI/HEA Irish Centre for High-End Computing (ICHEC) for the provision of computational facilities. We would also like to thank M. O’Riordan and L. Chen for useful discussions.
© 2019. The American Astronomical Society. All rights reserved.
- acceleration of particles
- cosmic rays
- methods: numerical