Approach to mathematical simulation of transmutational processes in nuclear power plants

Background. At the present time the study and simulation of nuclear kinetics or nuclide transformations in the process neutron irradiation in power reactor facilities are especially topical for solution of the problem of nuclear fuel cycle abridgement to provide profitability of nuclear power. The purpose of this article consists in describing and investigating essentially new mathematical models in simulation of nuclear-physical processes in reactor materials irradiation. Materials and methods. The initial model of the problem is similar to a linear system of the ordinary differential equations. Relations of nuclide reciprocity and accumulation on a nuclide set of nuclide strong-coherent subsets were entered. With the help of relations a transition from the initial continuous model to a discrete model was made. The discrete model describes nuclear kinetics as an oriented multigraph. The authors averaged the estimation of neutron-physical characteristics of reactor irradiation by means of averaging a stream at certain micro-campaigns in the process of power reactor facility functioning. Results. The problem of discrete optimization of the nuclide transformations was formulated in terms of the graph theory. The discrete problem is original in the discrete optimization theory. The problem concerns a class of NP-difficult problems. The authors author a method of averaging the estimation of neutron-physical characteristics of reactor irradiations for the period of several micro-campaigns in the problem of nuclear transmutations. Conclusions. The priority direction of modernization and technological development of the Russian economy consists in development of nuclear technologies, namely in realization of the closed fuel cycle with mixed fuel in fast power reactors. The considered model of calculation of nuclide transformations into materials at reactor irradiation can be successfully used for mathematical modelling of nuclear-physical processes with accumulation and burning out actinides in a fast reactor core.