Towards a fluid description of directional particle flux observations

We propose that, whenever directional flux measurements of a population of particles (e.g. solar energetic particles, cosmic rays, solar wind plasma) of well-defined energy resolution are available, new macroscopic fluid-like quantities (namely the energy dependent analog of density, mean velocity, anisotropic pressure, temperature and heat flux) can be rigorously estimated, thus describing the sub-flux referring to that energy range in fluid terms. Exact, closed relations for these quantities as functions of lower order spherical harmonics coefficients are analytically derived, offering a new interpretation of the anisotropy flux components in fluid terms. Among them, the, most commonly used, first order anisotropy vector is shown that can be interpreted as the direction of the populationʹs mean velocity and, for strongly isotropic distributions, the direction of heat flux. Indicative applications are presented, using energetic particle flux measurements of Ulysses spacecraft.