One-dimensional hybrid simulations of planetary ion
pickup: Techniques and verification
M. M. Cowee,1R. J. Strangeway,1C. T. Russell,1and D. Winske2
Received 30 July 2006; revised 20 September 2006; accepted 25 October 2006; published 20 December 2006.
 Previously, hybrid simulation techniques using massless fluid electrons and kinetic
ions have been successfully applied to study the electromagnetic plasma waves
generated by ion pickup in the solar wind, where instability is driven by the large drift
velocities of newborn ion populations. For ion pickup at Jupiter and Saturn’s
magnetospheres where instability is driven by heavy ions with a ring velocity
distribution, we show that the one-dimensional hybrid simulation technique can
successfully reproduce the behavior of this instability as predicted by linear dispersion
theory as well as the important nonlinear wave-particle interactions. The simulated ion
cyclotron waves have frequencies near the ion gyrofrequency and are generated as the
anisotropic newborn ion ring distribution scatters to a more isotropic configuration.
Simulated maximum wave amplitudes and instability growth rates increase with newborn
ion density and pickup velocity. For appropriate heavy pickup ion densities and velocities
the simulated wave amplitudes are within the range observed by spacecraft.
Citation: Cowee, M. M., R. J. Strangeway, C. T. Russell, and D. Winske (2006), One-dimensional hybrid simulations of planetary
ion pickup: Techniques and verification, J. Geophys. Res., 111, A12213, doi:10.1029/2006JA011996.
 Ion pickup processes occur in many planetary environ-
ments in our solar system. When neutral particles from
ionization, and charge exchange they become subject to
electric and magnetic forces. If pickup ions are significantly
accelerated they form an anisotropic population with suffi-
cient free energy for wave generation. Electromagnetic
plasma waves which appear to be generated by unstable
populations of newborn pickup ions have been identified in
the planetary environments of Earth [Le et al., 2001], Venus
[Russell et al., 2006], Mars [Barabash et al., 1991; Russell et
al., 1990], Jupiter [Warnecke et al., 1997; Russell and
Kivelson, 2001; Russell et al., 2003], and Saturn [Smith
and Tsurutani, 1983; Leisner et al., 2006]. At Venus, Mars,
and comets, newborn ions picked up solar wind can have
supra-Alfvenic speeds in the directions both parallel (drift)
and perpendicular (gyration) to the ambient magnetic field,
depending on the angle between the solar wind velocity and
the magnetic field. Inside Jupiter and Saturn’s magneto-
spheres, neutral particles from the satellites and rings are
ionized,picked upbythecorotating magnetodiskplasmaand
accelerated to sub-Alfvenic speeds in the direction perpen-
dicular to the planet’s ambient magnetic field. Because
Jupiter and Saturn’s magnetic fields are, to first order,
perpendicular to the plane of the magnetodisk where ion
pickup takes place, the newborn ion populations there will
have very little parallel drift velocity.
 Wavegenerationbypickupionpopulations inthesolar
wind has been well studied in cometary environments.
Observations of comets Giacobini-Zinner and Halley [Le et
al., 1989; Thorne and Tsurutani, 1987] detected right-hand
polarized waves near the water group ion gyrofrequencies.
Because newly ionized cometary ions have a large velocity
component parallel to the ambient magnetic field, the wave
frequency is Doppler shifted between the frame of reference
of the ions (or the spacecraft) and the solar wind; the waves
are left-hand polarized in the frame of the ions but right-hand
polarized in the solar wind. Hybrid simulations of this
instability have reproduced the waves and shown that as
the newborn cometary ions exchange energy with the waves
they pitch angle scatter forming a more isotropic velocity
distribution [Gary et al., 1989, and references therein].
