Propagation of statistical and nuclear data uncertainties in Monte Carlo burn-up calculations

Two methodologies to propagate the uncertainties on the nuclide inventory in combined Monte Carlo-spectrum and burn-up calculations are presented, based on sensitivity/uncertainty and random sampling techniques (uncertainty Monte Carlo method). Both enable the assessment of the impact of uncertainties in the nuclear data as well as uncertainties due to the statistical nature of the Monte Carlo neutron transport calculation. The methodologies are implemented in our MCNP–ACAB system, which combines the neutron transport code MCNP-4C and the inventory code ACAB.     

Integral form of nuclide generation and depletion equations for Monte Carlo simulation. Application to perturbation calculations

The general integral form of the nuclide generation/depletion equation suitable for a resolution by the Monte Carlo method is presented. A formal analogy between particle transport and nuclide generation/depletion is shown. Moreover, the Monte Carlo formulation of the nuclide generation/depletion problem allows to do perturbation calculation by using the correlated sampling method.     

Monte Carlo calculations on high speed machines

1. 1. Monte Carlo Calculations by a Modified Vector Processor.At Japan Atomic Energy Research Institute, four Monte Carlo codes KENO-IV, MORSE-DD, and VIM and MCNP were vectorized to examine the adaptability of vector processors for these codes. The performances and vectorization rates of the vectorized versions were not good except KENO-IV on SX-2 vector processor, on which the vectorized version attained three times faster speed compared to its scalar version. According to the experience with the vectorization, some additional features specialized for Monte Carlo calculations will improve the vectorization rates of the four codes. Functions of the features and anticipated effects are presented.

2. 2. Speedup of Monte Carlo Criticality Calculation by a Parallel Processor.The authors implemented the Monte Carlo code KENO-IV on a parallel processor system Topology 1000 with three processing units under control of SUN workstation. The Hansen-Roach 16-group cross section set was used for the calculation. A computation for a bare sphere of highly enriched uranium metal showed that the system attained 2.7 times speedup compared to that of one processing unit.

     

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.     

Monte Carlo calculations on vector supercomputers using GMVP

A multigroup general purpose Monte Carlo code GMVP has been developed. The vectorization algorithm is based on a stack-driven zone selection method. GMVP can treat repeated rectangular and hexagonal lattices together with combinatorial geometry which is quite useful to achieve a high gain by vectorization. The performance of the code was evaluated by solving various types of problems. In addition, the continuous energy code is under development and the performance is compare with conventional codes. The code was installed on other four different supercomputers to investigate portability and computer dependence of code performance.     

Monte Carlo calculations of local reactivity perturbations

Institute of Nuclear Power, Academy of Sciences of the Belorussian SSR. Translated from Atomnaya Énergiya, Vol. 71, No. 3, pp. 195–199, September, 1991.     

Fission matrix based Monte Carlo criticality calculations

We have described a fission matrix based method that allows to cancel the inactive cycles in Monte Carlo criticality calculations. The fission matrix must be sampled in the course of the Monte Carlo calculation using a space mesh with sufficiently small zones as it causes the fission matrix be insensitive to errors in the initial fission source. The k_eff and other quantities can be derived by means of the final fission matrix. The confidence interval for the k_eff estimate can be conservatively determined via the variance in the fission matrix.     

The bias in Monte Carlo eigenvalue calculations

We study the Monte Carlo estimation of eigenvalues of the stationary transport equation by source iterations with a fixed sample size. The sample-size-dependent eigenvalue bias, characteristic of the simplistic application of this kind of calculation, is analyzed and explained, and ways to control it are suggested. A two-point reactor model, the analysis of which is very simple, is qualitatively discussed to introduce the subject. A mathematical analysis of the model follows, and is then generalized to the application of the Monte Carlo procedure to realistic neutronic assemblies. Finally, algorithms which remove the bias are considered, and their respective effectiveness discussed.     

Evaluation of the systematic error of Monte Carlo calculations of neutron-physical properties using a multiprocessor computer

Algorithms for evaluating the systematic error of Monte Carlo calculations performed using different variants of an approximate solution of a homogeneous neutron transport equation (the method of a constant number of points of division and augmentation, and others), when the number of neutrons per generation is reduced to a number set a priori, are described. A relation for evaluating this error on multiprocessor computers is proposed. The computational results obtained for the systematic error by means of the theoretical relation and experimentally for a full-scale three-dimensional model of a VVER-1000 core are presented. Recommendations for choosing the number of particles per generation which gives an acceptably low error are made.     

