  Recent inertial confinement fusion experiments have shown primary fusion
spectral moments which are incompatible with a Maxwellian velocity distribution
description. These results show that an ion kinetic description of the reacting
ions is necessary. We develop a theoretical classification of non-Maxwellian
ion velocity distributions using the spectral moments. At the mesoscopic level,
a monoenergetic decomposition of the velocity distribution reveals there are
constraints on the space of spectral moments accessible by isotropic
distributions. General expressions for the directionally dependent spectral
moments of anisotropic distributions are derived. At the macroscopic level, a
distribution of fluid element velocities modifies the spectral moments in a
constrained manner. Experimental observations can be compared to these
constraints to identify the character and isotropy of the underlying reactant
ion velocity distribution and determine if the plasma is hydrodynamic or
kinetic.
