  Cosmic rays (CRs) with energies $\ll$ TeV comprise a significant component of
the interstellar medium (ISM). Major uncertainties in CR behavior on observable
scales (much larger than CR gyroradii) stem from how magnetic fluctuations
scatter CRs in pitch angle. Traditional first-principles models, which assume
these magnetic fluctuations are weak and uniformly scatter CRs in a homogeneous
ISM, struggle to reproduce basic observables such as the dependence of CR
residence times and scattering rates on rigidity. We therefore explore a new
category of "patchy" CR scattering models, wherein CRs are predominantly
scattered by intermittent strong scattering structures with small
volume-filling factors. These models produce the observed rigidity dependence
with a simple size distribution constraint, such that larger scattering
structures are rarer but can scatter a wider range of CR energies. To reproduce
the empirically-inferred CR scattering rates, the mean free path between
scattering structures must be $\ell_{\rm mfp} \sim 10$ pc at GeV energies. We
derive constraints on the sizes, internal properties, mass/volume-filling
factors, and the number density any such structures would need to be both
physically and observationally consistent. We consider a range of candidate
structures, both large-scale (e.g. H II regions) and small-scale (e.g.
intermittent turbulent structures, perhaps even associated with radio plasma
scattering) and show that while many macroscopic candidates can be immediately
ruled out as the primary CR scattering sites, many smaller structures remain
viable and merit further theoretical study. We discuss future observational
constraints that could test these models.
