The MHD slow mode wave has application to coronal seismology, MHD turbulence,
and the solar wind where it can be produced by parametric instabilities. We
consider analytically how a drifting ion species (e.g. He$^{++}$) affects the
linear slow mode wave in a mainly electron-proton plasma, with potential
consequences for the aforementioned applications. Our main conclusions are: 1.
For wavevectors highly oblique to the magnetic field, we find solutions that
are characterized by very small perturbations of total pressure. Thus, our
results may help to distinguish the MHD slow mode from kinetic Alfv\'en waves
and non-propagating pressure-balanced structures, which can also have very
small total pressure perturbations. 2. For small ion concentrations, there are
solutions that are similar to the usual slow mode in an electron-proton plasma,
and solutions that are dominated by the drifting ions, but for small drifts the
wave modes cannot be simply characterized. 3. Even with zero ion drift, the
standard dispersion relation for the highly oblique slow mode cannot be used
with the Alfv\'en speed computed using the summed proton and ion densities, and
with the sound speed computed from the summed pressures and densities of all
species. 4. The ions can drive a non-resonant instability under certain
circumstances. For low plasma beta, the threshold drift can be less than that
required to destabilize electromagnetic modes, but damping from the Landau
resonance can eliminate this instability altogether, unless $T_{\mathrm
e}/T_{\mathrm p}\gg1$.
