  How cosmic rays sample the multi-phase interstellar medium (ISM) in starburst
galaxies has important implications for many science goals, including
evaluating the cosmic ray calorimeter model for these systems, predicting their
neutrino fluxes, and modeling their winds. Here, we use Monte Carlo simulations
to study cosmic ray sampling of a simple, two-phase ISM under conditions
similar to those of the prototypical starburst galaxy M82. The assumption that
cosmic rays sample the mean density of the ISM in the starburst region is
assessed over a multi-dimensional parameter space where we vary the number of
molecular clouds, the galactic wind speed, the extent to which the magnetic
field is tangled, and the cosmic ray injection mechanism. We evaluate the ratio
of the emissivity from pion production in molecular clouds to the emissivity
that would be observed if the cosmic rays sampled the mean density, and seek
areas of parameter space where this ratio differs significantly from unity. The
assumption that cosmic rays sample the mean density holds over much of
parameter space; however, this assumption begins to break down for high cloud
density, injection close to the clouds, and a very tangled magnetic field. We
conclude by evaluating the extent to which our simulated starburst region
behaves as a proton calorimeter and constructing the time-dependent spectrum of
a burst of cosmic rays.
