Turbulence and particle acceleration in collisionless supernovae remnant shocks

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 cosmicray 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 sh is larger than a few times ξ CR c, where ξ 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 (wavenumbers along the shock normal). The transverse cascade of Alfvén waves simultaneously determines the dependence in k ⊥ . We also study the redistribution of turbulent energy between forward and backward waves, which occurs through the interaction of two Alfvén and one slow magnetosonic wave. Eventually the spectra at the longest wavelengths are found almost proportional to k −1 . Downstream, anisotropy is further enhanced through the compression at shock crossing.

Postshock turbulence and diffusive shock acceleration in young supernova remnants

“…The resonant instability involves wave-particle interaction on wave scales of the order of the particle gyro-radius r L (Skilling 1975;Bell & Lucek 2001). The non-resonant regime was adapted to SNR shock waves by Bell (2004) (see also Pelletier et al 2006;Zirakashvili & Ptuskin 2008; , Table 1. Summary of the notations used in this article to denote the various physical quantities and parameters involved in our description of high energy particle yield in supernova remnants (SNR).…”

“…The magnetic fluctuations are redistributed on larger scales, while the turbulence level evolves in a linear way. Bell (2004) and Pelletier et al (2006) discussed several saturation processes that all lead to an energy transfer from the dominant wavelength towards long wavelengths (see discussion in Riquelme & Spitkovsky 2009). One may then expect the coherence length of the turbulence to be transferred from a scale coh−L , where…”

“…Considering these uncertainties, we consider q(β) as a free parameter hereafter. Pelletier et al (2006) obtained a 1D stationary β = 2 powerlaw solution for the non-resonant wave spectrum. We can see from the above analysis that the energetic particle transport properties around the shock front depend on the possibility that nonresonant instability will deeply enter in the non-linear regime.…”

“…Diamond & Malkov (2007) and Pelletier et al (2006) also highlighted the importance of determining the saturation level of the magnetic fluctuations, which was partially discarded in the previous work. Pelletier et al (2006) demonstrated that both resonant and non-resonant regimes of the streaming instability have to be considered simultaneously to fix the magnetic field spectrum and strength at the shock front. In fast shocks, the non-resonant instability dominates the magnetic field generation, the level of fluctuation at the shock being found to be similar to the value derived by Bell (2004).…”

Reacceleration of electrons in supernova remnants

“…Estimates based on the shrinking of the driving particles' Larmor radius lead to high saturation levels of a few hundred µG (Zirakashvili et al 2008;Pelletier et al 2006). A significant backreaction, however, is a reduction in streaming velocity and hence a diminishing of the streaming anisotropy, that leads to a lower saturation level and only moderately amplified magnetic field (Luo & Melrose 2009).…”