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[en] This report presents a study comparing deterministic lattice physics calculations with Monte Carlo calculations for LWR fuel pin and assembly problems. The study has focused on comparing results from the lattice physics code CASMO-3 and HELIOS against those from the continuous-energy Monte Carlo code McCARD. The comparisons include kinf, isotopic number densities, and pin power distributions. The CASMO-3 and HELIOS calculations for the kinf's of the LWR fuel pin problems show good agreement with McCARD within 956pcm and 658pcm, respectively. For the assembly problems with Gadolinia burnable poison rods, the largest difference between the kinf's is 1463pcm with CASMO-3 and 1141pcm with HELIOS. RMS errors for the pin power distributions of CASMO-3 and HELIOS are within 1.3% and 1.5%, respectively
[en] Beeler's simulation of radiation damage annealing, KMC has been widely applied for analyses of material irradiation, gas surface interactions, statistical physics, etc. In the KMC simulations, the accuracy of numerical result depends on the reliability of transition data. The sensitivity analyses are useful to enhance the accuracy by ordering the transition data by importance and quantify the uncertainty of the KMC output and The Monte Carlo (MC) perturbation methods such as the differential operator sampling (DOS) and the correlated sampling have been successfully applied for the sensitivity calculations in the MC particle transport analyses. In this paper, I derive the Neumann series formulation corresponding to the KMC solution and then the DOS formulations for the KMC perturbation calculations. The effectiveness of the developed formulations is investigated for the Langmuir ian adsorption dynamics problem. I have derived the mathematical formulation which governs the KMC simulations. Based on the derived Neumann series solution, I have developed the KMC perturbation method which can efficiently and accurately estimate the changes of design parameters due to the transition data changes. The developed KMC perturbation method can be applied for the sensitivity and uncertainty analyses for various KMC simulations
[en] In the Monte Carlo (MC) eigenvalue calculations, the higher order eigenvalues and eigenfunctions can be useful to evaluate nuclear criticality safety, accelerate the fission source convergence and estimate the real variance. There have been several studies to obtain the higher order eigenfunctions in the MC power iteration method. Booth proposed a modified power iteration method that simultaneously determines the dominant and subdominant eigenvalues and eigenfunctions. Zhang et al. proposed a general solution strategy which extends Booth's modified power iteration method, and it is applied to continuous energy Monte Carlo simulation. The objective of this paper is to present a MC deflation algorithm without the source weight cancellation by scoring deflation responses in the fundamental mode eigenvalue calculation. In this study, the MC deflation method without source weight cancellation for the first order eigenfunction calculation is developed and verified by the onedimensional two-group problem, which shows good agreement with the reference solution from fission matrix method. In the method, source weight cancellation which is necessary for the previous studies is not needed by tallying deflation response in the fundamental mode eigenvalue calculation.
[en] Nowadays the accelerator-driven subcritical system (ADS) has been widely studied as a candidate of transmutation reactor. Applications of the conventional point kinetics equation (PKE) using the k-adjoint weighted kinetics parameters can be invalid for the time-dependent ADS analysis because it assumes that the reference system is critical. In this paper, we propose a new PKE with kinetics parameters weighted by the α-adjoint flux, solution to the adjoint α-mode eigenvalue equation, because the α- mode eigenvalue equation can accurately represent an off-critical system. In addition, algorithms to calculate the α-adjoint weighted kinetics parameters in the Monte Carlo (MC) α iteration method are presented and tested in an infinite homogeneous 2-group problem. A new point kinetic equation using the α-adjoint weighted kinetics parameters is derived by making the best of a fact that the subcritical system can be accurately represented by the α-mode eigenvalue equation, rather than the k-mode eigenvalue equation.
