Nonlinear Diffusive Shock Acceleration with Magnetic Field Amplification

We introduce a Monte Carlo model of nonlinear diffusive shock accelerationallowing for the generation of large-amplitude magnetic turbulence. The modelis the first to include strong wave generation, efficient particle accelerationto relativistic energies in nonrelativistic shocks, and thermal particleinjection in an internally self-consistent manner. We find that the upstreammagnetic field can be amplified by large factors and show that thisamplification depends strongly on the ambient Alfven Mach number. We also showthat in the nonlinear model large increases in the magnetic field do notnecessarily translate into a large increase in the maximum particle momentum aparticular shock can produce, a consequence of high momentum particlesdiffusing in the shock precursor where the large amplified field converges tothe low ambient value. To deal with the field growth rate in the regime ofstrong fluctuations, we extend to strong turbulence a parameterization that isconsistent with the resonant quasi-linear growth rate in the weak turbulencelimit. We believe our parameterization spans the maximum and minimum range ofthe fluctuation growth and, within these limits, we show that the nonlinearshock structure, acceleration efficiency, and thermal particle injection ratesdepend strongly on the yet to be determined details of wave growth in stronglyturbulent fields. The most direct application of our results will be toestimate magnetic fields amplified by strong cosmic-ray modified shocks insupernova remnants.Comment: Accepted in ApJ July 2006, typos corrected in this versio