(U) SENSMG: First-Order Sensitivities of Neutron Reaction Rates, Reaction-Rate Ratios, Leakage, k_eff, α, and Subcritical Multiplication Using PARTISN

Abstract

SENSMG is a tool for computing first-order sensitivities of neutron reaction rates, reaction-rate ratios, leakage, keff, α, and subcritical multiplication using the PARTISN multigroup discrete-ordinates code. 1 SENSMG computes sensitivities to all of the transport cross sections and data (total, fission, a nu, chi, and all scattering moments), four edit cross sections (absorption, capture, elastic scattering, and inelastic scattering), and the density for every isotope and energy group. It also computes sensitivities to the mass density for every material and derivatives with respect to all interface locations and outer boundaries. The tool can be used for one-dimensional spherical and slab (r) and two-dimensional cylindrical (r-z) geometries. The tool can be used for fixed-source and eigenvalue problems. For most responses, the tool implements Generalized Perturbation Theory (GPT) as discussed by Williams 2 and Stacey. 3 The tool is thus limited to computing sensitivities only for GPT-allowable responses. 4 For subcritical multiplication, the tool implements sensitivities derived by O'Brien 5 and Clark. 6 SENSMG has a similar role as the old SWANLAKE (Ref. 7), FORSS (Ref. 8), and SENSIT (Ref. 9) codes. It has capabilities similar to those of SUSD3D (Ref. 10), which also uses PARTISN. Section II of this report describes the theory behind adjoint-based sensitivities, gives the equations that SENSMG solves, and defines the sensitivities that are output. Section III describes the user interface, including the input file and command line options. Section IV describes the output. Section V gives some notes about the coding that may be of interest. Section VI presents some sample problems and discusses verification, which is ongoing. Section VII lists needs and ideas for future work. Appendix A lists most of the input files whose results are presented in Sec. VI. Appendix B provides some useful details on one of the cross-section libraries that SENSMG supports. a Technically, fission is an edit cross section in PARTISN because only the product with nu is used in the transport.

(U) Radiation Transport Sensitivity Capabilities Applicable to INRAD

“…15 Second-and higher-order uncertainty quantification is possible 15 and in fact desirable, because second-order contributions may be larger than one suspects. 16 For deterministic multigroup neutron problems, SENSMG can compute first-order 5,6 and secondorder sensitivities of a neutron response (but not keff) in a one-dimensional sphere or a two-dimensional cylinder (but not a stand-off point response) with respect to a cross section. [16][17][18][19] Cross sections for deterministic gamma-ray calculations are not generally appropriate for INRAD, so PARTISN and SENSMG would not generally be applied.…”

“…3 SENSMG can compute first-order sensitivities of keff with respect to a cross section in a one-dimensional sphere or a two-dimensional cylinder. 5,6 MCNP6 has a feature that would be very useful to determine the effect of changing cross-section libraries on keff, the KPERT card, but it has a bug that prevents its use. 23 SENSMG outputs the sensitivity of any response to each nuclide's Legendre scattering moment, 6 so it is easy to determine the relative importance of the scattering moments.…”

“…5,6 MCNP6 has a feature that would be very useful to determine the effect of changing cross-section libraries on keff, the KPERT card, but it has a bug that prevents its use. 23 SENSMG outputs the sensitivity of any response to each nuclide's Legendre scattering moment, 6 so it is easy to determine the relative importance of the scattering moments. MCNP6 doesn't usually deal in scattering moments, but the KSEN card has some capability for this for keff sensitivities.…”

“…SENSMG can compute the derivative of a response with respect to material interface locations in spheres and cylinders for multigroup neutron fixed-source and keff problems. 5,6 The derivatives describe the change in the response as the interface moves in a direction parallel to its surface normal. 34,35 MCNP had a preliminary capability for computing the keff sensitivity to system dimensions, 36 but there are no plans to put that capability into production.…”

“…The PARTISN multigroup discrete ordinates code 4 has a well-developed associated sensitivity capability, the SENSMG code. 5,6 There are two drawbacks of using PARTISN and SENSMG: 1) SENSMG is limited to onedimensional spherical and two-dimensional cylindrical geometries; and 2) in the case of twodimensional cylinders, the discrete-ordinates angular treatment cannot be used for stand-off detectors. Nevertheless, the comprehensive sensitivity capabilities of these codes may make them very suitable for INRAD applications, and they are discussed in this report.…”