A fully analytic space-time depletion benchmark for fixed-source and eigenvalue calculations and its application to Monte Carlo simulation

Highlights: • Benchmark for space-time coupled transport/depletion. • Analytical solution for fixed-source and eigenvalue problems. • Simple to implement and evaluate the analytical solution. • Benchmark has been implemented and demonstrated with MC21 code. • Convergence of coupled MC21 depletion calculations is assessed. - Abstract: Formal analysis of the convergence and stability of coupled neutron transport/depletion calculations is difficult due to the complicated nature of the nonlinear system of equations that must be solved. In this paper, we present a new benchmark problem for coupled neutron transport/depletion calculations along with its fully analytic solution. The benchmark problem – which we call the "Candlestick benchmark" because it models a progressive burnup from one end of a slab to another – is straightforward to implement and can be used to quantify the accuracy and stability of coupled transport/depletion calculations. Descriptions and solutions are provided for both a fixed-source and eigenvalue version of the benchmark. The Candlestick benchmark is a first-of-its-kind analytic solution to a nonlinear spatial depletion problem, and it is useful for the purpose of validating the solution methods used by reactor depletion solvers. As a demonstration of the usefulness of the Candlestick benchmark, we have used it to assess some of the convergence behaviors of Monte Carlo depletion calculations, including the effects of spatial discretization, temporal discretization, and stochastic error on the results of the calculation.