The young remnants of supernovae of thermonuclear origin are often surrounded by fast
(~1000 km/s) shocks which are spatially coincident with strong hydrogen emission
lines.  Typically observed in H-alpha, these two-component lines are direct probes of
the physical conditions in the pre- and post-shock gas.  In this talk, I begin with a
brief review of Balmer-dominated shocks.  I will argue why the scientific yields from
studying these shocks with high spatial and spectral resolutions are significantly
enhanced, and that integral field unit (IFU) spectrographs allow for such studies. 
Subsequently, I report on an IFU observation of the ~2000-3000 km/s shocks in the
northwestern portion of supernova (SN) 1006.  Using models which do not take cosmic
ray physics into account, the data is converted into maps of the shock velocity and
electron-to-proton temperature ratio; more than 50% of the (Voronoi-)binned data
points do not have a corresponding model solution.  Additionally, the presence of
non-Gaussianity is detected in the broad H-alpha line.  Taken together, our results
suggest the presence of non-thermal protons in these Balmer-dominated shocks, which
we identify as low-energy, hadronic cosmic rays.