The nonlinear saturation of the non-resonant kinetically driven streaming instability

A non-resonant instability for the amplification of the interstellar magnetic field in young Supernova Remnant (SNR) shocks was predicted by Bell (2004), and is thought to be relevant for the acceleration of cosmic ray (CR) particles. For this instability, the CRs streaming ahead of SNR shock fronts drive electromagnetic waves with wavelengths much shorter than the typical CR Larmor radius, by inducing a current parallel to the background magnetic field. We explore the nonlinear regime of the non-resonant mode using Particle-in-Cell (PIC) hybrid simulations, with kinetic ions and fluid electrons, and analyze the saturation mechanism for realistic CR and background plasma parameters. In the linear regime, the observed growth rates and wavelengths match the theoretical predictions; the nonlinear stage of the instability shows a strong reaction of both the background plasma and the CR particles, with the saturation level of the magnetic field varying with the CR parameters. The simulations with CR-to-background density ratios of n_CR/n_b=10^(-5) reveal the highest magnetic field saturation levels, with energy also being transferred to the background plasma and to the perpendicular velocity components of the CR particles. The results show that amplification factors >10 for the magnetic field can be achieved, and suggest that this instability is important for the generation of magnetic field turbulence, and for the acceleration of CR particles.