GEOPHYSICAL
RESEARCH LETTERS, 24, (17), 2143, 1997
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.
Observations
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.)
Conclusions
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.
References
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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
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_
Figure 3. Field-aligned L-mode solutions
to the dispersion relation for (a) delta-function pickup
ion ring distributions
(v
Figure 4. Dependence of the
SO
Figure 5. Upper panel shows
the SO