[en] Perturbation theory is a technique used for the estimation of changes in performance functionals, such as linear reaction rate ratio and eigenvalue affected by small variations in reactor core compositions. Here the algorithm of perturbation theory is developed for the multigroup integral neutron transport problems in 2D fuel assemblies with isotropic scattering. The integral transport equation is used in the perturbative formulation because it represents the interconnecting neutronic systems of the lattice assemblies via the tracking lines. When the integral neutron transport equation is used in the formulation, one needs to solve the resulting integral transport equations for the flux importance and generalized flux importance functions. The relationship between the generalized flux importance and generalized source importance functions is defined in order to transform the generalized flux importance transport equations into the integro-differential equations for the generalized adjoints. Next we develop the adjoint and generalized adjoint transport solution algorithms based on the method of cyclic characteristics (MOCC) in DRAGON code. In the MOCC method, the adjoint characteristics equations associated with a cyclic tracking line are formulated in such a way that a closed form for the adjoint angular function can be obtained. The MOCC method then requires only one cycle of scanning over the cyclic tracking lines in each spatial iteration. We also show that the source importance function by CP method is mathematically equivalent to the adjoint function by MOCC method. In order to speed up the MOCC solution algorithm, a group-reduction and group-splitting techniques based on the structure of the adjoint scattering matrix are implemented. A combined forward flux/adjoint function iteration scheme, based on the group-splitting technique and the common use of a large number of variables storing tracking-line data and exponential values, is proposed to reduce the computing time when both direct and adjoint solutions are required. A problem that arises for the generalized adjoint problem is that the direct use of the negative external generalized adjoint sources in the adjoint solution algorithm results in negative generalized adjoint functions. A coupled flux biasing/decontamination scheme is applied to make the generalized adjoint functions positive using the adjoint functions in such a way that it can be used for the multigroup rebalance technique. Next we consider the application of the perturbation theory to the reactor problems. Since the coolant void reactivity (CVR) is a important factor in reactor safety analysis, we have decided to select this parameter for optimization studies. We consider the optimization and adjoint sensitivity techniques for the adjustments of CVR at beginning of burnup cycle (BOC) and k_eff at end of burnup cycle (EOC) for a 2D Advanced CANDU Reactor (ACR) lattice. The sensitivity coefficients are evaluated using the perturbation theory based on the integral transport equations. Three sets of parameters for CVR-BOC and k_eff-EOC adjustments are studied: (1) Dysprosium density in the central pin with Uranium enrichment in the outer fuel rings, (2) Dysprosium density and Uranium enrichment both in the central pin, and (3) the same parameters as in the first case but the objective is to obtain a negative checkerboard CVR at beginning of cycle (CBCVR-BOC). To approximate the sensitivity coefficient at EOC, we perform constant-power burnup/depletion calculations for 600 full power days (FPD) using a slightly perturbed nuclear library and the unperturbed neutron fluxes to estimate the variation of nuclide densities at EOC. Sensitivity analyses of CVR and eigenvalue are included in the study. In addition the optimization and adjoint sensitivity techniques are applied to the CBCVR-BOC and k_eff-EOC adjustment of the ACR lattices with Gadolinium in the central pin. Finally we apply these techniques to the CVR-BOC, CVR-EOC and k_eff-EOC adjustment of a CANDU lattice of which the burnup period is extended from 300 to 450 FPDs. The cases with the central pin containing either Dysprosium or Gadolinium in the natural Uranium are considered in our study.

[en] A major challenge for future Fast Reactors could be the recycling of minor actinides (MA) in the core fuel, in order to minimize wastes and contribute to meet both the sustainability objective and the reduction of the burden on a geological disposal. Although the most outstanding issues will be found in the development and validation of the appropriate fuels, the presence of MA in the core can potentially deteriorate the core reactivity coefficients. In the present paper we will show however that there is no physical limit to the amount of MA in the core fuel, but that a careful physics analysis can indicate the most appropriate measures to reduce the MA impact on the reactivity coefficients, and in particular, for Na cooled reactors, on the Na void reactivity coefficient.

[en] It is widely accepted that the current status of neutronics calculations for fast reactor design is such that present uncertainties on nuclear data should still be significantly reduced, in order to get full benefit from advances in modeling and simulation. Only a parallel effort in advanced simulation, in high accuracy validation experiments and in nuclear data improvement will provide designers with more general and well validated calculation tools to meet tight design target accuracies to further improve safety and economics. The present paper presents very recent results related to nuclear data uncertainty impact assessment, as a new step in the frame of an international activity, sponsored by OECD-NEA.

[en] A target accuracy assessment using new available covariance data, the AFCI 1.2 covariance data, has been carried out. At the same time, the more theoretical issue of taking into account correlation terms in target accuracy assessment studies has been deeply investigated. The impact of correlation terms is very significant in target accuracy assessment evaluation and can produce very stringent requirements on nuclear data. For this type of study a broader energy group structure should be used, in order to smooth out requirements and provide better feedback information to evaluators and cross section measurement experts. The main difference in results between using BOLNA or AFCI 1.2 covariance data are related to minor actinides, minor Pu isotopes, structural materials (in particular Fe56), and coolant isotopes (Na23) accuracy requirements.

