  The bulk propagation speed of GeV-energy cosmic rays is limited by frequent
scattering off hydromagnetic waves. Most galaxy evolution simulations that
account for this confinement assume the gas is fully ionized and cosmic rays
are well-coupled to Alfv\'en waves; however, multiphase density
inhomogeneities, frequently under-resolved in galaxy evolution simulations,
induce cosmic ray collisions and ionization-dependent transport driven by
cosmic ray decoupling and elevated streaming speeds in partially neutral gas.
How do cosmic rays navigate and influence such a medium, and can we constrain
this transport with observations? In this paper, we simulate cosmic ray fronts
impinging upon idealized, partially neutral clouds and lognormally-distributed
clumps, with and without ionization-dependent transport. With these
high-resolution simulations, we identify cloud interfaces as crucial regions
where cosmic ray fronts can develop a stair-step pressure gradient sufficient
to collisionlessly generate waves, overcome ion-neutral damping, and exert a
force on the cloud. We find that the acceleration of cold clouds is hindered by
only a factor of a few when ionization-dependent transport is included, with
additional dependencies on magnetic field strength and cloud dimensionality. We
also probe how cosmic rays sample the background gas and quantify collisional
losses. Hadronic gamma-ray emission maps are qualitatively different when
ionization-dependent transport is included, but the overall luminosity varies
by only a small factor, as the short cosmic ray residence times in cold clouds
are offset by the higher densities that cosmic rays sample.
