Improved treatments of the ionizing photon mean free path in
  semi-numerical simulations of reionization
  Efficient and accurate simulations of the reionization epoch are crucial to
exploring the vast uncharted parameter space that will soon be constrained by
measurements of the 21 cm power spectrum. One of these parameters, $R_{\rm
max}$, is meant to characterize the absorption of photons by residual neutral
gas inside of ionized regions, but has historically been implemented in a very
simplistic fashion acting only as a maximum filtering scale. We leverage the
correspondence between excursion set methods and the integrated flux from
ionizing sources to define two physically-motivated prescriptions of the mean
free path of ionizing photons that smoothly attenuate the contribution from
distant sources. Implementation of these methods in semi-numerical reionization
codes requires only modest additional computational effort due to the fact that
spatial filtering is still performed on scales larger than the characteristic
absorption distance. We find that our smoothly-defined mean free path
prescriptions more effectively suppress large-scale structures in the
ionization field in semi-numerical reionization simulations compared to the
standard $R_{\rm max}$ approach, and the magnitude of the mean free path
modulates the power spectrum in a much smoother manner. We show that this
suppression of large-scale power is significant enough to be relevant for
upcoming 21 cm power spectrum observations. Finally, we show that in our model
the mean free path plays a larger role in regulating the reionization history
than in models using $R_{\rm max}$.
