Interaction of neutronics and acoustics in a gaseous core nuclear rocket

Acoustic wave propagation in a gaseous core nuclear rocket is investigated by a theoretical model. Slab geometry in a long initially uniform cavity is assumed for simplicity and the reflector-heat sink is taken to be of infinite thickness. Blackness theory is used to determine the transmission of thermal neutrons (and thereby the generation of heat) in the fissionable gas of the cavity. Mutual feedback between neutron dynamics and gas dynamics occurs by means of the density-dependence of the blackness coefficients. Numerical results indicate that neutronic feedback can be a significant influence toward stabilization of acoustic oscillations. The critical wave length (which is twice the critical core length) without neutronic feedback is calculated to be 100 cm while critical wave lengths of 150 and 232 cm were obtained for carbon and beryllium reflectors, respectively. These results show that the critical core lengths are still comparable to or shorter than typical reference core lengths (300 cm). Thus, while neutronic feedback has an effect on acoustic instability, the effect is not strong enough to alter the general conclusion that acoustic instability is a potential problem area for gaseous reactor development.