Under the right conditions, self sustaining fission waves can form in fertile nuclear materials. These waves result from the transport and absorption of neutrons and the resulting production of fissile and fissionable isotopes. When these fission, additional neutrons are produced and the chain reaction propagates until it is poisoned by the buildup of fission products. Fission waves are a form of breed-burn reaction and it is typically assumed that they are soliton-like and self stabilizing in the absence of thermal feedback and unstable when it is present. However, we show that the situation is more complicated. In uranium, coupling of the neutron field to the 239U->239Np->239Pu decay chain can lead to a Hopf bifurcation without thermal feedback. The fission reaction then ramps up and down, along with the wave velocity. The critical driver for the instability is a delay, caused by the half-life of 239U, between the time evolution of the neutron field and the production of 239Pu. This allows the 239Pu to accumulate and burn out in a self limiting oscillation that is characteristic of a Hopf bifurcation. In the presence of thermal feedback, the hardness of the neutron spectrum dictates whether the fission wave is stable, unstable, or will undergo a Hopf bifurcation. Time dependent results are obtained using a numerical implementation of a reduced order reaction-diffusion model for a fast neutron field. Monte Carlo simulations in combination with a linear stability analysis are used to confirm the results for the full system and to establish the parameter space where the Hopf occurs.
Andrew Osborne obtained his Ph.D in high energy physics from the University of Glasgow in Scotland working on optimization methods for track identification in particle detectors. After his Ph.D studies, he worked as an analyst for the JP Morgan Chase investment bank in Glasgow and New York City where he developed software for risk management of credit derivatives under complex market scenarios. He returned to academia as a postdoctoral researcher at the University of Texas at Austin, where he worked on the application of high performance computing to the design and analysis of advanced nuclear reactors. Andy began his appointment as an assistant professor at the Colorado School of Mines in January 2018. His research interests are high performance computing for reactor multiphysics, numerical methods and software engineering.