To quantify the amount of reflection in each case, we have decomposed the electric and magnetic fields into the so-called Elsässer variables (Elsässer, 1950), which for Alfvén waves can be written as , where the plus sign refers to waves propagating in the +μ direction (i.e., northward along the field line) and the minus sign to waves in the −μ direction. Evaluating these values at a latitude of 50° in the main Alfvén wing, we find that the reflection coefficients are 2.0%, 36.5% and 71.4% for the 0.1, 1.0 and 10.0 S cases, respectively. Mura et al. (2018) have shown that the tails can extend for over 100° in longitude around Jupiter. While these results favor a high Pedersen conductance, it is difficult to explain such extended tails even for the 10 S case.
The field-aligned currents at the ionosphere show similar characteristics. Figures 8a and 8b show the currents in the northern hemisphere for the runs shown in Figures 7a and 7b, respectively. A first point is that, unsurprisingly, the currents are stronger for higher conductance. The low conductance case shows a near absence of current between the MAW and RAW spots, and by the second reflected spot, the currents are much weaker. On the other hand, in the high conductance case the currents remain strong between the MAW and RAW, although still weaker than the MAW spot. In this case, there are strong reflections at both the ionosphere and the torus boundary. Reflections from the low Alfvén speed torus and the high conductance ionosphere both lead to reduction in the electric field and enhancement in the field-aligned current, leading to stronger currents even though the Poynting flux is low in between the main spots. In the high conductance case, the upward and downward currents are seen to switch positions due to multiple reflections and phase mixing as the waves propagate. These simulations suggest that a strong and relatively continuous current structure would be associated with high ionospheric conductance. This effect is possibly related to the bifurcated footprint seen far down the Io tail by Mura et al. (2018) and Szalay et al. (2018).