Comparison of solutions to the thirteen-moment and standard transport equations for low speed thermal proton flows

We have compared solutions obtained from the general 13-moment system of transport equations with those obtained from the standard collision-dominated transport equations for conditions corresponding to low speed thermal proton flow in the topside ionosphere in the vicinity of the plasmapause. In general, the solutions obtained from the 13-moment system of equations, which allows for different species temperatures parallel and perpendicular to the geomagnetic field and non-classical heat flows, are different from those obtained from the standard transport equations, which account for isotropic temperatures and classical collision-dominated heat flows. Within the plasmasphere, where the electron density is high, the differences between the 13-moment and standard solutions are typically small. However, outside the plasmasphere where the electron density is lower and in the ionosphere above SAR-arcs, where substantial electron and proton heat flows occur, there can be significant differences between the 13-moment and standard solutions. Generally, the differences are much larger for the protons than for the electrons. Our 13-moment solutions indicate that the proton and electron distributions are anisotropic with the difference between parallel and perpendicular temperatures approaching 4000 K for the protons and 2500 K for the electrons in the ionosphere above SAR-arcs. Also, above SAR-arcs the 13-moment heat flow equations yield proton heat flows as much as a factor of 10 lower and electron heat flows as much as a factor of 2 lower than those predicted by the classical collision-dominated heat flow expressions for the same boundary conditions.