A comparative study of the time-dependent standard 8-, 13- and 16-moment transport formulations of the polar wind

The ionosphere, composed of O(+), H(+), and electrons is modeled with four different transport formulations. The equations corresponding to the standard set, the 8-, 13-, and 16-moment approximations are presented, and the collision terms are expressed. Using a time-dependent technique, the ionosphere is studied between altitudes of 200 and 8600 km. The production of electrons and O(+) ions is described by a neutral atmosphere simplified photoionization scheme, while the energy deposition is supported by a downward electron heat flow of -0.005 erg/sq cm per s imposed at the topside boundary. When the models reach a steady state equilibrium, the electron solutions show differences due to the introduction of temperature anisotropies and heat flows between the components parallel and perpendicular to the magnetic field. As a corollary, the ions show structures depending on the level of approximation. A depletion of a factor of 10 is then applied to the ion densities above a certain altitude, and the development of the perturbation is followed for 1000 s for all the models.