  We reexamine nonlinear diffusive shock acceleration (DSA) at cosmological
shocks in the large scale structure of the Universe, incorporating
wave-particle interactions that are expected to operate in collisionless
shocks. Adopting simple phenomenological models for magnetic field
amplification (MFA) by cosmic-ray (CR) streaming instabilities and Alfv'enic
drift, we perform kinetic DSA simulations for a wide range of sonic and
Alfv'enic Mach numbers and evaluate the CR injection fraction and acceleration
efficiency. In our DSA model the CR acceleration efficiency is determined
mainly by the sonic Mach number Ms, while the MFA factor depends on the
Alfv'enic Mach number and the degree of shock modification by CRs. We show that
at strong CR modified shocks, if scattering centers drift with an effective
Alfv'en speed in the amplified magnetic field, the CR energy spectrum is
steepened and the acceleration efficiency is reduced significantly, compared to
the cases without such effects. As a result, the postshock CR pressure
saturates roughly at ~ 20 % of the shock ram pressure for strong shocks with
Ms>~ 10. In the test-particle regime (Ms<~ 3), it is expected that the magnetic
field is not amplified and the Alfv'enic drift effects are insignificant,
although relevant plasma physical processes at low Mach number shocks remain
largely uncertain.
