The BURNUP package of applied programs used for computing the isotopic composition of materials of an operating nuclear
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BURNUP Package of Applied Programs Used for Computing the Isotopic Composition of Materials of an Operating Nuclear Reactor M. S. Yudkevich* National Research Centre Kurchatov Institute, pl. Kurchatova 1, Moscow, 123182 Russia Received March 14, 2011
Abstract—This paper described the procedure of implementation and the possibilities of the BURNUP program. The purpose of the program is to predict the change in the nuclear composition of the materials of which a reactor is made in the course of its run and compute the radiation characteristics of the materials after their irradiation. Keywords: reactor, composition of materials, burnup, radiation characteristics. DOI: 10.1134/S1063778812140116
INTRODUCTION In presentday programs intended for computing neutronphysics characteristics of power and research reactors, uranium burnup, plutonium production, and formation of fission products are taken into account. In MCU programs [1], the burnup module performs this function, and as this module, the programs of the BURNUP package are used. The BURNUP package consists of several pro grams. The function of one of them, STEP, is to pre dict the change in the isotopic composition of the fuel, elements of the reactor control and protection system, other materials of the reactor in the course of its run. The DELAY program makes it possible to calculate activation of structural components, accumulation of radionuclides, sources of delayed gamma radiation and neutron radiation, and other radiation character istics of a shutdown reactor. The goal of this published work is to provide infor mation on the capabilities of the package. At the same time, the algorithms implemented and organization of the operation of the programs contained in this pack age as a module being a part of the reactorrelated pro gram are described. 1. TRANSMUTATION OF NUCLEI IN A NEUTRON FIELD The nuclide composition of a material irradiated with neutrons varies with time. This takes place as a result of various reactions of neutrons with nuclei and decay of radioactive nuclei being formed. Let us consider a neutron multiplying system (hereinafter referred to as a reactor) that consists of several zones with different compositions. In some of * Email: [email protected]
these zones, fissionable nuclides are contained. It is required to determine the composition of a reactor some time T later under the known dependence of power on time P(t). Let us give index numbers i to nuclides which either initially were in the reactor or appeared in the course of its operation, and denote their concentration as Ci—content per unit volume. At each time instant, the law of conservation of the number of nuclides can be written as a system of differential equations ⎧d C i = – ( λ i + σ i Φ ) + ( λ ji + σ ji Φ ) C j ; ⎪ dt ⎪ j ⎨ ⎪ λ ij ; σ i = σ ij , ⎪ λi = ⎩ j j
∑
∑
(1)
∑
∫
where Φ = A f ( E ) dE is the neutron flux; f(E) is its energy spectrum; A is the normalization factor that is proportional to the reactor power; σji =
∫
[ σ ji ( E )f ( E ) dE ]/
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