Cosmic Rays Self-arising Turbulence with Universal Spectrum −8/3

Abstract

In the inertial subrange of scales, an exact compressible turbulence universal spectrum law −8/3 for the density fluctuations of cosmic rays (CRs) in the frame of the known two-fluid model of CR dynamics is obtained. It is shown that the origin of this scaling law may be due to the arising of shocks at the breaking of the nonlinear simple waves of CRs near the scale of their Larmor’s radii, as it is well known for the solar wind with the same turbulent spectrum law −8/3. The consistency of the turbulence spectrum −8/3 of CRs with the observed nonthermal differential energy distribution of CRs with a similar index −8/3 due to the possibility of self-reacceleration of the CRs on the self-arising shocks is stated. The turbulent diffusion mechanism for the observed CRs energy spectrum breaks is considered.