Second-order sensitivity analysis of uncollided particle contributions to radiation detector responses using ray-tracing

Abstract

The Second-Level Adjoint Sensitivity System (2nd-LASS) that yields the second-order sensitivities of a response of uncollided particles with respect to isotope densities, cross sections, and source emission rates has previously been derived and solved using the off-the-shelf discrete ordinates code PARTISN. In this paper, the 2nd-LASS equations are solved using ray-tracing for the case when the response is evaluated at a point on the boundary (the partial current density or scalar flux). The resulting second derivatives, including all mixed partial derivatives as well as derivatives involving material mass densities, are compared with analytic and PARTISN results for a homogeneous sphere and PARTISN results for a two-region sphere. Second derivatives computed using ray-tracing are within 0.003% of those computed using PARTISN and are over 100 times faster to compute for the spherical test problems.