Generalizing the Moments Method for Primary Neutron Spectra

Motivated by recent experimental results Hartouni et al. (2023); Mannion et al. (2023) which identified the presence of non-Maxwellian ion velocity distributions in ICF plasmas, we revisit the moments method for analysing the shapes of primary neutron spectra emitted by plasmas undergoing thermonuclear burn. We assume that the ion distribution functions are of an arbitrary form and develop a set of "generalized" moments, that are ordered in terms of increasing powers of centre of mass velocity, but for which the effects of shifts of centre of mass velocity (equivalent to fluid velocity in the case of Maxwellian ion distributions) are suppressed. This set of generalized moments provides the most sensitive measure of relative velocity contributions to the shape of the neutron spectrum (an effect that has been colloquially referred to as "viso"). We also demonstrate that pairs of antipodal neutron spectral detectors are most suitable for measuring these contributions.