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

Abstract

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 $V_{\mathrm{sh}}$ is larger than a few times ${\xi }_{\mathrm{CR}}c$, where ${\xi }_{\mathrm{CR}}$ 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 Alfvén 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 Alfvén 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.

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

References in corpus (2)

• Cosmic ray production in supernova remnants including reacceleration: the secondary to primary ratio
• Turbulence and particle acceleration in collisionless supernovae remnant shocks: II- Cosmic-ray transport

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• The Heating of Thermal Electrons in Fast Collisionless Shocks: The Integral Role of Cosmic Rays
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• Magnetic Field Amplification and Rapid Time Variations in SNR RX J1713.7-3946
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• Cosmic-ray acceleration and gamma-ray signals from radio supernovae
• On the growth of the thermally modified non-resonant streaming instability
• The double signature of local cosmic-ray acceleration in star-forming regions
• Nonthermal properties of supernova remnant G1.9+0.3