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.
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