Monte Carlo Perturbation Methods Research Articles

Monte Carlo perturbation method for optimum surface geometry due to sloshing motion

For the nuclear criticality safety of a fuel solution, it is important to identify the maximum positive reactivity induced by the upper surface sloshing motion. Deterministic methods for obtaining optimum surface geometry have been previously developed. This study proposes a Monte Carlo perturbation method for this purpose. Surface importance (SI) is defined as a small reactivity added by an upward lifting of a point on the upper surface. The reactivity is obtained using the correlated sampling method. The optimum geometry is attained by iteratively changing the surface geometry such that the SI distribution is eventually flattened throughout the upper surface. Examples of optimum surface geometries are presented for the bare and water-reflected fuel solutions.

Source Nuclide Density First-Order and Second-Order Sensitivities in Monte Carlo Codes

Application of perturbation capabilities for density sensitivities in Monte Carlo radiation transport codes has been limited because changing source nuclide densities or source material densities changes the intrinsic source, and in most Monte Carlo codes, the user-input source is independent of the user-input materials. The perturbation capability then has no way of accounting for changes in the intrinsic source. This paper derives the sensitivity of a response with respect to a source nuclide density in terms of a portion due to the transport operator and a portion due to the source rate density. The Monte Carlo perturbation method computes the portion due to the transport operator, and the portion due to the source rate density is computed in postprocessing using parameters from the precomputed intrinsic source calculation. This paper derives first- and second-order sensitivities. The equations require the response to be separated by contribution from each of the sources modeled. A test problem containing several (α,n) and spontaneous fission neutron sources verifies the method.

Criticality evaluation considering nonuniformity effect using Monte Carlo perturbation method

ABSTRACT The objective of this study is to evaluate nonuniformity effect relevant to criticality safety evaluation by means of the flattened principle of fuel importance distribution. We proposed a novel approach using an MVP3.0 perturbation function with JENDL-4.0 and then built a tool to calculate the nonuniformity effect. The tool estimated an optimum fuel distribution that corresponding to the highest multiplication factor in a homogeneity model of UO2–H2O slurry. Consequently, nonuniformity effects specified by the reactivity of a multiplication factor were as much as 0.5 to 5.6%dk/k. Further, preliminary evaluations of heterogeneity effects on optimum fuel distributions were computed using statistical geometry model incorporated in MVP3.0 and then heterogeneity effects observed in optimum fuel distributions also reached 2.3%dk/k at the maximum in multiplication factor. Thus, the effects of both nonuniformity and heterogeneity should be properly taken into account in criticality evaluations.

Temperature perturbation method using on-the-fly treatment of the cross-sections in the resolved resonance region

A negative fuel temperature reactivity coefficient is an important reactor physical parameter that indicates the inherent reactor operating safety. However, existing Monte Carlo perturbation methods still cannot accurately and efficiently predict the derivative of the k-eigenvalue with respect to temperature. The main difficulty lies in calculating the derivatives of the microscopic cross-section with respect to the temperature. This paper presents a Temperature Perturbation Method (TPM) that incorporates on-the-fly cross-section treatment as well as the free gas model into the differential operator method to calculate derivatives of the k-eigenvalue with respect to fuel temperature. TPM was then used to predict the k-eigenvalue at various temperatures for the Mosteller pin model. The differences between TPM and the direct difference method are less than 3% within 3 times of standard deviation. The results indicate that TPM can accurately and efficiently estimate the derivatives of the k-eigenvalue with respect to the fuel temperature.

Exact Monte Carlo calculation method for K-eigenvalue change using perturbation source method

ABSTRACT The ‘perturbation source method’ (PSM) is a Monte Carlo perturbation method that calculates an exact k-eigenvalue change caused by cross-section changes. Although the PSM, which can consider the effect of fission source perturbation, was proposed long ago, it has garnered minimal interest as a Monte Carlo perturbation method. The applicability of the PSM has not been thoroughly elucidated hitherto. This study revisits the PSM and reviews the associated Monte Carlo algorithm. Some improvements have been made to improve the efficiency. The PSM is applied to some numerical tests that involve the replacement of a fuel material with light water, a density change in a water hole, an interface shift between a fuel and reflector, and an external boundary extension. The performance of the PSM for these tests is compared with that of another exact Monte Carlo perturbation method, which is the correlated sampling method. The PSM can yield an accurate k-eigenvalue change even for large cross-section changes such as the replacement of a material with another material. The PSM used in this study is the exact method except for the approximation related to the spatial discretization for fission source perturbation. Furthermore, it exhibits superiority in terms of accuracy and computational efficiency, particularly for large perturbations added in a small region.

