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This research was motivated by the recent observations indicating very strongmagnetic fields at some supernova remnant shocks, which suggests in-situgeneration of magnetic turbulence. The dissertation presents a numerical modelof collisionless shocks with strong amplification of stochastic magneticfields, self-consistently coupled to efficient shock acceleration of chargedparticles. Based on a Monte Carlo simulation of particle transport andacceleration in nonlinear shocks, the model describes magnetic fieldamplification using the state-of-the-art analytic models of instabilities inmagnetized plasmas in the presence of non-thermal particle streaming. Theresults help one understand the complex nonlinear connections between thethermal plasma, the accelerated particles and the stochastic magnetic fields instrong collisionless shocks. Also, predictions regarding the efficiency ofparticle acceleration and magnetic field amplification, the impact of magneticfield amplification on the maximum energy of accelerated particles, and thecompression and heating of the thermal plasma by the shocks are presented.Particle distribution functions and turbulence spectra derived with this modelcan be used to calculate the emission of observable nonthermal radiation.

Modeling Magnetic Field Amplification in Nonlinear Diffusive Shock Acceleration