A theory of local and global processes which affect solar wind electrons, 1. The origin of typical 1 AU velocity distribution functions—Steady state theory
Authors: Scudder Jack D. , Olbert Stanislaw 
Published: February 2008

A new detailed first principle kinetic theory for electrons is presented which is neither a classical fluid treatment nor an expospheric calculation. This new theory illustrates the global and local properties of the solar wind expansion that shape the observed features of the electron distribution function fe, such as its bifurcation, its skewness, and the ‘differential’ temperatures of the thermal and suprathermal subpopulations. Our approach starts with the Boltzmann equation and retains the effects of Coulomb collisions via a Krook collision operator without recourse to wave‐particle effects. We conclude that Coulomb collisions determine the population and shape of fe in both the thermal (E <kT) and suprathermal (E >kT) energy regimes. We find that electrons with E >7kT constitute a special subpopulation of the suprathermals, insofar as Coulomb collisions are concerned; these we call ‘extrathermals.’ The electrons in the thermal portion of fe have undergone ∼10‐20 Coulomb collisions for cumulative momentum transfer en route to the observer at 1 AU; this population is thus more removed from the properties of coronal electrons than the suprathermal population. This latter group retains a strong memory of coronal conditions, since they have undergone only a few momentum transfer collisions. The thermal population is most nearly in collisional contact with the local dynamics (compressions, rarefactions, etc.) of the solar wind. The suprathermal portion of fe is determined by Coulomb collisional interactions with the distribution of solar wind material on radial scale of the heliopause itself. In this respect the suprathermal portion of fe is found to be responsive to the consequences of the global dynamics of the solar wind expansion. We find that this subpopulation is an attenuated vestige of collisional populations deep in the corona (1.03–10 Rs) which has been redistributed via Coulomb multiple pitch angle scattering on magnetically open field lines. The suprathermal particles moving toward the sun are computed to be observed as a result of Coulomb‐collision‐induced backscattering at larger (1–10 AU) heliocentric distances than that of the observer. Based on this theoretical picture, quantitative estimates for the partition of thermal and suprathermal phase density, the break in the velocity distribution, and the magnitude of the skewness (heat flux density) agree well with those typically observed near 1 AU. These calculations predict that the extrathermal fraction of the phase density, the extrathermal temperature, and the net heat flux density carried by electrons should be anticorrelated with the local bulk speed in quasi‐steady‐state flows and that the radial variation of extrathermal temperature inside 1 AU should be essentially independent of heliocentric distance. Our work also shows that the observation of suprathermal particles cannot be taken as a priori evidence for in situ wave particle interaction(s), since we can theoretically calculate a suprathermal population of solar wind electrons at 1 AU by assuming wave‐particle interactions are not present anywhere in the heliospheric cavity; the combination of inhomogeneity and the Coulomb ‘window’ above E*=7kTc naturally gives rise to this leakage of nonlocal collisional populations in superposition with local collisional populations. This work suggests that the local cause and effect precept which permeates the physics of denser media must be relaxed for electrons in sparse and radically inhomogeneous plasmas such as those found in the solar wind between the lower corona and the interstellar medium. The local form of transport laws and equations of state (e.g., Q =−κ ▽,T,P=NkT), which are familiar from collision‐dominated plasmas, must be replaced with global relations that explicitly depend on the relative position of the observer to the boundaries of the system.