Monte Carlo perturbation methods using “virtual density” theory for calculating reactivity due to geometry change

The “virtual density” theory in the field of neutronics is a method to quantify reactivity of a reactor core due to geometry changes by altering the material density or nuclear cross section instead of explicitly changing the geometry. The Monte Carlo perturbation methods—differential-operator sampling (DOS) and correlated sampling (CS)—can efficiently yield accurate small reactivity for cross section changes. However, Monte Carlo perturbation methods have weakness in their inability to deal with geometry changes. This study incorporates the virtual-density theory into the Monte Carlo perturbation methods. When an entire core expands or swells uniformly, keff of the perturbed core can be calculated by simply changing the material density without changing the geometry. Regarding uniform expansion or swelling, conventional Monte Carlo perturbation methods—where cross sections change proportionally to the material density—can predict the altered keff. According to the virtual-density theory, keff perturbed due to a uniform anisotropic expansion or swelling can be predicted by stretching or shrinking the mean free path of neutrons in only one direction without changing the geometry. A new Monte Carlo algorithm is developed to incorporate the path length-stretching or -shrinking in only one direction into a random-walk process in a Monte Carlo keff-eigenvalue calculation. The new Monte Carlo algorithm provides accurate keff values for uniform anisotropic expansion and swelling regardless of the perturbation degree. New formulations of the Monte Carlo perturbation methods are derived to predict the change in keff due to a uniform anisotropic expansion or swelling. Both Monte Carlo perturbation methods can accurately and efficiently predict changes in keff for a small uniform anisotropic expansion or swelling.

Improvement and performance evaluation of the perturbation source method for an exact Monte Carlo perturbation calculation in fixed source problems

This paper presents improvement and performance evaluation of the “perturbation source method”, which is one of the Monte Carlo perturbation techniques. The formerly proposed perturbation source method was first-order accurate, although it is known that the method can be easily extended to an exact perturbation method. A transport equation for calculating an exact flux difference caused by a perturbation is solved. A perturbation particle representing a flux difference is explicitly transported in the perturbed system, instead of in the unperturbed system. The source term of the transport equation is defined by the unperturbed flux and the cross section (or optical parameter) changes. The unperturbed flux is provided by an “on-the-fly” technique during the course of the ordinary fixed source calculation for the unperturbed system. A set of perturbation particle is started at the collision point in the perturbed region and tracked until death. For a perturbation in a smaller portion of the whole domain, the efficiency of the perturbation source method can be improved by using a virtual scattering coefficient or cross section in the perturbed region, forcing collisions. Performance is evaluated by comparing the proposed method to other Monte Carlo perturbation methods. Numerical tests performed for a particle transport in a two-dimensional geometry reveal that the perturbation source method is less effective than the correlated sampling method for a perturbation in a larger portion of the whole domain. However, for a perturbation in a smaller portion, the perturbation source method outperforms the correlated sampling method. The efficiency depends strongly on the adjustment of the new virtual scattering coefficient or cross section.

Improved Monte Carlo-perturbation method for estimation of control rod worths in a research reactor

A hybrid method dedicated to improve the experimental technique for estimation of control rod worths in a research reactor is presented. The method uses a combination of Monte Carlo technique and perturbation theory. Perturbation method is used to obtain the equation for the relative efficiency of control rod insertion. A series of coefficients, describing the axial absorption profile are used to correct the equation for a composite rod, having a complicated burn-up irradiation history. These coefficients have to be determined – by experiment or by using some theoretical/numerical method. In the present paper they are derived from the macroscopic absorption cross-sections, obtained from detailed Monte Carlo calculations by MCNPX 2.6.F of the axial burn-up profile during control rod life. The method is validated on measurements of control rod worths at the BR2 reactor. Comparison with direct MCNPX evaluations of control rod worths is also presented.

Efficiency of Monte Carlo perturbation calculations

Using the Monte Carlo method for the solution of particle transport problems, statistical difficulties usually arise in the calculation of small effects caused by small modifications of the system properties. For sufficiently small perturbations, the use of special perturbation techniques is the only practicable way to estimate the effects with reasonable expense. Two Monte Carlo perturbation methods are briefly described and the efficiency is tested for a realistic example. It is shown that the computational efficiency can be increased by perturbation methods.

Free energy of solids and dense liquids by the Monte Carlo perturbation method.

We propose that the free energy of solids and dense liquids can be calculated by combining perturbation theory with direct evaluation of free-energy difference by Monte Carlo sampling. The method provides a novel, convenient, and direct approach to the free energy of both solids and liquids without using thermodynamic integration or upper-bound approximations. Monte Carlo perturbation results for model two-dimensional systems are shown to be in very good agreement with free energy obtained by standard techniques.