Monte Carlo Perturbation Theory Research Articles

Research on the calculation method of sensitivity coefficients of reactor power to material density based on Monte Carlo perturbation theory

The ability to calculate the material density sensitivity coefficients of power with respect to the material density has broad application prospects for accelerating Monte Carlo-Thermal Hydraulics iterations. The second-order material density sensitivity coefficients for the general Monte Carlo score have been derived based on the differential operator sampling method in this paper, and the calculation of the sensitivity coefficients of cell power scores with respect to the material density has been realized in continuous-energy Monte Carlo code RMC. Based on the power-density sensitivity coefficients, the sensitivity coefficients of power scores to some other physical quantities, such as power-boron concentration coefficients and power-temperature coefficients considering only the thermal expansion, were subsequently calculated. The effectiveness of the proposed method is demonstrated in the power-density coefficients problems of the pressurized water reactor (PWR) moderator and the heat pipe reactor (HPR) reflectors. The calculations were carried out using RMC and the ENDF/B-VII.1 neutron nuclear data. It is shown that the calculated sensitivity coefficients can be used to predict the power scores accurately over a wide range of boron concentration of the PWR moderator and a wide range of temperature of HPR reflectors.

A new approach to the stabilization and convergence acceleration in coupled Monte Carlo–CFD calculations: The Newton method via Monte Carlo perturbation theory

Abstract This paper proposes the adoption of Monte Carlo perturbation theory to approximate the Jacobian matrix of coupled neutronics/thermal-hydraulics problems. The projected Jacobian is obtained from the eigenvalue decomposition of the fission matrix, and it is adopted to solve the coupled problem via the Newton method. This avoids numerical differentiations commonly adopted in Jacobian-free Newton–Krylov methods that tend to become expensive and inaccurate in the presence of Monte Carlo statistical errors in the residual. The proposed approach is presented and preliminarily demonstrated for a simple two-dimensional pressurized water reactor case study.

Excess energy and equation of state of fluids with hard-core potential models from a second-order Monte Carlo perturbation theory

Monte Carlo simulations in the NVT ensemble of the reference hard-sphere fluid have been performed to obtain the “exact” first- and second-order terms in the inverse temperature expansion of the free energy of fluids with hard-core potentials. The results have been used to obtain parametrizations of the free energy of fluids with Sutherland potentials with variable range as well as for a fluid with a hard-core Lennard–Jones potential. The results for the excess energy and the equation of state are compared with simulation data available in the literature for these fluids.

Tests of Monte Carlo perturbation theory for the free energy of liquid copper

Monte Carlo perturbation theory, in which terms in the thermodynamic perturbation series are evaluated by Monte Carlo averaging, has potentially large advantages in efficiency for calculating free energies of liquids from ab initio potential surfaces. In order to test the accuracy of perturbation theory for liquid metals, a series of calculations has been done on liquid copper, modeled by an embedded atom potential. A simple 1/r(12) pair potential is used as the reference system. The free energy is calculated to third order in perturbation theory, and the results are compared to an exact formula. It is found that for optimal reference potential parameters, second order perturbation theory is essentially exact. Second and third order theories give accurate results for significantly nonoptimal reference parameters. The relation between perturbation theory and reweighting is discussed, and an approximate formula is derived that shows an exponential dependence of the efficiency of reweighting on the second order free energy correction. Finally, techniques for application to ab initio potentials are discussed. It is shown that with samples of 100 configurations, it is possible to obtain accuracy and precision at the level of approximately 1 meV/atom.

Performance Evaluation of Third-Order Thermodynamic Perturbation Theory and Comparison with Existing Liquid State Theories

To evaluate the performance of a recently proposed third-order thermodynamic perturbation theory (TPT), we employ the third TPT for calculation of thermodynamic properties such as compressibility factor, internal energy, excess chemical potential, gas-liquid coexistence curve, and critical properties of several fluids. By comparing the third-order TPT results with corresponding simulation data available in literature and supplied in the present report and theoretical results from several other theoretical approaches, one concludes that the third-order TPT is, in general, more accurate than other approaches such as Barker-Henderson second-order TPT using a macroscopic compressibility approximation (MCA-TPT), self-consistent Ornstein-Zernike approach, Monte Carlo perturbation theory, and a specially devised equation of state. Specifically, the third-order TPT can predict quantitatively a double critical phenomena of gas-liquid transition and a low-density liquid (LDL)-high-density liquid (HDL) transition associated with a soft core (SC) potential fluid very satisfactorily, but the predictions for the LDL-HDL transition based on the second-order MCA-TPT are quantitatively very bad or qualitatively incorrect. The failure of the second-order MCA-TPT for the SC fluid can be ascribed to the facts that for the SC potential the second-order and third-order terms of the perturbation expansion are not small quantities and that the second-order term is underestimated by the MCA. It is concluded that the present third-order version of the TPT is reliable for varying model fluids.

Thermodynamic properties of van der Waals fluids from Monte Carlo simulations and perturbative Monte Carlo theory

Computer simulations have been performed for fluids with van der Waals potential, that is, hard spheres with attractive inverse power tails, to determine the equation of state and the excess energy. On the other hand, the first- and second-order perturbative contributions to the energy and the zero- and first-order perturbative contributions to the compressibility factor have been determined too from Monte Carlo simulations performed on the reference hard-sphere system. The aim was to test the reliability of this "exact" perturbation theory. It has been found that the results obtained from the Monte Carlo perturbation theory for these two thermodynamic properties agree well with the direct Monte Carlo simulations. Moreover, it has been found that results from the Barker-Henderson [J. Chem. Phys. 47, 2856 (1967)] perturbation theory are in good agreement with those from the exact perturbation theory.

Neutronic Sensitivity Analysis of the Experimental Test Reactor TIBER II Blanket Design

In this paper, the TIBER II blanket design is chosen for a neutronic sensitivity analysis using Monte Carlo perturbation theory. A preliminary analysis is carried out with both deterministic and Monte Carlo simulation codes to estimate the sensitivity of the tritium breeding in the blanket to the atomic density ratio of tungsten multiplier and aqueous solution breeder. Derivatives of the neutron collision density in the blanket are then sampled using the collision estimator in the MORSE code. It is found that for small perturbations, the neutron fluxes and tritium breeding rates can be predicted quite accurately, thus saving substantial computing in a preliminary design study.

Two-group Monte Carlo perturbation theory and applications in fixed-source problems

The collision estimator is used in a second-order derivative sampling scheme for fixed-source problems involving a perturbation in the material density. The analytical formulation of a one-group problem in a finite slab with forward scattering is demonstrated to obtain exact expressions for the collision density and its derivatives. The track length estimator is also used for comparisons in some cases. Results are presented for a two-group multi-region problem using the MORSE code. The predicted collision densities in zones close to the source are found to be in excellent agreement with those obtained in full ‘re-runs’.