Preprint typeset using LATEX style emulateapj v. 5/2/11 SIMULATIONS OF ION ACCELERATION AT NON-RELATIVISTIC SHOCKS: II) MAGNETIC FIELD AMPLIFICATION AND PARTICLE DIFFUSION

We use large hybrid (kinetic ions – fluid electrons) simulations to study ion acceleration and gen-eration of magnetic turbulence due to the streaming of energetic particles that are self-consistently accelerated at non-relativistic shocks. When acceleration is efficient (at quasi-parallel shocks), we find that the magnetic field develops transverse components and is significantly amplified in the pre-shock medium. The total amplification factor is larger than 10 for shocks with Mach number M = 100, and scales with the square root of M. We find that in the shock precursor the energy spectral density of excited magnetic turbulence is proportional to the spectral energy distribution of accelerated particles at corresponding resonant momenta, in good agreement with the predictions of quasilinear theory of diffusive shock acceleration. We discuss the role of non-resonant hybrid (Bell’s) instability, which is predicted and found to grow faster than resonant instability in shocks with M & 30. Ahead of these strong shocks we distinguish two regions: the far upstream, where magnetic field amplification is pro-vided by the current of escaping ions via Bell’s instability, and the precursor, where amplification is provided by the current of diffusing ions. The interface between these regions (free-escape boundary) is determined by the migration to larger wavelengths of non-resonant modes in the nonlinear stag