Abstract. During the Galileo-Io flyby, nearly field-aligned, left-hand circularly polarized ion-cyclotron waves were observed in a band near the sulfur-dioxide ion gyrofrequency. We have performed a warm plasma dispersion analysis using nominal Io torus composition ratios, pickup ion "ring"-type velocity-space distributions, and a thermal background plasma of typical torus temperature. Analysis shows that the SO+ wave is dominant, particularly as the ring begins to broaden. The observed spectral peak indicates that the ring distribution of pickup SO+ is highly unstable and generates waves, but there is unlikely to be sufficient time for ions to fully thermalize before dissociation occurs. Assuming wave-particle scattering of ions towards a "bispherical shell"-type distribution, a free-energy analysis and comparison with observed wave amplitudes suggests that the ions are not scattered far from the ring and/or that the SO+ composition ratio in the Io torus falls off considerably from Io wake values.
Figure 1. Galileo magnetic field observations at Io [Kivelson et al, 1996] in right-handed System III coordinates (see text). The Jovian dipole field B lies mainly along , north-south. The plot clearly shows predominantly transverse (Br, B) fluctuations in this particular interval.During the Galileo spacecraft approach to the Jovian satellite Io on December 7, 1995, a band of field-aligned, left-handed, nearly circularly polarized waves appeared at frequencies consistent with ion cyclotron resonance in a multicomponent plasma. Figure 1 shows high- resolution magnetic field data [Kivelson et al, 1996] for a 1.5 minute period in the torus, in right-handed System III (1995) coordinates where is directed southward along Jupiter's spin axis, is positive in the direction of Jovian rotation, and r is radially outward from Jupiter. Near Io's orbit, the Jovian dipole field B lies mainly along , north-south. Predominantly transverse (Br, B) fluctuations were seen in the torus plasma (outside of the Io wake region). The main spectral peak is seen near the SO+ ion gyrofrequency (~0.4 Hz). Properties of the observed waves are discussed in detail by Russell et al. [this issue] and Warnecke et al. [this issue]. Figure 2 shows averaged profiles of the relevant plasma and wave parameters for the Io flyby.
Figure 2. Average profiles of the total ion density [Frank et al., 1996] the field magnitude [Kivelson et al., 1996], total RMS amplitude, the calculated Alfven wave speed (VA= B/( u_ mN)) and gyrofrequencies of the heavy ions in the plasma torus (=qB/m).The torus plasma population is continually being replenished by the ionization of neutral particles from Io. The plasma corotation velocity V_CO = 74 km/s is greater than Io's orbital velocity V_IO = 17 km/s. Thus the downstream "wake" of Io and Io's Alfven wing are ahead of Io in its orbit. The Jovian background magnetic field, B, is approximately perpendicular to the co-rotating plasma velocity and new pickup ions initially gyrate about B forming a "ring"-type distribution with only a small drift parallel to B and ring injection velocity Vinj = v = V_CO - V_IO = 57 km/s relative to the bulk (previously implanted) torus plasma. Due to near-parallel observed wave propagation (typically ~7 degrees off-axis) [Warnecke et al., this issue; Russell et al., this issue], and approximately perpendicular pickup geometry, new pickup ions see the waves with little Doppler shift.
where N is the species number density, v// and
are the velocities parallel and perpendicular to
the ambient magnetic field, vr is the perpendicular ring velocity, vb the parallel beam (drift)
velocity, v_T// = (2 k_B T// /
= (2 k_B T
are the parallel and perpendicular thermal
velocities, and erfc is the complementary error function. The ring distribution for new pickup
ion populations can be prescribed by a delta-function for the idealized initial ion-implantation
geometry, with vr = Vinj = 57 km/s, vb = 0 for perpendicular pickup, and v_T// =
v_T = 0.
Alternatively, the ring may be given a thermal spread. In addition, Maxwellian thermal
background distributions with vr = vb = 0 are included for the previously picked-up and
thermalized corotating torus plasma populations. Typically, in the torus region the new pickup
ions in the high energy "tail" of the distribution account for ~10 to 20% of the total ion
population [Bagenal, 1985; 1994]. The electrons, present to ensure charge neutrality, are
assumed to be cold, with v_T// =
v_T = 0.
We define the species gyrofrequency =qB/m positive for ions, = ( - k// vb - ) / (k// v_T//) and = ( - k// vb) / (k// v_T//) where is the wave frequency and k// the parallel wave vector, and let r = vr / v_T . The L-mode dispersion relation for parallel propagation is then given by
where Z() is the plasma dispersion function [Fried and Conte, 1961], Z'() = dZ()/ d, and _ps is the species plasma frequency.
