Analytical calculation of the fuel temperature reactivity coefficient for pebble bed and prismatic high temperature reactors for plutonium and uranium–thorium fuels

We analytically evaluated the fuel coefficient of temperature both for pebble bed and prismatic high temperature reactors when they utilize as fuel plutonium and minor actinides from light water reactors spent fuel or a mixture of 50% uranium, enriched 20% in ²³⁵U, and 50% thorium. In both cores the calculation involves the evaluation of the resonances integrals of the high absorbers fuel nuclides ²⁴⁰Pu, ²³⁸U and ²³²Th and it requires the esteem of the Dancoff–Ginsburg factor for a pebble bed or prismatic core. The Dancoff–Ginsburg factor represents the only discriminating parameter in the results for the two different reactors types; in fact, both the pebble bed and the prismatic reactors share the same the pseudo-cross-section describing an infinite medium made of graphite filled by TRISO particles. We considered only the resolved resonances with a statistical spin factor equal to one and we took into account 267, 72, 212 resonances in the range 1.057–5692, 6.674–14485, 21.78–3472 eV for ²⁴⁰Pu, ²³⁸U and ²³²Th, respectively, for investigating the influence on the fuel temperature reactivity coefficient of the variation of the TRISO kernel radius and TRISO particles packing fraction from 100, 200 to 300 μm and from 10% to 50%, respectively. Finally, in the pebble bed core, we varied the radius of the pebble for setting a fuel temperature reactivity coefficient similar to the one of a prismatic core.