The reflections of the Alfvén wave at each ionosphere and at the torus boundary are very clear, as shown in illustrations of the wave propagation paths (e.g., Bonfond et al., 2008; Crary & Bagenal, 1997). By comparing the maximum Poynting flux in the torus with the Poynting flux just outside the torus, we estimate that 53% of the wave energy is transmitted through the torus boundary in the low-density case, while 64% is transmitted in the high-density case where the contrast in Alfvén speeds is less. These results are in contrast with the claim of Chust et al. (2005) that most of the power is reflected at this boundary and does not reach the Jovian atmosphere. Since Io moves at 0.46°/minute with respect to the co-rotating plasma (e.g., Hinton et al., 2019), the distance between the Main Alfvén Wing (MAW, using the terminology of Bonfond et al. (2013)) in one hemisphere and the Reflected Alfvén Wing (RAW) in the conjugate ionosphere is about 6° in the low-density case and 8° in the high-density case, consistent with the travel times noted above.
However, since the torus does not have a sharp boundary, there are minor reflections through the system. Weak waves propagating between each ionosphere and the near boundary of the torus can be seen, much like in Figure 2 of Crary and Bagenal (1997). Figure 3a shows the same data as in Figure 2a, but with the color bar saturated at 1 W/m2 to bring out these weaker reflections. These show up particularly well in a map of the perpendicular electric field scaled to the ionosphere under the assumption that the field lines are equipotentials (Figure 3b). These secondary reflections appear to be stronger after the first reflected Alfvén wing. Although these waves are much weaker than the MAW, they still carry Poynting fluxes about 20 mW/m2 in the low-density case. This can be compared with electron energy fluxes of 10 mW/m2 downstream in the tail (Szalay et al., 2018). In addition, due to the very short travel time between the torus boundary and the nearer ionosphere, the reflections from the torus boundary and the ionosphere are very close together, so these two waves arrive almost simultaneously, smearing out the effect of the trailing spots. The Poynting flux decreases on each bounce due to the finite conductance of the ionosphere (1 S for this run) and the pattern becomes more complicated due to interference between the various bouncing waves.