Time eigenvalues emerge in several key applications related to neutron transport problems, including reactor start-up and reactivity measurements. In this context, experimental validation and uncertainty quantification would demand to assess the variation of the dominant time eigenvalue in response to a variation of nuclear data. Recently, we proposed the use of a Generalized Iterated Fission Probability method (G-IFP) to compute adjoint-weighted tallies, such as kinetic parameters, perturbations and sensitivity coefficients, for Monte Carlo time (or alpha) eigenvalue calculations. With the massive use of parallel Monte Carlo calculations, it would be therefore useful to trade the memory burden of the G-IFP method (which is comparable to that of the standard IFP method for k-eigenvalue problems) for computation time and to rely on history-based schemes for such adjoint-weighted tallies. For this purpose, we investigate the use of the super-history method as applied to estimating adjoint-weighted tallies within the α-k power iteration, based on previous work on k-eigenvalue problems. Verification of the algorithms is performed on some simple preliminary tests where analytic solutions exist. In addition, the performances of the proposed method are assessed by comparing the super-history and the G-IFP methods for the same sets of benchmark problems.
A chebyshev polynomial method for optimal control with state constraints
