A Cosmic Ray Acceleration Mechanism Based on Background Flow Velocity Inhomogeneities Yielding Power-Law Spectra

TL;DR

This paper proposes a new cosmic ray acceleration mechanism based on background flow velocity inhomogeneities, deriving power-law spectra consistent with observations and suggesting it complements shock acceleration.

Contribution

It introduces a novel acceleration mechanism involving BFVIs, deriving the resulting cosmic ray spectra and explaining observed power-law indices.

Findings

Spectral index range of [-5, -3] matches galactic cosmic ray observations.

Mechanism may also explain solar energetic particle power laws.

Higher-order effects could produce indices smaller than -5.

Abstract

In this article, momentum transport generated by the combined effects of pitch-angle diffusion and Background Flow Velocity Inhomogeneities (BFVIs) is proposed to obtain a cosmic rays acceleration mechanism, starting from the well-known focusing equation describing particle diffusion and acceleration. The inhomogeneities of background flow velocity is ubiquitous in astrophysical environment. The isotropic distribution function equation of charged energetic particles is derived, and its solution is obtained, demonstrating the form of momentum power laws of cosmic rays. In addition, if it is assumed that cosmic rays penetrate compressible plasma waves or turbulence, for quasi-steady states, the spectral index $\delta$ of the momentum power law spectrum of cosmic rays is found to be in the range $[-5, -3]$, which includes the observed power law indices of galactic cosmic rays. The results obtained in this article demonstrate that the mechanism proposed in this article, along with shock acceleration, may also contribute to the acceleration of galactic cosmic rays. Furthermore, when momentum convection effect and higher-order momentum derivative terms are considered, the indices of power laws should be smaller than $-5$. This may explain the power laws of solar energetic particle events.