A new analytic solution of the one-speed neutron transport equation for adjacent half-spaces with isotropic scattering

This paper derives a new analytic solution of the one-speed neutron transport equation for two isotropically scattering half-spaces, where each half-space has its own isotropic internal source. The constant source problem has been studied previously by Auerbach (1961), and this analysis has been generalised to consider a source whose strength varies linearly with position. This problem arises in connection with assessing the accuracy of linear treatments of the thermal emission source in Monte Carlo thermal radiation transport algorithms. Simple expressions for the angular flux at the interface as well as its zeroth and first moments are provided as a function of the scattering ratios in the two half-spaces.

► Extended previous work by Auerbach to a linearly varying source in each half-space. ► New analytic expressions derived for the radiation field at the interface for this problem. ► Simple expressions for the zero and first angular moments. ► Relevant to the analysis of source tilts for Monte Carlo thermal radiation transport. ► Useful verification test problem for transport codes.