Justin M. Pounders

A Subcritical, Helium-Cooled Fast Reactor for the Transmutation of Spent Nuclear Fuel

A design concept and supporting analysis are presented for a He-cooled fast reactor for the transmutation of spent nuclear fuel. Coated transuranic (TRU) fuel particles in a SiC matrix are used. The reactor operates subcritical (k ≤ 0.95), with a tokamak D-T fusion neutron source, to achieve >90% TRU burnup in repeated five-batch fuel cycles, fissions 1.1 tonnes/full-power year, and produces 700 MW(electric) net electrical power. The reactor design is based on nuclear, fuels, materials, and separations technologies being developed in the Generation-IV, Next Generation Nuclear Plant, and Advanced Fuel Cycle Initiative programs and similar international programs, and the fusion neutron source is based on the physics and technology supporting the ITER design.

On the Diffusion Coefficients for Reactor Physics Applications

Abstract The definition of the multigroup diffusion coefficient for reactor physics problems is not unique; rather, it is based on limiting approximations made to the Boltzmann transport equation. In this paper, we present several new diffusion closures in an attempt to gain increased accuracy over the standard P1-based diffusion theory. First, the Levermore-Pomraning flux-limited diffusion theory is applied to reactor physics problems both in its original form and in a new modified form that makes the methodology more robust with respect to the energy variable. Additionally, two novel definitions of the diffusion coefficient are introduced that permit a neutron flux that is greater than first order in angle. These various diffusion theories are completed by developing consistent boundary conditions for each case. Diffusion theory solutions are computed for each unique closure and are compared against transport theory analytically for a simple half-space problem and numerically for a suite of simplified one-dimensional reactor problems. Conclusions and observations are made for each diffusion method in terms of its underlying assumptions and accuracy of the benchmark solutions.

Cellwise Block Iteration as a Multigrid Smoother for Discrete-Ordinates Radiation-Transport Calculations

ABSTRACT We improve the convergence properties of cellwise block iteration for discrete-ordinates radiation-transport calculations by adapting it for use as a smoother within a multigrid method. Cellwise block iteration by itself converges very slowly for optically thin spatial cells. However, multigrid methods involve a sequence of increasingly coarser grids such that cells on the coarsest grid should be optically thick, for which cellwise block iteration converges quickly. This fast convergence on the coarsest grid should enable fast convergence overall. A novel aspect of this paper is that, along with the usual first-order form of the transport equation, we also consider the Self-Adjoint Angular Flux (SAAF) form. We present numerical results generated using several multigrid methods based on cellwise block iteration for smoothing that demonstrate our approach yields robust convergence regardless of cell optical thickness as specified by the finest grid as well as for heterogeneous media. In addition, we find that the multigrid methods for the SAAF form of the transport equation have superior convergence properties as compared to those for the first-order form.

A Coarse-Mesh Method for the Time-Dependent Transport Equation

Abstract A new solution technique is derived for the time-dependent transport equation. This approach extends the steady-state coarse-mesh transport method that is based on global-local decompositions of large (i.e., full-core) neutron transport problems. The new method is based on polynomial expansions of the space, angle, and time variables in a response-based formulation of the transport equation. The local problem (coarse-mesh) solutions, which are entirely decoupled from each other, are characterized by space-, angle-, and time-dependent response functions. These response functions are, in turn, used to couple an arbitrary sequence of local problems to form the solution of a much larger global problem. In the current work, the local problem (response function) computations are performed using the Monte Carlo method, while the global (coupling) problem is solved deterministically. The spatial coupling is performed by orthogonal polynomial expansions of the partial currents on the local problem surfaces, and similarly, the time-dependent response of the system (i.e., the time-varying flux) is computed by convolving the time-dependent surface partial currents and time-dependent volumetric sources against precomputed time-dependent response kernels.