Comparison of depletion algorithms for large systems of nuclides

Abstract In this work five algorithms for solving the system of decay and transmutation equations with constant reaction rates encountered in burnup calculations were compared. These are Chebyshev rational approximation method (CRAM), which is a new matrix exponential method, the matrix exponential power series with instant decay and a secular equilibrium approximations for short-lived nuclides, which is used in ORIGEN, and three different variants of transmutation trajectory analysis (TTA), which is also known as the linear chains method. The common feature of these methods is their ability to deal with thousands of nuclides and reactions. Consequently, there is no need to simplify the system of equations and all nuclides can be accounted for explicitly. The methods were compared in single depletion steps using decay and cross-section data taken from the default ORIGEN libraries. Very accurate reference solutions were obtained from a high precision TTA algorithm. The results from CRAM and TTA were found to be very accurate. While ORIGEN was not as accurate, it should still be sufficient for most purposes. All TTA variants are much slower than the other two, which are so fast that their running time should be negligible in most, if not all, applications. The combination of speed and accuracy makes CRAM the clear winner of the comparison.