Stability region for a prompt power variation of a coupled-core system with positive prompt feedback

A stability analysis using a one-group model is presented for a coupled-core system. Positive prompt feedback of a γp /SUB j/ form is assumed, where p /SUB j/ is the fractional power variation of core j. Prompt power variations over a range of a few milliseconds after a disturbance are analyzed. The analysis combines Lapunov's method, prompt jump approximation, and the eigenfunction expansion of coupling region response flux. The last is treated as a pseudo-delayed neutron precursor. An asymptotic stability region is found for p /SUB j/. For an asymmetric flux variation over a system of two coupled cores, either p /SUB I/ or p /SUB II/ can slightly exceed, by virtue of the coupling effect, the critical value (β/γ-1) of a single-core case. Such a stability region is increased by additional inclusion of the coupling region fundamental mode in the treatment. The coupling region contributes to stability through its delayed response and coupling. An optimum core separation distance for stability is found