(U) Analytic First and Second Derivatives of the Uncollided Leakage for a Homogeneous Sphere
Los Alamos National Lab. (LANL), Los Alamos, NM (United States), Jeffrey Favorite, USDOE Assistant Secretary for Human Resources and Administration · 2017
The second-order adjoint sensitivity analysis methodology (2nd-ASAM), developed by Cacuci, has been applied by Cacuci to derive second derivatives of a response with respect to input parameters for uncollided particles in an inhomogeneous transport problem. In this memo, we present an analytic benchmark for verifying the derivatives of the 2nd-ASAM. The problem is a homogeneous sphere, and the response is the uncollided total leakage. This memo does not repeat the formulas given in Ref. 2. We are preparing a journal article that will include the derivation of Ref. 2 and the benchmark of this memo.