  The highly amplified magnetic fields suggested by observations of some
supernova remnant (SNR) shells are most likely an intrinsic part of efficient
particle acceleration by shocks. This strong turbulence, which may result from
cosmic ray driven instabilities, both resonant and non-resonant, in the shock
precursor, is certain to play a critical role in self-consistent, 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 non-linear 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, non-resonant) 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.
