Transport Corrections and Sensitivities in the Discrete-Ordinates Method

Methods for approximately accounting for the terms neglected in a finite (L’th-order) Legendre expansion of the scattering source in the transport equation are called transport corrections. This paper derives adjoint-based sensitivities of a neutron or gamma-ray transport response for problems that use diagonal, Bell-Hansen-Sandmeier (BHS), or n’th-Cesàro-mean-of-order-2 (Cesàro) transport corrections in the discrete-ordinates method. For diagonal and BHS transport corrections, there is a sensitivity to the L + 1ʹth scattering cross-section moment, and the sensitivity to nuclide and material densities requires this contribution. For the Cesàro transport correction, the sensitivities to the scattering cross section for the l’th moment are multiplied by a simple function of l and the scattering expansion order L. Numerical results for a k_eff problem and a fixed-source problem verify the derivation and implementation of the sensitivity equations into the SENSMG multigroup sensitivity code. The Cesàro transport correction yields inaccurate responses for both problems.