  We present a time-dependent cosmic-ray modified shock model for which the
calculated H-alpha emissivity profile agrees well with the H-alpha flux
increase ahead of the Balmer-dominated shock at knot g in Tycho's supernova
remnant, observed by Lee et al (2007). The backreaction of the cosmic ray
component on the thermal component is treated in the two-fluid approximation,
and we include thermal particle injection and energy transfer due to the
acoustic instability in the precursor. The transient state of our model that
describes the current state of the shock at knot g, occurs during the evolution
from a thermal gas dominated shock to a smooth cosmic-ray dominated shock.
Assuming a distance of 2.3 kpc to Tycho's remnant we obtain values for the
cosmic ray diffusion coefficient, the injection parameter, and the time scale
for the energy transfer of 10^{24} cm^{2} s^{-1}, 4.2x10^{-3}, and 426 y,
respectively. We have also studied the parameter space for fast (300 km s^{-1}
- 3000 km s^{-1}), time-asymptotically steady shocks and have identified a
branch of solutions, for which the temperature in the cosmic ray precursor
typically reaches 2-6x10^{4} K and the bulk acceleration of the flow through
the precursor is less than 10 km s^{-1}. These solutions fall into the low
cosmic ray acceleration efficiency regime and are relatively insensitive to
shock parameters. This low cosmic ray acceleration efficiency branch of
solutions may provide a natural explanation for the line broadening of the
H-alpha narrow component observed in non-radiative shocks in many supernova
remnants.
