Abstract 1 Modification of the Integral Kinetic Model for the Fast Burst Reactor with Subcr

(2) where indices “r” and “b” refer to reactor and subcritical block, respectively; Vr and Vb - volumes of reactor and block. Inserting (2) into (1) and integrating the equation for reactor, expression (1) can be written in the form of two integral equations
2
τ & & & & & P (r , τ ) = ∫ ∫ α (r , r ′, τ, τ′ )P (r ′, τ′ )dr ′dτ′ + 0V
& & s & & ∫ ∫ α (r , r ′, τ, τ′ )Q (r ′, τ′ )dr ′dτ′
0V
τ
(1) & & Here α (r , r ′, τ, τ ′ ) - distribution of the secondary fissions at the point with coordinate r and at time moment τ , provided that the first fission took place in the point with the space-time coordinates & & ( r ′ , τ′ ); α s (r , r ′, τ, τ′ ) - the analogous function for fissions which were originated by the external & & & & & source with intensity Q (r , τ ) . Thus, α (r , r ′, τ, τ′ ) and α s (r , r ′, τ, τ′ ) are the kernels of the integral equation (1). Let us consider the short-time neutron transient processes in the coupled system consisting of the compact fast burst reactor (with neutron lifetime ~ 10-8 – 10-6 s) and deep subcritical module (block) with thermal spectrum of neutrons (average lifetime is about 10-4 – 10-3 s). For simplicity we will & assume Q (r , τ ) = 0 and neglect of delayed neutrons. Let us designate & & & & & Pr (r , τ ) = N r (τ )ψ r (r ); r ∈ Vr ; ∫ ψ r (r )dr = 1; & Vr P (r , τ ) = & & & P (r , τ ) = N (r , τ ); r ∈ Vb ; b b & & α rr (r , r ′, τ, τ′ ), & & & & α rb (r , r ′, τ, τ′ ), α (r , r ′, τ, τ′ ) = & & α br (r , r ′, τ, τ′ ), & & α (r bb , r ′, τ, τ′ ), & r ∈ Vr ; & r ∈ Vr ; & r ∈ Vr ; & r ∈ Vr ; & r ′ ∈ Vb ; & r ′ ∈ Vb ; & r ′ ∈ Vb ; & r ′ ∈ Vb ;
(3) where
Proc. Intern. Conf. M&C’99-MadFra bibliotekid, 1999
© - 1999 Institute of Physics and Power Engineering, Technical Physics Laboratory http://www-tpl.ippe.rssi.ru E-mail: tpl@ippe.rssi.ru
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Modification of the Integral Kinetic Model for the Fast Burst Reactor with Subcritical Module
Andrey V. Gulevich, Oleg F.Kukharchuk and Alexander P.Barzilov State Scientific Center of the Russian Federation Institute for Physics & Power Engineering Obninsk (Russia) gulevich@ippe.rssi.ru; kuh@ippe.rssi.ru;barzilov@ippe.rssi.ru Abstract A modified integral kinetics model for coupled fast burst reactor and subcritical module has been developed. The model is based on the mathematical formalism of Green’s functions, which may be calculated effectively using the Monte-Carlo method. Neutron transfer in the Universal Critical Facility (Obninsk, IPPE) consisting central fast reactor and external subcritical module has been studied. Some experimental and calculational results are presented. 1 Introduction Coupled reactor systems have been widely used in reactor physics. In particular, systems including a coupled burst reactor with a subcritical module provide an opportunity of additional applications for traditional pulsed reactors (Snopkov, 1992). It is presumed that a similar facility, consisting of a fast burst reactor together with a thermal subcritical laser module, could be used to make the realization of inertial confinement fusion (Dyachenko, 1991). It is important to note that such system has to operate under conditions of high power prompt neutron pulses. Another important application of coupled reactors is that in acceleration-driven systems with fast and thermal blankets, proposed recently (Barzilov, 1995a, Batskikh, 1998). An important and challenging problem of advanced reactor physics and neutronics is theoretical and experimental investigation of fundamental processes of neutron transport, as well as the nuclear safety of systems mentioned above. The theory of coupled reactors was founded by R.Avery more than forty years ago (Avery, 1958). Several effective approaches to the coupled reactor kinetics simulation have been elaborated since (Bellini-Morante, 1966, Kolesov, 1975), including integral models (Poupko, 1989, Khoruzhy, 1989). Unfortunately the use of these models for simulation of space-time neutron kinetic processes in the system consisting of fast burst reactor and subcritical “thermal” block may require a lot of computer’s time. The aim of this paper is to modify the integral kinetic model (Poupko, 1989), so that it could be able to describe the non-stationary neutron transport in the coupled reactor systems and to verify it using the experimental data. 2 Integral kinetic neutron model & Space-time distribution of the fission density P (r , τ ) in the multiplicative neutron medium 9 may be described by using the integral transport equation (Gulevich, 1992)