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The kinetics equations in a multiplying medium with free boundaries

✍ Scribed by A. Belleni-Morante; G. Lauro

Publisher: John Wiley and Sons
Year: 1990
Tongue: English
Weight: 400 KB
Volume: 13
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.1670130307

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✦ Synopsis

Abstract

We study a mathematical model of neutron multiplication in a slab 𝒮, by taking into account temperature feedback effects and considering one group of delayed neutrons. The thickness 2__a__ of 𝒮 is time dependent because of temperature variations due to the energy released by fissions.

Starting from a quite detailed picture of the physical phenomena occurring in 𝒮, we derive a system of three coupled ordinary differential equations for the total number of neutrons F̂ = F̂(t), for the total number of precursors Ĉ = Ĉ(t), and for the half‐thickness of 𝒮, a = a(t).

We finally examine some stability properties of such a system of ordinary differential equations.

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