Abstract
AbstractWe 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 2a 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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