Conclusion
The above examples confirm the validity of the analysis of optimal operating conditions for producing certain nuclides-fission products-in the framework of the maximum principle and also confirm the validity of the resulting conclusions concerning the form of the optimal mode. When fission products without burnup are produced, the nonclassical modes are optimal: they consist of alternating phases of minimum and maximum control. When neutron capture takes place in the intermediate links, classical control may appear in the optimal mode.
It was shown that the concept of direct and inverse optimization can be successfully used. When this concept is used, one can consider in place of one optimization problem another one which in some cases is more conveniently solved with the aid of computational methods and optimization programs.
The results are important for practice because they make it possible to determine correlations between the burnup of nuclear fuel and the production of fission products.
Similar content being viewed by others
Literature Cited
A. P. Rudik, The Optimization of the Physical Characteristics of Nuclear Reactors [in Russian], Atomizdat, Moscow (1979).
A. I. Volovik, A. S. Gerasimov, and V. P. Glushakov, A Numerical Scheme of Optimizing the Production of Fission Products in a Nuclear Reactor, Preprint ITEF-128 of the Institute of Theoretical and Experimental Physics [in Russian] (1981).
A. I. Volovik, A. S. Gerasimov, and V. P. Glushakov, “Dependence of the Production of90Sr,137Cs,144Ce, and147Pm upon the Neutron Spectrum of the Reactor,” Problems of Atomic Science and Engineering, Series Physics and Engineering of Nuclear Reactors [in Russian], No. 5(27), p. 58 (1982).
I. A. Krylov and F. L. Chernous'ko, “The Algorithm of the Method of Successive Approximations in Problems of Optimal Control,” Zh. Vychisl. Mat. Mat. Fiz.,12 No. 1, 14 (1972).
L. S. Pontryagin, V. G. Boltyanskii, R. M. Gamkrelidze, and E. F. Mishchenko, Mathematical Theory of Optimal Processes [in Russian], Fizmatgiz, Moscow (1965).
Additional information
Institute of Theoretical and Experimental Physics. Moscow Engineering Physics Institute. Translated from Atomnaya Énergiya, Vol. 70, No. 5, pp. 322–326, May, 1991.
Rights and permissions
About this article
Cite this article
Gerasimov, A.S., Rudik, A.P., Glebov, V.B. et al. Optimal operating conditions for the production of some fission products in nuclear reactors. At Energy 70, 395–399 (1991). https://doi.org/10.1007/BF01124513
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01124513