Efficiency and reliability of deep-penetration Monte Carlo calculations

With the help of model calculations the influence of various Monte Carlo techniques on efficiency and reliability of deep-penetration calculations is investigated. The application of these techniques is interpreted in the frame of the importance function method. Conclusions are drawn with respect to an automatic determination of optimal parameters during the calculation.     

Fast assessment of the error in the neutron distribution in a large reactor in Monte Carlo calculations

It is suggested that there is a close analogy between the statistical error of local characteristics in a Monte Carlo calculation of a large reactor and random deviations of the multiplication properties of these cells from a nominal value within technological tolerance limits. It is well-known that the latter result in global and strongly correlated deformations of the neutron field which are especially noticeable in large reactors. The scale of the deformations, or the statistical error, of the neutron field is determined by a formula obtained from an analysis of the influence of technological tolerances. Model Monte Carlo calculations confirm that this analogy is correct. __________ Translated from Atomnaya énergiya, Vol. 103, No. 2, pp. 115–119, August, 2007.     

Monte Carlo calculations of low energy electron backscatter coefficients

Experimental values of the electron backscatter coefficient, η, are compared with results obtained from a one-dimensional, multiple scattering Monte Carlo transport code, for normally incident electrons in the 3–100 keV range. For electron energies less than 10 keV the th     

Monte Carlo neutron-photon calculations applied to ignitor tokamak machine

Ignitor is an Italian designed compact Tokamak machine to demonstrate the ignition feasibility of D-T and D-D high density plasma.

Peculiar problems concerning shielding, activation and material damaging due to high energy neutron irradiation and complex geometry are faced.

The geometry including also toroidal configurations, the very severe requirements for personnel accessibility after operation and the insulation stringent characteristics pushed to perform a detailed analysis by MNCP Monte Carlo code.

The results are crucial in the determination of the choice and the size of the shielding materials and have a strong impact on the maximum admissible duration of the irradiation, i.e. of the whole experiment.     

Improvement on the two-phase-flow void fraction determination using Monte Carlo calculations

In this paper, a modified one-shot photon-attenuation method is presented for the determination of the average void fraction in a two-phase-flow system. The modification over the conventional one-shot method is established by a series of Monte Carlo Calculations. Through a benchmark test, it is validated that the accuracies of the void-fraction prediction can be significantly improved. The application of this new technique is demonstrated using a mixed air-water flow channel. Results show that, the improvement gained using this modified method is essential at low void fractions where the conventional one-shot method suffers high uncertainty. Another important correction made in this work is on the condition of the variation of void distribution with time. It is found that this correction can be significant when the void fractions in the flow channel are large.     

Use of the Monte Carlo method for multi-group reactor calculations

The article describes a multi-group method for two-dimensional reactor calculations in which the solution of the kinetic equation in the transport approximation is found for each group by the Monte Carlo method. The calculated results are in satisfactory agreement with the experimental data.Translated from Atomnaya Énergiya, Vol. 16, No. 2, pp. 119–122, February, 1964     

An efficient parallel computing scheme for Monte Carlo criticality calculations

The existing parallel computing schemes for Monte Carlo criticality calculations suffer from a low efficiency when applied on many processors. We suggest a new fission matrix based scheme for efficient parallel computing. The results are derived from the fission matrix that is combined from all parallel simulations. The scheme allows for a practically ideal parallel scaling as no communication among the parallel simulations is required, and inactive cycles are not needed.     

Microcomputer Monte Carlo electron transport codes for beta skindose calculations

The adaptation of a one-dimensional Monte Carlo election transport program (called ZEBRA) for use on microcomputers in a program called Eltran2 is described. The purpose of this adaptation was to reduce the cost of the Monte Carlo calculations. Eltran2 has, in turn, been modified into a two-dimensional program called Eltran3 for computing the dose from a point or a disk source to a cylindrical target. For Monte Carlo calculations, theoretical beta energy spectra are calculated based on the Fermi beta decay theory. The calculated average energies of spectra agree with the values in related publications to within 6%. An extended study has been done using Eltran2 and Eltran3 to facilitate the design of, a beta/gamma skin dose monitor. The programs calculate the effects of angular distribution of source electrons and the radial distribution of the hot particle dose. It is found that the hot particle dose averaged over a live skin area of 1 cm² significantly underestimates the real dose value at the very small area just under the hot particle by a factor of about 1000     

On multicriterial optimization in reactor problems using Monte Carlo calculations

A cylindrical water-uranium lattice depending on three parameters is optimized taking into consideration seven performance criteria.