Objective Function in the Problem of Optimal Laser-Assisted Separation of Isotopes by the Method of Selective Retardatio
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OBJECTIVE FUNCTION IN THE PROBLEM OF OPTIMAL LASER-ASSISTED SEPARATION OF ISOTOPES BY THE METHOD OF SELECTIVE RETARDATION OF CONDENSATION K. A. Lyakhov and A. N. Pechen’
UDC 51-74
Abstract. A design of an industrial concentration plant based on the method of selective retardation of condensation in an external laser field was earlier proposed. In this paper, we review recent results on optimization criteria (objective functions) proposed for the search for optimal parameters of this scheme, related to the geometry and operational characteristics of the plant. As constraints in the optimization problem, we consider the influence of the condensation rate and the resonance and nonresonance absorption in a separation cell on its geometry. Separating cells play the role of absorbers in laser resonators. Keywords and phrases: optimal control, boron isotopes, dynamics of supercooled and rarefied gas flow. AMS Subject Classification: 49K99
1. Introduction. The problem of obtaining tons of boron-10 isotopes is quite acute in nuclear power engineering. This is due to the fact that this isotope possesses many attractive properties associated with its large cross-section of absorption of thermal and fast neutrons. Although other competitors, for example, gadolinium and cadmium, have much greater cross-sections, they have a wider spectrum of resonance absorption and a harder gamma radiation in the transmutation process. Isotopically pure boron is also used in the semiconductor industry and nuclear medicine, but its high cost hinders the development of these uses. The aim of this work is to highlight the authors’ recent results related to the mathematical statement of the problem on optimal separation of boron isotopes by the method of selective inhibition of condensation in supercooled gas jets by means of laser radiation (see [1, 2]). The attractiveness of this method, in addition to the relatively low energy consumption (compared with the other currently used methods—centrifugation and chemical exchange), is its high productivity due to higher selectivity, universality (it is suitable for separation of both light and heavy isotopes provided that the pressure of the saturated vapor of the substance is sufficiently large at room temperature), and compactness (and hence it is less capital-intensive). 2. Operational principles. At the initial stage of extraction of target isotopes from the natural mixture, BCl3 is diluted with a gas carrier having good aerodynamic properties (for example, argon) to the molar fraction, which, on one hand, should be sufficiently large to provide an acceptable extraction rate, and on the other hand, sufficiently small to minimize the resonance loss of excitation in the collision of various isotopes) in a mixing tank, where the gas is maintained at room temperature and a certain preset pressure. Then the gas expands from it through a slotted nozzle into a separation cell, where it is irradiated by a repeatedly reflected laser beam, so that for a small angle of deviation from the perpendicular direction,
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