Numerical solution of Bloch's equation for neutron spin precession

The increasing importance of polarization in neutron scattering instrumentation for condensed matter research means that Monte Carlo design tools must be able to track neutron spin during neutron transport. In particular, we must be able to solve Bloch's precession equation for arbitrary magnetic induction configurations, including time-dependence. Since Monte Carlo simulations require averaging a large number of neutron histories, the computational procedure must be fast, as well as accurate and precise. A suitable algorithm is presented here, in the context of the Neutron Instrument Simulation Package (NISP), a Monte Carlo package developed at Los Alamos National Laboratory for neutron scattering instrument design. Accuracy is assessed by the comparison to simple cases for which analytical expressions are known, and precision and execution time are shown for a case with a non-uniform magnetic induction field.