  The first critical fast Mach number is defined for a magnetohydrodynamic
shock as the Mach number where the shock transitions from subcritical, laminar,
behavior to supercritical behavior, characterized by incident ion reflection
from the shock front. The ensuing upstream waves and turbulence are convected
downstream leading to a turbulent shock structure. Formally this is the Mach
number where plasma resistivity can no longer provide sufficient dissipation to
establish a stable shock, and is characterized by the downstream flow speed
becoming subsonic. We revisit these calculations, including in the MHD jump
conditions terms modeling the plasma energy loss to accelerated particles and
the presence of waves associated with these particles. The accelerated particle
contributions make an insignificant change, but the associated waves have a
more important effect. Upstream waves can be strongly amplified in intensity on
passing through the shock, and represent another means of shock dissipation.
The presence of such waves therefore increases the first critical fast Mach
number, especially at quasi-parallel shock where wave excitation is strongest.
These effects may have significance for the solar regions where shock waves
accelerate particles and cause Type II and Type III radio bursts, and also
contribute to the event-to-event variability of SEP acceleration.
