Abstract
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.
Highlights
Several key applications in reactor physics, encompassing reactor period measurements in nearly critical configurations, reactor noise analysis techniques such as the Rossi alpha or Feynman alpha in steady-state configurations, or material control and accountability in critical assemblies, require the assessment of the asymptotic evolution of the neutron population [1, 2]
To the standard Iterated Fission Probability (IFP) in k-eigenvalue calculations, the major drawback of the Generalized Iterated Fission Probability (G-IFP) implementation in time-eigenvalue problems is the strong increase in memory footprint
A good agreement with respect to analytical solutions is found. These findings show that the super-history method is unbiased for direct time-eigenvalue calculations
Summary
Several key applications in reactor physics, encompassing reactor period measurements in nearly critical configurations, reactor noise analysis techniques such as the Rossi alpha or Feynman alpha in steady-state configurations, or material control and accountability in critical assemblies, require the assessment of the asymptotic evolution of the neutron population [1, 2] This is usually achieved by determining the dominant time (or α) eigenvalue associated to the Boltzmann operator for the problem under analysis [1]. Experimental validation, uncertainty quantification and bias estimation through data assimilation may further require computing the perturbation and sensitivity coefficients of the dominant α eigenvalue with respect to nuclear data This topic has recently drawn attention both in deterministic [3, 4] and Monte Carlo methods [5, 6]. The proposed algorithms will be tested for timeeigenvalue sensitivity coefficients and compared to the G-IFP method
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
