The general collision-count source method for ray effects mitigation in S_N problems using Monte Carlo coupling

We introduce and demonstrate a method to mitigate ray effects in solutions of the discrete ordinates (S_N) approximation of the transport equation through coupling the S_N solver to the n-collided flux computed with a Monte Carlo simulation. This method is inspired by the classical approach of coupling the uncollided flux from a Monte Carlo simulator, or other semi-analytic estimator, that we extend in this work to compute an arbitrarily-high collision-count, n-collided flux that is free from ray effects by Monte Carlo. This flux is used to compute the (n+1)-collided source that drives the S_N solver to obtain the flux of particles that experience more than (n+1) collisions. The sum of these two fluxes is the full solution of the transport equation with ray effects that diminish with increasing n. For demonstration purposes we employ a simple model of an experimental setup designed to compute the recorded neutron count rate of the BeRP ball measured by the SNAP detector at a distance of 100 cm. Due to the long trajectory that the neutrons travel in air between the source and detector a straight solution with S_N methods exhibits severe ray effects that do not decrease sufficiently with increasing angular quadrature order N. This model has reference results that were generated with OpenMC using 32 group isotropic-scattering cross-sections. We test our new method on this model by using the steady-state, multigroup, S_N code THOR which uses the methods of short characteristics to discretize the spatial variable on tetrahedral cells, coupled to the special-purpose, multigroup Monte Carlo code Hammer. Hammer is designed to tally the neutron flux on THOR's tetrahedral cells by energy group for a user-selected collision-count n. Our results establish that for this model problem, ray effects in the coupled solution decrease with increasing n, and the neutron count rate approaches its asymptotic value faster. Specifically, the 6th or 7th collision source coupled with the S₂ discrete ordinates solver is sufficient to eliminate noticeable ray effects in this configuration. These results represent a verification of the method compared to reference multigroup Monte Carlo calculations.