### Asymptotic Diffusion Theory for Efficient Full-Core Simulations of Nuclear Reactors

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Travis Trahan, University of Michigan
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Nuclear power is the most abundant, cheap, reliable, and clean source of base-load electricity. However, it is imperative that every nuclear reactor design be thoroughly studied and have its safe operability verified through computer simulation, both before construction and throughout the reactor’s lifetime. A key component of reactor simulation is the calculation of the neutron “flux,” which is intimately tied to the reactor power, fuel utilization, and temperature distribution. “Exact” calculations of the neutron flux can be made by solving the Boltzmann neutron transport equation. Efforts at the Knolls/Bettis Atomic Power Laboratories and the Consortium for Advanced Simulation of Light Water Reactors (CASL) at Oak Ridge National Laboratory are aimed at performing these calculations for full-core analyses. However, the industrial nuclear power community has more limited computational resources, and transport calculations are not yet practical for full-core reactor design. Instead, the neutron flux typically is calculated by solving the simpler neutron diffusion equation – an approximation to the transport equation obtained by assuming that the flux is well approximated as a simplified function of angle. A further approximation is made when the geometrically complicated structure of the core is “homogenized” over coarse regions, thereby reducing the number of spatial unknowns. We have systematically derived a new homogenized diffusion approximation through an asymptotic analysis of the transport equation in the limit of a large, spatially periodic medium. The new diffusion equation correctly allows neutrons to diffuse at different rates in different spatial directions, unlike the standard diffusion equation, which (incorrectly) does not allow this. The method is being implemented in the Michigan PArallel Characteristics Transport (MPACT) Code. We demonstrate the accuracy of the new approximation with numerical comparisons.

**Abstract Author(s): **Travis J. Trahan, Edward W. Larsen