Moments in time: Numerical analysis of a method for time-resolved neutron spectroscopy

Time-resolved neutron information is essential for understanding the dynamics of inertial confinement fusion (ICF) implosions, providing key indicators that distinguish igniting from non-igniting plasmas and revealing the underlying causes of shot-to-shot performance variations. The moments method framework offers a practical pathway to extract such temporally resolved quantities using only a small number of neutron time-of-flight detectors. For example, one only needs four detectors to extract the burn-averaged rate of change of ion temperature, a well-defined physically useful quantity. In this work, we evaluate and validate the moments method across several levels of complexity. We first employ a controlled toy model to test the foundational assumptions and mathematical structure of the approach. We then demonstrate that the method generalizes to realistic one-dimensional simulation data of direct drive implosions with a 25 kJ laser driver that include time-dependent ion temperature evolution and hydrodynamic burn dynamics. Together, these results establish the moments method as an experimentally accessible and robust tool for extracting unique and independent information such as the burn-averaged rates of change of fluid velocity and ion temperature with time from neutron time-of-flight measurements, broadening the diagnostic capability of existing neutron detector systems. Fielding this diagnostic on ICF campaigns would improve our understanding of failure modes, helping to determine causes for improved or reduced performance during implosions, informing future target and laser drive design.