Figure 3. Field-aligned L-mode solutions to the dispersion relation for (a) delta-function pickup ion ring distributions (v ~57 km/s, v// = 0), and (b) the growing modes of case a recalculated for T=5 eV rings. In both cases the species composition ratios of Table 1 are used, the rings contain 10% of O+ and S+ components (280/cc, 80/cc, respectively) and 100% of SO+ component (200/cc), with T=100 eV thermal background O+ and S+. The top panel in each plot shows the wavemode frequency (normalized to the S+ gyrofrequency), and the lower panel shows the corresponding normalized growth rates. Plot is against wavenumber in inverse S+ inertial lengths.The dispersion relation solutions for field-aligned L-mode waves are given in Figure 3a for the "cold" delta-function ring. The peak growth-rate due to SO+ is higher than all other modes over a broad wavenumber range, despite the input SO+ composition ratio of only 5% (200/cc ring) compared with the O+ total (ring+background) ratio of 70%. For the S+ and O+ components, the unstable waves may be gyro-resonantly damped by the thermal background of torus ions of the same species. (Note that this is different to the situation at comets where the cometary heavy ions are implanted into a background solar wind plasma of mainly protons with very different gyrofrequency to the implanted heavy ions.) For molecular ions, however, the ring is dominant. The H+ component does not significantly contribute to the dispersion. The ring-type distribution is unstable and the ions may scatter on self-generated waves. Our input ring distribution can be given a thermal spread to represent the broadening due to these wave-particle interations and particle collisions. Results are given in Figure 3b for a 5 eV thermal spread (which corresponds to a small fraction of the pickup energy or the thermal energy of the background plasma). As the ring spreads, growth rates at larger k are reduced significantly, and the absence of an SO+ thermal background population leaves the SO+ wavemode dominant for all k. Note that the S+ wave damps where the SO+ peak growth occurs. Growth rate peaks for each mode are a little below the respective ion gyrofrequency for the perpendicular pickup geometry. If a v// drift velocity of vb ~10 km/s is given to the ring distribution (e.g. if the pickup geometry is not exactly perpendicular in the region of deflected flow and field close to Io) then a wavemode also exists at frequencies just slightly above the SO+ gyrofrequency (see also Warnecke et al. [this issue]).
Figure 4. Dependence of the SO+ peak growth rate on (a) the ring-to-background density ratio of SO+ (100% is all ring, 0% is all thermalized background), (b) the ring temperature, and (c) the initial ring injection velocity, Vinj . In all cases, background plasma O+ and S+ at T=100 eV is included, using the torus species composition ratios in Table 1.Figure 4 shows the effects of changing the ring temperature, the ring injection velocity Vinj , and the ring-to-background ratio on the peak growth rate of the SO+ wave. The most dramatic dependence is on the ring-to-background density ratio. For SO+ we expect rapid dissociation and/or recombination in chemical collisional reactions to produce the predominant oxygen and sulphur components of the observed torus plasma. Therefore we do not expect a fully thermalized SO+ background component.
for the perpendicular pickup geometry, where the Vinj injection velocity (corotating plasma velocity ~57 km/s) determines the energy of the initial ring. The ratio R =(Vph/Vinj) determines what fraction of the ring energy is released on scattering to the bispherical shell distribution, i.e. how "squashed" the average shell radius is compared to a sphere of radius Vinj. (Detailed derivations and shell geometry are previously published by Huddleston and Johnstone .) The equation relates the observed wave power amplitudes < B > (see Figure 2) to the number density of SO+ ions needed to generate these waves, assuming that rates both of wave damping (compared to growth) and wave propagation across the torus (Vph/( x torus width)) are small. These approximations are reasonable in the absence of a thermalized SO+ plasma component to damp the waves (as previously discussed), and for the relatively small phase velocity along B (Vph ~55 km/s found from the dispersion analysis) and huge size of the torus and neutral cloud. Ion cyclotron waves are observed out to ~20 Io radii (20 x 1820 km) on the inbound Galileo trajectory, and at least to 7 Io radii from Io outbound (See also Russell et al., this issue).
Figure 5. Upper panel shows the SO+ ion density inferred from the observed RMS amplitude, assuming the ions release energy to generate waves while scattering to the "bispherical shell"- type distribution. The dashed line represents the SO+ density at 5% of the observed total ion density N as seen in the Io wake [Frank et al. 1996]. The lower panel presents an estimate of the % scattering that has taken place (0% = ring, 100% = shell) based on the observed wave amplitude and SO+ density 5% of the total observed ions.Currently, plasma composition measurements are not yet available over the entire Galileo-Io flyby, and the SO+ density is not well known. Therefore, we compare two contrasting scenarios in Figure 5. Firstly, the top panel of Figure 5 shows the N_SO+ profile along the Galileo trajectory inferred from the observed RMS amplitude, in the full-scattering approximation of the above equation. This is the lower-limit of the density required to generate the observed waves because if the ions are scattered less on average, then the free energy released per ion is less and thus more ions are needed to generate the same waves. On the other hand, if the SO+ density throughout the Galileo pass is assumed to be 5% of the total observed ions (as seen by PLS in the wake region), then in the lower panel we calculate the % scattering (in terms of energy release) that has taken place. Figure 5 suggests either that an average ion does not scatter far from the ring before dissociation or recombination occurs, or that SO+ densities in the torus are considerably lower than the 5% of total ions seen in the wake. The latter is likely in an expanding cloud of rapidly dissociating sulfur-dioxide from Io. (Note that results of Warnecke et al.  are also consistent with a fall-off of N_SO+ with distance from Io.)
This work was supported by the National Aeronautics and Space Administration through the Jet
Propulsion Laboratory's grants JPL 958510 and JPL 958694. FB is grateful to the co-authors for
their hospitality at UCLA.