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Theoretical Analysis of Coupled-Core Reactors with the Method of the Moderator Region Response Function

Minoru Shinkawa, Yoshihiro Yamane, Kojiro Nishina, Hajime Tamagawa

Nuclear Science and Engineering

Volume 67 / Number 1 / July 1978 / Pages 19-33


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One-dimensional, one-energy-group diffusion theory is applied to a coupled-core slab reactor to derive kinetic equations for the system, with different modes of formulation taken for moderator regions and for core regions. For the former, the diffusion equation is exactly solved to obtain the time-dependent neutron currents from moderator to core (the moderator response function) in response to the neutron incident current in the form of a unit impulse on the boundary. For the core regions, the neutron flux ψ(x,t) is written as a product of a shape function, (x,t), and a time function, P(t), as suggested by Henry, with P(t) chosen to represent the time variation of total importance over the respective core. The boundary terms that arise in the equations for P(t) are combined with incoming neutron currents at the boundaries, which in turn are expressed in terms of the moderator region response functions above. The equations for P(t) derived by such procedures include the coupling effect between the two cores, without a need for the conventional, a priori assumption of coupling coefficient. For the Argonaut two-slab core, the transfer functions are obtained and compared with existing values. The value of the conventional coupling coefficient is also inferred by reducing the present form of coupling terms by approximation. From the approximation needed in the procedure, the limitation of the coupling coefficient approach is discussed.

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