Kinetic simulations of turbulent magnetic-field growth by streaming cosmic rays

The acceleration of cosmic rays to high energies is thought to occur at supernova-remnant shocks via the mechanism of diffusive shock acceleration. Efficient acceleration requires turbulent, amplified magnetic fields in the shock's upstream region. I will present results of multidimensional particle-in-cell simulations aimed at observing the magnetic field amplification that is expected to arise from the cosmic-ray current ahead of the shock. We find that the initial structure and peak strength of the amplified field is somewhat sensitive to the choice of parameters, but that the field growth saturates in a similar manner in all cases: the back-reaction on the cosmic rays leads to net transfer of momentum to the interstellar medium, substantially weakening their relative drift while also implying the development of a modified shock.