A Numerical Solution of the Time-Dependent Neutron Transport Equation Using the Characteristic Method. Applications to ICF and to Hybrid Fission-Fusion Systems

Abstract: In this work we present a solution of the one-dimensional spherical symmetric time-dependent neutron transport equation (written for a moving system in lagrangian coordinates) by using the characteristic method. One of the objectives is to overcome the negative flux problem that arises when the system is very opaque and the angular neutron flux can become negative when it is extrapolated in spatial meshes --- as, for example, in diamond scheme adopted in many codes. Although there are recipes to overcome this problem, it can completely degrade the numerical solution if repeated many times. The solution presented here can be easily coupled to radiation-hydrodynamics equations, but it is necessary an additional term to maintain neutron conservation in a moving system in lagrangian coordinates. Energy multigroup method and a former SN method to deal with the angular variable are used, with the assumption of isotropic scattering and the transport cross sections approximation. An artifice is employed for emulating the neutron upscattering when neutron energy is lower than the temperature of the medium. The consistency of the numerical solution is checked by making at each time-step the balance of neutrons in the system. Two examples of applications are shown using a neutronic-radiation-hydrodynamic code to which the solution here presented was incorporated: one consists of a heterogeneous pellet of DT (deuterium-tritium) tamped by an highly-enriched uranium or plutonium (a symbiotic fusion-fission system); and the other is a very complex and also a symbiotic fission-fusion-fission system composed by layers of the thermonuclear fuels LiDT, LiD and a highly-supercritical fission fuel. The last is considered an extreme case for testing the time-dependent neutron transport solution presented here.