Ion Cyclotron Waves in the Io Torus During the Galileo Encounter: Warm Plasma Dispersion Analysis

D.E. Huddleston, R.J. Strangeway, J. Warnecke, C.T. Russell, and M.G. Kivelson
Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California

F. Bagenal
University of Colorado, Boulder, Colorado

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.

        The Io torus ion composition observed by the Voyager PLS instrument consists of predominantly O+, S++, and S+ ions and very few SO+ molecular ions [Bagenal, 1994]. Voyager was unable to distinguish composition at the orbit of Io but detected SO+ ions ( 1%) inside 5.3 R_J (Jovian radii) suggesting an extended neutral cloud of sulfur-dioxide molecules [Bagenal, 1985]. The Galileo plasma instrument saw a similar composition of atomic ions in the Io "wake" near closest approach [Frank et al., 1996], and estimated SO+ at 5% of the total density N. The exact composition in the hot torus is not well known at the present time. We shall find that the dominant wave growth rates are relatively insensitive to the proportions of the atomic ions but depend quite strongly on the percentage of SO+ which is poorly determined. In this paper we use the nominal composition ratios given in Table 1, a total ion density Ni = 4000 /cc and charge-neutral conditions (Ne = Ni). Given that mass-per-charge (m/q) data do not distinguish between O+ and S++, we assume m/q=16 corresponds to O+ for the purpose of the dispersion analysis since both have the same gyrofrequency and the addition of S++ would introduce no new gyro-resonances. We use pickup ion "ring"-type distributions as inputs to a warm plasma dispersion analysis to investigate the unstable wave modes in the torus plasma.

Dispersion Relation

        In specifying the L-mode dispersion for parallel propagation, we assume that the distribution function for each species can be represented by:

where N is the species number density, v// and v 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// / m) and v_T = (2 k_B T / m) 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.

Ion Scattering and Wave Amplitude

        As the co-rotating torus plasma flows past Io in its orbit, we may consider the pickup ions and their associated waves that are added to each "parcel" of torus plasma. Wave-particle interactions scatter the ions in velocity-space on spherical surfaces centered on the ±Vph field-aligned wave phase velocities. The "bispherical shell"-type distribution (previously discussed in the context of cometary and heliospheric pickup ions [e.g. Galeev and Sagdeev, 1988; Huddleston and Johnstone, 1992]) is the likely result if wave-particle scattering is fast compared to ion dissociation/recombination rates, thermalization, or removal of ions from the region. In addition to the wave-particle interactions, ion-ion or ion-neutral collisions may help define the pickup ion velocity-space distribution.

        For a density N_SO+ ions scattering from a pickup ring to a bispherical shell type distribution, the maximum free energy available to generate waves is described by [Huddleston and Johnstone, 1992]

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 [1992].) 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. [1997] are also consistent with a fall-off of N_SO+ with distance from Io.)


        We have performed a warm plasma dispersion analysis for conditions in the Io plasma torus. Results show that for a given ion number density, the heaviest pickup ion components are the most likely to produce growing wavemodes from an unstable ring-type distribution, as we expect because the energy of the ring distribution scales with ion mass. Adding a thermal background of the same species damps the unstable waves to a degree depending on the relative ring-to-background ratio, the temperature of the background, and the steepness of the ring distribution. Wavemodes of the lower-mass species are damped the most for a given ring-to-background ratio of the species component.

        Field-aligned dispersion relation solutions have been presented here. We found no perceptible difference in the dispersion solutions for parallel-propagating waves or the observed 7-degree off-axis propagation. The peak frequencies generated are a little below the pickup ion gyrofrequencies for the perpendicular pickup case, and additionally just above the gyrofrequency if a small v// drift velocity is added to the ring [Warnecke et al., this issue]. For delta-function pickup ion ring distributions with a thermal background, the solutions are rather complex. The frequencies generated extend up to the resonant ion gyrofrequency, but with very large k (low phase speed Vph = / k, group velocity d /dk near zero). As the ring spreads, an increasing ring temperature reduces wave growth rates particularly at large k, and this makes the SO+ peak growth rate become particularly prominent.

        The plasma torus is continually being replenished with newly-ionized particles from Io. The dominant spectral peak observed near the SO+ gyrofrequency suggests these waves are generated by newly-implanted SO+ ions in a region of the torus where old, corotating SO+ has since dissociated. This implies the SO+ pickup ring is highly unstable, and the distribution has time to generate waves but insufficient time to thermalize before dissociation occurs. The SO+ wave is therefore dominant partly because the ring energy scales with ion mass, but mainly because of the absence of thermalized SO+ torus plasma to damp these waves. A free-energy analysis suggests that the SO+ ion densities in the Io torus are considerably lower than the wake values and fall off with distance from Io. We hope that the observed Galileo PLS ion distributions when available may help us to constrain our calculations in the future.

Acknowledgments. 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.


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