Nonlinear Dynamics of the Nuclear Breeding Process

Abstract

The time evolution of the nuclear breeding process, modeled as a mixture of three different species of interacting particles (neutrons, fissile and fertile atoms, respectively) diffusing in a host medium, is studied by means of the set of nonlinear integro-partial differential Boltzmann equations governing the relevant distribution functions f₁, f₂, f₃. It is shown that the Boltzmann system for the f_j’s yields, under suitable assumptions, a system of conservation equations for the number densities ρ ₁, ρ ₂, ρ ₃, which are defined by just integrating the corresponding f_j over the velocity domain. The zero-dimensional approach, for which the conservation system is a nonlinear first-order ordinary differential system, is first studied on the basis of the theory of dynamical systems, with particular regard to the stability of the fixed points. Curves representing some numerical results for the phase trajectories are presented. The space-dependent problem is then sketched, for which the conservation system can be instead of fully hyperbolic type. Finally, properties and open problems related to this latter case are shortly discussed on both mathematical and physical ground.