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reactor kinetics; integral transport equation; Monte Carlo method
In this paper, the linear problem of reactor kinetics with delayed neutrons is studied whose formulation is based on the integral transport equation. Besides the proof of existence and uniqueness of the solution, a special random process and random variables for numerical elaboration of the problem by Monte Carlo method are presented. It is proved that these variables give an unbiased estimate of the solution and that their expectations and variances are finite.
[1] J. Mika, D. Obradovič, R. Stankiewicz: Spectral properties of a multigroup transport operator with delayed neutrons in plane geometry. Bulletin of the Boris Kidrič Institute of Nuclear Sciences 19 (1968).
[2] S. V. Shikhov: Problems of mathematical theory of reactors. Atomizdat, Moscow, 1973. (Russian)
[3] J. Kyncl: On Cauchy problem for the equations of reactor kinetics. Aplikace matematiky 34 (1989), 197–212. MR 0996896
[4] M. B. Emmett: The MORSE Monte Carlo Radiation Transport Code System. ORNL – 4972 (1975); also ORNL – 4972 – R1 (1983) and ORNL – 4972 – R2 (1984).
[5] M. Borysiewicz, J. Mika: Time behaviour of thermal neutrons in moderating media. J. Math. Anal. Appl 26 (1969), 461–478. DOI 10.1016/0022-247X(69)90193-0
[6] M. M. R. Williams: The slowing down and thermalization of neutrons. North-Holland publishing company, Amsterdam, 1966.
[7] A. Weinberg and E. Winger: The Physical Theory of Neutron Chain Reactors. Chicago, 1958. MR 0113336
[8] G. V. Gnedenko: The theory of probability. Nauka, Moscow, 1973.
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