‘Non-classical’ transport of collisionless solar wind protons

A practical transport model for collisionless solar wind protons is presented. The key idea is to extend the usual decomposition of solar wind fluid variables, into ‘averages’ and ‘fluctuations’, to the proton distribution function. Although the instantaneous distribution may be anisotropic, it is expected that magnetic fluctuations will tend to isotropize the average distribution. A simple transport model is then constructed, based on relaxation to isotropy of the average proton distribution. Such a model puts the fluid description of the collisionless solar wind on a firm basis, and makes clear that the fluid description can only be justified for such an average. Anomalous transport coefficients, which relate the heat flux and pressure tensor to lower-order moments, can then be calculated in terms of the isotropization time. In addition to the usual heat flux and viscosity, one finds that isotropization of the average distribution requires the allowance of a fluid frame mass flux, which is also related to lower-order moments via a transport coefficient. This mass flux is a general consequence of formulating a fluid dynamics that separates averages from fluctuations, and so its effects need to be considered wherever wave dissipation is thought to be occurring in the solar wind. One also recovers a transport equation for the nearly-isotropic proton distribution which reduces to the cosmic-ray transport equation in the limit of fast particles. Because this transport equation describes how shears, compressions, and accelerations of the flow influence the proton distribution, it unifies our understanding of collisionless dissipation over the range of particle speeds.