Figure 9 shows the resulting relationship between the parallel potential drop (more precisely, the integrated parallel electric field, since the field is not purely electrostatic) and the field-aligned current at the ionosphere with these parameters for a run that is otherwise the same as that shown in Figures 7b and 8b, which is the low-density case and a Pedersen conductance of 10 S at Jupiter. This figure shows the current-limiting effect of our model, with the currents being limited to about 10 μA/m2 leading to potentials up to 100 kV. These parameters are consistent with the kinetic results of Ray et al. (2009), indicating that our model is a reasonable approximation to these results.
Figure 10a shows the field-aligned current from this run. The current pattern is spread out somewhat from the corresponding run without the parallel electric field (Figure 8b). Strong parallel electric fields lead to a perpendicular component of the Poynting flux that broadens the magnetic perturbation. The amplitude of the magnetic perturbation fixes the total current that should flow in the flux tube, so that the current limitation requires the current to flow over a larger area. This leads to a splitting of the current pattern. In addition, the current is limited to about 10 μA/m2 compared to almost twice that in Figure 9b. Figure 10b shows the parallel potential. The color bar in this figure has been limited to 25 kV to bring out some of the weaker potentials (the actual potential in the main spot is about 100 kV as in Figure 9. Note that in contrast to the field-aligned current plot, the red colors indicate regions of upward parallel electric field.
These figures show that while the main spots are accompanied by strong parallel electric fields, the secondary reflections of the wave from the torus boundary are not. This is largely due to the current-limiting nature of the current-voltage relation. This raises the question of how these auroral features in this region, as seen in the JIRAM data, are generated. It is likely that effects not included in our model, such as the filamentation of the currents due to nonlinear effects or feedback from the ionosphere, are important.