http://arxiv.org/abs/1401.7679
We use large hybrid (kinetic ions-fluid electrons) simulations to study ion acceleration and generation 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 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 Bell’s instability, which is predicted and found to grow faster than resonant instability in shocks with $M\gtrsim 30$. Ahead of these strong shocks we distinguish two regions: the far upstream, where magnetic field amplification is provided 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 stage. Finally, we measure ion diffusion in the self-generated turbulence, and find that it can be described by Bohm diffusion in the amplified field: the mean free path is of the order of the ion gyroradius, and the scattering rate is proportional to the energy in magnetic modes with resonant wavelengths. The obtained scalings for magnetic field amplification and ion diffusion enable the inclusion of self-consistent microphysics into phenomenological models of cosmic ray acceleration in supernova remnants.
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