[en] In this paper, a conventional method to control the neutron population for super-critical systems is implemented. Instead of considering the cycles, the simulation is divided in time intervals. At the end of each time interval, neutron population control is applied on the banked neutrons. Randomly selected neutrons are discarded, until the size of neutron population matches the initial neutron histories at the beginning of time simulation. A time-dependent simulation mode has also been implemented in the development version of SERPENT 2 Monte Carlo code. In this mode, sequential population control mechanism has been proposed for modeling of prompt super-critical systems. A Monte Carlo method has been properly used in TART code for dynamic criticality calculations. For super-critical systems, the neutron population is allowed to grow over a period of time. The neutron population is uniformly combed to return it to the neutron population started with at the beginning of time boundary. In this study, conventional time-dependent Monte Carlo (TDMC) algorithm is implemented. There is an exponential growth of neutron population in estimation of neutron density tally for super-critical systems and the number of neutrons being tracked exceed the memory of the computer. In order to control this exponential growth at the end of each time boundary, a conventional time cut-off controlling population strategy is included in TDMC. A scale factor is introduced to tally the desired neutron density at the end of each time boundary. The main purpose of this paper is the quantification of uncertainty propagation in neutron densities at the end of each time boundary for super-critical systems. This uncertainty is caused by the uncertainty resulting from the introduction of scale factor. The effectiveness of TDMC is examined for one-group infinite homogeneous problem (the rod model) and two-group infinite homogeneous problem. The desired neutron density is tallied by the introduction of scale factor. The uncertainty propagated in neutron density resulting from the uncertainty in scale factor at the end of each time interval can be calculated
[en] In order to eliminate this huge memory consumption in the current adjoint estimation method, we have developed a new method in which the pedigree of a single history is utilized by applying the MC Wielandt method. The Wielandt method allows the estimations of the adjoint flux and adjoint-weighted parameters within a single cycle neutron simulations. The effectiveness of the new method is demonstrated in the kinetics parameter estimations for an infinite homogeneous two-group problem and the Godiva facility. We have developed an efficient algorithm for the adjoint-weighted kinetics parameter estimation in the MC Wielandt calculations which can significantly reduce the memory usage. From the numerical applications, it is demonstrated that the new method can predict the kinetics parameters with great accuracy
[en] In the Monte Carlo (MC) eigenvalue calculations, the sample variance of a tally mean calculated from its cycle-wise estimates is biased because of the inter-cycle correlations of the fission source distribution (FSD). Recently, we proposed a new real variance estimation method named the history-based batch method in which a MC run is treated as multiple runs with small number of histories per cycle to generate independent tally estimates. In this paper, the history-based batch method based on the weight correction is presented to preserve the tally mean from the original MC run. The effectiveness of the new method is examined for the weakly coupled fissile array problem as a function of the dominance ratio and the batch size, in comparison with other schemes available
[en] The effective delayed neutron fraction, βeff, and the prompt neutron generation time, Λ, in the point kinetics equation are weighted by the adjoint flux to improve the accuracy of the reactivity estimate. Recently the Monte Carlo (MC) kinetics parameter estimation methods by using the self-consistent adjoint flux calculated in the MC forward simulations have been developed and successfully applied for the research reactor analyses. However these adjoint estimation methods based on the cycle-by-cycle genealogical table require a huge memory size to store the pedigree hierarchy. In this paper, we present a new adjoint estimation in which the pedigree of a single history is utilized by applying the MC Wielandt method. The effectiveness of the new method is demonstrated in the kinetics parameter estimations for infinite homogeneous two-group problems and the Godiva critical facility
[en] Since the early 1990’s, accelerator-driven subcritical systems (ADSs) have been proposed and tested throughout the world by its merits of the high flexibility in nuclear fuel cycles as well as the unique safety concept. It is well known that the spatial distribution and energy spectrum of neutron flux calculated from the k-mode eigenvalue equation can be significantly different from those for a highly subcritical system with an external source. One of the related subjects is the point kinetics analysis for the initially subcritical system with kinetics parameters weighted by an adequate adjoint function. In this paper, we develop Monte Carlo (MC) algorithms to estimate the kinetics parameters of the point kinetics equation (PKE) based on the inhomogeneous adjoint equation in the MC fixed source calculations. The developed method is verified in an infinite homogeneous two-group problem by comparing its numerical results with analytic solutions. We have developed a MC method to calculate the kinetics parameters in the PKE for ADS, which requires the adjoint estimation in the MC fixed source calculations. The MC algorithms are derived based on the physical meaning of the adjoint function which is the solution to the inhomogeneous adjoint equation. The validity of the proposed method is demonstrated through a simple two-group problem by showing that the MC results agree very well with the analytic solutions.
[en] Nowadays the accelerator-driven subcritical system (ADS) has been widely studied as a candidate of transmutation reactor. In order to enhance the accuracy of the point kinetics analysis for an ADS, Nishihara et al. proposed a PKE using kinetics parameters weighted by Green’s function. In our previous research, we proposed a PKE formulation with kinetics parameters weighted by the α-adjoint flux, the fundamental mode solution to the adjoint α-mode eigenvalue equation, because the α-mode eigenvalue equation can accurately represent an off-critical system. In this paper, the physical meaning of the α-adjoint flux is derived by applying the power iteration method for the α-mode eigenvalue equation. Using this physical meaning, algorithms to calculate the α-adjoint weighted kinetics parameters in the Monte Carlo (MC) α iteration method are developed and tested in an infinite homogeneous 2-group problem and the KUCA Th-ADS experimental benchmark. The physical meaning of the α-adjoint is explained.