Stability instability and Hopf bifurcation in fission waves

Edward Teller was the first to show that it would be possible for self-propagating fission waves to form in fertile nuclear materials. It is typically assumed that these waves would be asymptotically stable. However, we show here that coupling of the neutron field to the ²³⁹U->²³⁹Np->²³⁹Pu decay chain can lead to a Hopf bifurcation. The fission reaction then ramps up and down, along with the wave velocity. Time-dependent results are obtained using a numerical implementation of a reaction-diffusion model for a fast neutron field. A linear stability analysis of the underlying equations and the full system isotopics confirms the results and shows the parameter space over which the Hopf occurs.