Stability instability and Hopf bifurcation in fission waves

Abstract

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 239 U-> 239 Np-> 239 Pu 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. Isotopic feedback causes stability, instability, or Hopf bifurcation in fission waves Fission waves can be unconditionally stable against thermal perturbations Edward Teller was the first to show that it would be possible for self-propagating fission waves to form in fertile nuclear materials. Osborne and Deinert show here that coupling of the neutron field to the 239 U-> 239 Np-> 239 Pu decay chain can lead to waves that are stable, unstable, or that undergo a Hopf bifurcation with an oscillatory limit cycle.