The article describes a set of studies for estimating and substantiating the limit mass of graphite removed during the resource characteristic management of RBMK reactors. The limit mass is understood as the maximum mass of graphite that can be removed from the reactor core at the stages of resource characteristic management without violating the operational limits of neutron-physical characteristics during the operation of power units over a period of 45 years. The substantiation of the limit mass was made based on the detailed computational simulation of reactor operation for realistic operational scenarios of the third and fourth power units of the Leningrad NPP. Particular attention is paid to the change in the void coefficient for the predicted states of reactors. The uncertainty of the limit mass of removed graphite is analyzed. The trueness of the calculated predictive estimates of neutron-physical characteristics and the limit mass of removed graphite is confirmed by the measurement results. It is shown that, by taking into account the considered operational scenarios for the reactors of the third and fourth power units of the Leningrad NPP, nuclear safety is ensured.

Uncertainty of predictive calculations of the neutronic characteristics of the RBMK-1000 reactor due to the lack of information about the cutting scheme to be used in the repair of graphite masonry is assessed. The main schemes of the repair of graphite masonry are considered.

The paper describes a qualitatively new CNET library of few-group neutron cross sections designed to simulate neutronic parameters in RBMK-1000 reactors. The CNET library makes use of a neural network to approximate cell (node) constants registered with a large group of full-scale calculations of various reactor states. We explore problems faced when approximating neutron cross sections using machine learning techniques and, specifically, neural networks. An approach is described to solve these problems following JSC VNIIAES guidelines to develop a new CNET library. The results of validating the MNT-CUDA high-accuracy program featuring the CNET library are presented.

An approach is proposed to expand the range of operational neutronic problems to be solved through combining various models of neutron transport (multigroup with detailed geometry description and two-group with a homogeneous description) in separate parts of the design area. The approach is deployed in the high-precision engineering program MNT-CUDA (version 2.0), capable of full-scale reactor engineering calculations using the Monte Carlo group method with an option of detailed description of neutron transport over the entire system or inside specific areas. The algorithm proposed uses GPU parallel computing. New features of the program are demonstrated. The results of studying the accuracy of combined calculations are presented and analyzed.

Statistical errors in sampling neutron fields in physically large systems like an RBMK are analyzed both qualitatively and quantitatively. Recommendations concerning the choice of parameters for calculations are given. A new procedure for Monte Carlo RBMK calculations with model corrections on the basis of data from in-core detectors is proposed. Dedicated software based on the CUDA software and hardware platform is developed for computational research. Results of testing the procedure and software in question via calculations for real RBMK reactors are discussed.

The considered inverse problems deal with the calculation of the unknown values of nuclear installations by means of the known (goal) functionals of neutron/{gamma}-ray distributions. The example of these problems might be the calculation of the automatic control rods position as function of neutron sensors reading, or the calculation of experimentally-corrected values of cross-sections, isotopes concentration, fuel enrichment via the measured functional. The authors have developed the new method to solve inverse problem. It finds flux density as quasi-solution of the particles conservation linear system adjointed to equalities for functionals. The method is more effective compared to the one based on the classical perturbation theory. It is suitable for vectorization and it can be used successfully in optimization codes.

There is uncertainty with experimental data as well as with input data of theoretical calculations. The neutron distribution from the variational principle, which takes into account both theoretical and experimental data, is obtained to increase the accuracy and speed of neutronic calculations. The neutron imbalance in mesh cells and the discrepancy between experimentally measured and calculated functionals of the neutron distribution are simultaneously minimized. A fast-working and simple-programming iteration method is developed to minimize the objective functional. The method can be used in the core monitoring and control system for (a) power distribution calculations, (b) in- and ex-core detector calibration, (c) macro-cross sections or isotope distribution correction by experimental data, and (d) core and detector diagnostics.