Production of Magnetic Turbulence by Cosmic Rays Drifting Upstream of Supernova Remnant Shocks

We present results of twoand three-dimensional Particle-In-Cell simulations of magnetic-turbulence production by isotropic cosmic-ray ions drifting upstream of supernova remnant shocks. The studies aim at testing recent predictions of a strong amplification of short-wavelength non-resonant wave modes and at studying the subsequent evolution of the magnetic turbulence and its backreaction on cosmic ray trajectories. We confirm the generation of the turbulent magnetic field due to the drift of cosmic-ray ions in the upstream plasma, but show that an oblique filamentary mode grows more rapidly than the non-resonant parallel modes found in analytical theory. The growth rate of the field perturbations is much slower than is estimated for the parallel plane-wave mode using a quasilinear analytical approach, and the amplitude of the turbulence saturates at about δB/B ∼ 1. The backreaction of the magnetic turbulence on the particles leads to an alignment of the bulk-flow velocities of the cosmic rays and the background medium. This is an essential characteristic of cosmic-ray modified shocks: the upstream flow speed is continuously changed by the cosmic rays. The deceleration of the cosmic-ray drift and the simultaneous bulk acceleration of the background plasma account for the saturation of the instability at moderate amplitudes of the magnetic field. Previously published MHD simulations have assumed a constant cosmic-ray current, which excludes a backreaction of the generated magnetic field