Turbulence and particle acceleration in collisionless supernovae remnant shocks: I-Anisotropic spectra solutions

Details Turbulence and particle acceleration in collisionless supernovae remnant shocks: I-Anisotropic spectra solutions Turbulence and particle acceleration in collisionless supernovae remnant shocks: I-Anisotropic spectra solutions

2006-03-17

arxiv.org/abs/astro-ph/0603461v1

Astronomy and Astrophysics

Astrophysics

13 pages, 3 figures, accepted for publication Astronomy & Astrophysics main journal

Scientific paper

10.1051/0004-6361:20054737

This paper investigates the nature of the MHD turbulence excited by the streaming of accelerated cosmic rays in a shock wave precursor. The two recognised regimes (non-resonant and resonant) of the streaming instability are taken into account. We show that the non-resonant instability is very efficient and saturates through a balance between its growth and non-linear transfer. The cosmic-ray resonant instability then takes over and is quenched by advection through the shock. The level of turbulence is determined by the non-resonant regime if the shock velocity $V_{\rm sh}$ is larger than a few times $\xi_{\rm CR} c$, where $\xi_{\rm CR}$ is the ratio of the cosmic-ray pressure to the shock kinetic energy. The instability determines the dependence of the spectrum with respect to $k_\parallel$ (wavenumbers along the shock normal). The transverse cascade of Alfv\'en waves simultaneously determines the dependence in $k_{\perp}$. We also study the redistribution of turbulent energy between forward and backward waves, which occurs through the interaction of two Alfv\'en and one slow magneto-sonic wave. Eventually the spectra at the longest wavelengths are found almost proportional to $k_{\parallel}^{-1}$. Downstream, anisotropy is further enhanced through the compression at shock crossing.

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