Neutron emissions with different durations have been observed during thunderstorms. These neutrons can be produced by microsecond to millisecond fast Terrestrial Gamma-ray Flashes correlated with lightning, or by Gamma-ray Glows lasting several seconds to minutes. In both cases, the neutrons are produced through a photonuclear reaction of gamma rays in the energy range of 10 to 30 MeV with nuclei of air molecules. Here we present simulations of gamma-ray beams propagating downward from different source altitudes. In our analysis the primary photons with energies between 10 and 30 MeV are separated into four energy intervals, each of 5 MeV width. From these data, arbitrary spectra of primary photons and of their products can be composed. Our results indicate that the neutrons are created essentially along the trajectory of the primary photons and that they reach ground within a transversal area of radius below 500 m. This lateral spreading is dominated by neutron diffusion due to collisions with air molecules. A secondary longer lasting photon pulse at sea level is predicted as well by our simulations. We have introduced this Terrestrial Gamma-ray Flash afterglow already in (Rutjes et al. 2017, https://doi.org/10.1002/2017GL075552). It is due to neutron capture by air molecules, and it has recently been observed by Bowers et al. (2017, https://doi.org/10.1002/2017GL075071) and Enoto et al. (2017, https://doi.org/10.1038/nature24630).