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.