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