[en] The adjoint transport solution algorithm based on the method of cyclic characteristics (MOCC) is developed for the heterogeneous 2-dimensional geometries. The adjoint characteristics equation associated with a cyclic tracking line is formulated, then a closed form for adjoint angular flux can be determined. The acceleration techniques are implemented using the group-reduction and group-splitting techniques. To demonstrate the efficacy of the algorithm, the calculations are performed on the 17*17 PWR and Watanabe-Maynard benchmark problems. Comparisons of adjoint flux and k_eff results obtained by MOCC and collision probability (CP) methods are performed. The mathematical relationship between pseudo-adjoint flux obtained by CP method and adjoint flux by MOCC method is presented. It appears that the pseudo-adjoint flux by CP method is equivalent to the adjoint flux by MOCC method and that the MOCC method requires lower computing time than the CP method for a single adjoint flux calculation

[en] The adjoint transport solution algorithm based on the method of cyclic characteristics (MOCC) is developed for the heterogeneous 2D geometries. The adjoint characteristics equation associated with a cyclic tracking line is formulated, then a closed form for adjoint angular flux can be determined. The acceleration techniques are implemented using the group-reduction and group-splitting techniques. To demonstrate the efficacy of the algorithm, the calculations are performed on the 37 pin CANDU cell and on the Watanabe-Maynard benchmark problem. Comparisons of adjoint flux and k_eff results obtained by MOCC and collision probability (CP) methods are performed. The mathematical relationship between pseudo-adjoint flux obtained by CP method and adjoint flux by MOCC method is presented. (author)

[en] A target accuracy assessment using new available covariance data, the AFCI 1.2 covariance data, has been carried out. At the same time, the more theoretical issue of taking into account correlation terms in target accuracy assessment studies has been deeply investigated. The impact of correlation terms is very significant in target accuracy assessment evaluation and can produce very stringent requirements on nuclear data. For this type of study a broader energy group structure should be used, in order to smooth out requirements and provide better feedback information to evaluators and cross section measurement experts. The main difference in results between using BOLNA or AFCI 1.2 covariance data are related to minor actinides, minor Pu isotopes, structural materials (in particular Fe56), and coolant isotopes (Na23) accuracy requirements.

[en] This paper describes a comparative study of two Uncertainty Quantification (UQ) techniques for reactor neutronics analysis. Adjoint- and sampling-based uncertainty quantification approaches are applied to a simplified model of a sodium-cooled fast reactor to evaluate uncertainty in four integral parameters (void reactivity, Doppler reactivity, K_eff, and control rod reactivity). Results obtained with the two UQ methodologies are compared and discussed. This preliminary work, performed in a well-studied field like neutronics, will inform sensitivity and uncertainty method selection for future calculations in other disciplines like coupled neutronics/thermo-hydraulics. (authors)

[en] A GPT algorithm for estimation of eigenvalues and reaction-rate ratios is developed for the neutron transport problems in 2D fuel assemblies with isotropic scattering. In our study the GPT formulation is based on the integral transport equations. The mathematical relationship between the generalized flux importance and generalized source importance functions is applied to transform the generalized flux importance transport equations into the integro-differential forms. The resulting adjoint and generalized adjoint transport equations are then solved using the method of cyclic characteristics (MOCC). Because of the presence of negative adjoint sources, a biasing/decontamination scheme is applied to make the generalized adjoint functions positive in such a way that it can be used for the multigroup re-balance technique. To demonstrate the efficiency of the algorithms, perturbative calculations are performed on a 17 x 17 PWR lattice. (authors)

[en] The Working Party on Evaluation Cooperation (WPEC) of the OECD Nuclear Energy Agency Nuclear Science Committee established a Subgroup to develop a systematic approach to define data needs for advanced reactor systems and to make a comprehensive study of such needs for Generation- IV (Gen-IV) reactors. The subgroup has been established at the end of 2005, and a final report has been published in 2008. A comprehensive sensitivity and uncertainty study has been performed to evaluate the impact of neutron cross-section uncertainty on the most significant integral parameters related to the core and fuel cycle of a wide range of innovative systems, even beyond the Gen-IV range of systems. In particular, results have been obtained for the Advanced Breeder Test Reactor (ABTR), the Sodium-cooled Fast Reactor (SFR), the European Fast Reactor (EFR), the Gas-cooled Fast Reactor (GFR) and the Lead-cooled Fast Reactor (LFR), the Accelerator Driven Minor Actinide Burner (ADMAB). These systems correspond to current studies within the Generation-IV initiative, the Advanced Fuel Cycle Initiative (AFCI), and the advanced fuel cycle and Partitioning/Transmutation studies in Japan and Europe. State-of-the-art sensitivity and uncertainty methods have been used and they will be shortly described in the full paper. The integral parameter uncertainties have been calculated at first using covariance data developed in a joint effort of several laboratories contributing to the Subgroup activity. This set of covariance matrices is referred to as BOLNA. The discussion in the present paper is mostly focused on integral parameter (like keff, reactivity coefficients, power distributions etc) uncertainty due to neutron cross-section uncertainties. Fission spectrum uncertainties and the effect of resonance parameter uncertainty on Doppler have been also examined. The integral parameters considered are both related to the reactor core performances but also to some important fuel cycle-related parameters, like the transmutation potential, the doses in a waste repository or the neutron source at fuel fabrication