The bias in Monte Carlo calculations of the neutron-physical characteristics of full-scale models of reactors and storage sites for nuclear fuel is investigated. The bias is shown to arise directly from the nature of the Monte Carlo solution of the eigenvalue problem and estimates of similar bias without loss of generality are proposed.As computers become more powerful, the Monte Carlo method is used more and more for calculating full-scale models of storage sites for spent nuclear fuel and of nuclear-reactor cores. This is increasing interest in understanding the specific features of the Monte Carlo solution of the homogeneous stationary neutron-transport equation.In Monte Carlo modeling, the solution and all its linear functionals are determined to within a factor, and therefore ratios of the functionals, i.e., linear-fractional functionals, are meaningful. When such functionals are calculated, biases arise in their estimates and not their values.The questions studied in the present paper have been attracting the attention of many specialists (see, for example, [1-7]). A set of model problems has been developed to check the proposed algorithms (for example, [8]).The most important result in this field is an asymptotic formula for determining the bias of the estimate of k eff , which is valid for large values of the number of neutrons in a generation. The formula makes it possible to estimate efficiently the systematic error in k eff in practical calculations, though it has been derived only for a method of simulation with a constant number of neutrons in a generation, a finite-dimensional model of a reactor, and the simplest analog estimate of k eff from the number of neutrons produced in the fissioning of a nucleus.The question of whether or not the systematic errors in the reaction rates calculated by the methods of generations can be estimated and the range of application of the formulas for the bias of the estimates of k eff can be expanded has thus far remained open. In the present paper, without loss of generality, general and asymptotic formulas for determining the bias of any estimates of any reaction rates calculated by simulation according to generations are obtained for real neutron-multiplication systems. It is important that all proposed proofs are technically simple and give a clear picture of the mechanism leading to the appearance of biases and the possibilities for estimating them.Formulation of the Problem. The problem is to calculate by the method of generations the main intrinsic value of k eff and the normalized reaction rates of neutrons, determined for the main eigenfunction Ψ(x) of the equation for the generation density of fission neutrons in a conditionally critical reactor. This equation can be written in operator form as follows:(1)

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In 1972In -1990, under the auspices of the Time International Collective, an extensive program of investigations was carried out on the physics of uranium-water VVl~R-type lattices [I-3]. Specialists from ten countries participated in these investigations. Experiments were carried out on the critical ZR-6 assembly at the TslFI (Budapest). About 300 different configurations of the active zone were investigated. One of the main purposes of the program was to obtain reliable experimental data to verify the library of constants and programs for designing VV~R reactors.Over a period of many years, experimental data [1, 2] have been used to verify the precision and engineering programs of neutron-physical calculations on VVI~ER reactors. However, in earlier publications [1, 2], only a two-dimensional model of the assembly was described, the accuracy of which gave rise to some doubts. Hence, the results of a verification of the constants and programs based on the two-dimensional model of the assembly did not always look convincing. In 1995-1996 a reappraisal of the experiments was made [1, 2], and, in particular, a detailed three-dimensional model was set up. Under the auspices of the International Criticality Safety Benchmark Evaluation Project (ICSBEP), the reappraisal experiments obtained the status of a benchmark. The three-dimensional model and the refined results of the experiments were published in [4]. A new estimate of the experiments, including a three-dimensional description of the assembly, considerably increased the value of the previously published experimental information. This enables the reliability of the verification of the library of constants and the programs based on it to be improved.The mathematical modeling of the experiments using precision programs and esttmated nuclear data is an inseparable part of the expertise provided by the ICSBEP in confering on it the status of benchmark experiments. It enables the quality and correctness of the descriptions of the experiments and the reliability of the estimate of their accuracy to be verified.The purpose of this paper is to describe the precision modeling of experiments on the ZR-6 assembly based on mathematical models [4]. The Monte Carlo method, using the MCU-RFFI/A program [5, 6] with the DLC/MCUDAT-2.1 library of constants, was used to calculate 150 different configurations of the active zone. All the measured parameters of the configurations investigated, including the criticality, the reactivity coefficients, the distribution of the rates of the reactions etc. were calculated. This became possible after producing an electronic atlas with a description of the two-dimensional (2D) and three-dimensional (3D) models, and also the results of experiments. The atlas enables the computation process to be automated. The paper only includes some of the results obtained: a brief description of the atlas and the criticality parameters calculated for the 2D and 3D models [4].A Brief Review of the Physical Experiments. The ZR-6 assembly was a cylindrical ...

Nuclear power plants are promising power sources for the development of space [1]. The stringent restrictions imposed on the size and mass of space reactors by the launching system have made it necessary to develop small heterogeneous thermionic converter reactors in which the thermionic converters are built into the core. For space, two types of reactors with the minimum dimensions are under consideration: reactors with a fast and intermediate neutron spectrum using zirconium hydride as the moderator. In the last few years the possibility has been considered of launching from the territory of the USA a Russian "Topaz-2" space nuclear power plant with a thermionic reactor having single-element power-generating channels [2], taking into consideration the safety requirements adopted in the USA [3].The "Topaz-2" reactor is a heterogeneous epithermal reactor loaded with highly enriched uranium dioxide fuel. The reactor is cooled with a sodium-potassium alloy. Zirconium hydride is the moderator. The core, which contains 37 singleelement power-generating channels, is surrounded by a radial beryllium reflector with 12 rotating regulating drums with absorbing segments. End reflectors are located at the top and bottom.Neutron-physical calculations of the "Topaz-2" reactor are difficult to perform for the following reasons: its small size, its complicated heterogeneous structure, the highly enriched fuel, the power-generating channels which are built into the core and have molybdenum and tungsten electrodes, the zirconium hydride moderator, the rotating regulating drums in the side reflector, the complicated neutron energy spectrum, the high neutron leakage, and the increase of reactivity occurring when the reactor is accidentally submerged in water. Because of its complexity, such a reactor is calculated by the Monte Carlo method. Two Monte Carlo programs have been used in the USA and Russia for neutron-physical calculations: the MCNP program of the Los Alamos National Laboratory (LANL) [4] and the MCU-2 program of the Russian Scientific Center "Kurchatovskii Institut" [5].Our objective in the present work is to test the programs and nuclear-data libraries that are employed in computational investigations of the neutron-physical characteristics of the "Topaz-2" reactor, including accident situations associated with submersion in water.The MCU-2 system includes a program for Monte Carlo calculations of the reactor and libraries of constants which contain data for the thermal energy range, taking into account the chemical bonds of atoms, the crystalline structure of the neutron moderator, the resonance parameters of nuclides in the region of allowed resonances, and a 26-group system of constants. The program has a modular structure and contains physical and geometric modules as well as control and source modules. The physical module models neutron collisions in the fast and resonance energy regions as well as in the thermal energy range (in the thermalization region). A universal geometric module, based on the method of com...

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