Analysis of Doppler-Limited Power Excursions in a Water-Moderated Oxide Core

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Abstract
A calculational model for the Doppler reactivity feedback in a thermal, low-enrichment oxide core with non-uniform temperature distribution is derived on the basis of the UO2 resonance integral varying as the square root of the absolute temperature. An analytical solution of the prompt-approximation, space-independent neutron kinetic equation, with the Doppler feedback written as a function of the fission energy, is obtained and application made to the self-limiting power-excursion tests conducted in the SPERT I oxide core. Comparison of the experimental and calculated Doppler effects, peak powers, burst energies and burst shapes is made for various published values of the UO2 resonance integral temperature coefficient, which acts as a scaling factor in the calculations. The values used cover a spread of about 20% of the mean value, and excellent agreement with experiment is obtained for the smallest values of the coefficient. Systematic agreement is obtained between the calculated and experimental Doppler effects over the entire experimental range of adiabatic fuel-temperature rises attained in the short-period SPERT tests. This agreement implies the validity of a square-root temperature dependence for the Doppler effect in a thermal oxide core, in contrast with a logarithmic or a T1/2 dependence, for which similar calculations give results which differ significantly from the experimental data.

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