Turbulence Dissipation and Particle Injection in Nonlinear Diffusive Shock Acceleration with Magnetic Field Amplification

The highly amplified magnetic fields suggested by observations of some supernova remnant shells are most likely an intrinsic part of efficient particle acceleration by shocks. This strong turbulence, which may result from cosmicray-driven instabilities, both resonant and nonresonant, in the shock precursor, is certain to play a critical role in selfconsistent, nonlinear models of strong, cosmic-ray-modified shocks. Here we present a Monte Carlo model of nonlinear diffusive shock acceleration (DSA) accounting for magnetic field amplification through resonant instabilities induced by accelerated particles, and including the effects of dissipation of turbulence upstream of a shock and the subsequent precursor plasma heating. Feedback effects between the plasma heating due to turbulence dissipation and particle injection are strong, adding to the nonlinear nature of efficient DSA. Describing the turbulence damping in a parameterized way, we reach two important results: first, for conditions typical of supernova remnant shocks, even a small amount of dissipated turbulence energy ( 10%) is sufficient to significantly heat the precursor plasma; and second, the heating upstream of the shock leads to an increase in the injection of thermal particles at the subshock by a factor of several. In our results, the response of the nonlinear shock structure to the boost in particle injection prevented the efficiency of particle acceleration and magnetic field amplification from increasing. We argue, however, that more advanced (possibly nonresonant) models of turbulence generation and dissipation may lead to a scenario in which particle injection boost due to turbulence dissipation results in more efficient acceleration and even stronger amplified magnetic fields than without the dissipation. Subject headinggs: acceleration of particles — cosmic rays — magnetic fields — shock waves — supernova remnants — turbulence