SAR arcs are rather stable phenomena compared to discrete aurora and, when modelling the phenomena, a steady state electron energy equation can be used. In the 300-500 km altitude interval the principal energy loss mechanisms are
The ultimate energy source of SAR arcs can be found in the magnetospheric ring current region. At least three different theories have been proposed (see, e.g., Kozyra et. al., 1987; Fok et. al., 1991):
The Coulomb collisions between ring current protons and plasmaspheric cold electrons proved to be too inefficient to produce the energy needed. However, the finding of heavier ions in the ring current changed the situation, since they actually dominate the low-energy (E<17 keV) portion of the ring current in the plasmapause region. It made the ring current O+ potentially the major source of SAR arc energy (Kozyra et. al., 1987). During the expansion phase of the magnetic substorm the plasmasphere becomes smaller as the plasmapause moves to lower L shells (L = 2-4) due to the enhanced cross-tail potential. As the recovery phase proceeds, the plasmasphere begins to refill over the energetic ring current. Thus a region of overlap develops between the enhanced (due to substorm injections) ring current and cold plasmaspheric population, making extensive Coulomb collision rates between O+ and electrons possible. This region of overlap maps along field lines to low altitudes in the SAR arc region of the subauroral ionosphere. It is also possible that a feedback phenomenon occurs: formed positive temperature gradient along the field lines could lead to upward flow of minor heavy ions (like O+) due to thermal diffusion, and thus increase plasmapheric heavy ion concentration (forming heavy ion torus/shell?). At least measurements by DE 1 and 2 show close association between plasmaspheric O+ and/or O++ density enhancements and ionospheric Te peak (Horwitz et. al., 1986).
Example of nearly simultaneous DE-1, DE-2, and Chatanika radar measurements. The inner plasmapause region seen in DE-1 density measurements is colocated with signatures in Te measured by DE-2 (from Green et. al., 1986).
A general association between subauroral Te peaks and plasmaspheric density gradients have been seen, making them more reliable low-altitude plasmapause signatures than electron density changes (mid-latitude troughs; see, e.g., Green et. al., 1986). This can be seen also in the Figure. Note that the Te signature coincides with the inner plasmapause, i.e., it never shows the dusk bulge characteristic of the equatorial plasmasphere. The Te peaks correlate also with ionospheric ne troughs (e.g., Watanabe et. al., 1989), although this is not very well seen in the Figure (probably because of the high altitude; note that the main ionospheric trough is, at least in the evening sector, clearly poleward of the plasmapause). The often seen sharp poleward edge in the latitudinal profile of Te enhancements can be explained by the drop in heat capacity and reduction in the coefficient of heat conductivity, both of which are results of the corresponding drop in density at the plasmapause, particularly at the inner plasmapause (Brace et. al., 1988). In addition, the magnitude of the subauroral Te peak , which is an indication of the amount of energy transferred to the ionospheric electrons from the magnetospheric heat source, shows an interesting behaviour. Although the electron densities at equinox are, on average, about 2.5 times higher than those of solstice, there is no seasonal variation to be seen in Te peaks (Fok et. al., 1991). This implies compensating changes in the magnetospheric heat source, and actually similar seasonal changes in the magnetospheric O+ content have been measured. Of cource this is easy to explain if the O+ ions of the ring current originate from the ionosphere. The magnitude of the Te peaks are naturally also related to the magnetic activity (Dst index, see Fok et. al., 1991).
Actually there is also another possible heat source in the nighttime mid-latitude ionosphere, namely the photoelectron energy that is stored in the plasmasphere during the daytime. The best way to separate these sources (ring current versus photoelectrons) would be to study a series of Te profiles taken over 2- or 3-day period during heating events, since the photoelectron component is much more steady and predictable (Brace et. al., 1988). In addition, it is possible that the heating is due to photoelectrons produced continuosly in the conjugate hemisphere, which is sunlit (Evans et. al., 1983, Rodger et. al., 1986). The latter is an important heat source during winter time (Fok et. al., 1991), weakening the response of the magnitude of the Te peak to magnetic activity.