 In the Jovian and Saturnian magnetospheres, left-hand
polarized waves were detected at frequencies near the local
pickup ion gyrofrequencies because in the perpendicular
pickup geometry of these environments Doppler shifts are
small [Warnecke et al., 1997; Leisner et al., 2006]. The
perpendicular pickup geometry favors the generation of
highly anisotropic ‘‘ring’’-type ion velocity distributions
with T?> Tk, where ? and k denote directions relative to
the ambient field, B0(Figure 1). Instability driven by a zero
drift ring velocity distribution was previously simulated
using hybrid techniques for conditions conditions in the
Earth’s magnetotail by Convery and Gary ; however,
they used ring densities, velocities, and temperatures much
higher than occurs at Jupiter and Saturn and did not consider
heavy ions. Machida et al.  used the hybrid simulation
to reproduce proton cyclotron waves near the Jovian moon,
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 111, A12213, doi:10.1029/2006JA011996, 2006
1Institute of Geophysics and Planetary Physics, University of
California, Los Angeles, California, USA.
2Los Alamos National Laboratory, Los Alamos, New Mexico, USA.
Copyright 2006 by the American Geophysical Union.
1 of 9
Io, but analytic study has shown that protons do not play a
role in the generation of the heavy ion cyclotron waves
observed there [Huddleston et al., 1997]. Machida et al.
from inward radial diffusion rather than ion pickup and did
not consider heavy ion cyclotron waves as they had not been
observed at Io by Voyager [Thorne and Scarf, 1984]. They
concluded that extending the study to include more realistic
conditions in the Jovian magnetosphere, which would
include heavy ions, was not possible at that time because of
the increased computational runtime and cumulative numer-
 This paper presents the first self-consistent simulation
of the heavy ion, zero-drift, ring anisotropy instability result-
ing from ion pickup into the sub-Alfvenic plasma environ-
ments at Jupiter and Saturn. We use ion pickup waves in the
Io plasma torus as our primary example to show that the
instability behavior is well reproduced in simulations. Using
the hybrid simulation is important because although linear
dispersion theory has explained the existence of pickup ion
waves at Io and predicted their dispersion properties, it
cannot predict wave amplitudes which are key to relating
the observed waves to specific plasma or pickup ion con-
ditions. Additionally, linear dispersion theory cannot predict
during ion pickup. Simulations with ion injection to model
the continuous creation of new pickup ions is not included
this study but will be the subject of future work.
 The paper is organized as follows: section 2 briefly
summarizes the observations of ion cyclotron waves and
plasma conditions in the Io torus; section 3 describes the
linear dispersion analysis; section 4 describes the hybrid
simulation technique; section 5 shows that the hybrid
simulation reproduces the behavior predicted by linear
theory at Io; section 6 discusses future application of the
one-dimensional (1-D) hybrid simulation to understanding
the ion pickup processes in planetary environments. In
addition, section 5 briefly shows simulation results appli-
cable to Saturn’s E-ring.
2.Observations at Io
 The Galileo spacecraft collected magnetic field data
during six of its seven passes by Io and observed ion
cyclotron waves each time. To first order, the waves were
left-hand circularly polarized and propagated along the
ambient magnetic field with frequencies near the local ion
gyrofrequency. Wave amplitude varied along each pass,
conditions and the mass loading process. On every pass
waves near the gyrofrequencies of SO2
observed and S+waves were also observed on two of the
passes. During some periods of time only one of the two
a distance of 7 RIoinward and 20 RIooutward of Io. For a
more detailed discussion of the wave properties and example
wave spectra, refer to Russell and Kivelson  and
Russell et al. .
 During the Voyager flyby, plasma composition mea-
surements showed the surrounding plasma torus was mainly
composed of thermalized atomic O and S ions with only less
than 1% SO2
Io measured similar composition at closest approach with an
amplitudes of the waves are directly proportional to the
number density,mass,and pickup velocity ofions generating
them, Huddleston et al.  estimated the SO2
loading rate at Io as ?8 ? 1026ions/s. This value is sensitive
+ions [Bagenal, 1994]. The first Galileo pass by
+density of 5% [Kivelson et al., 1996]. Assuming that the
Figure 1. SchematicillustrationofthepickupgeometryofIogenicions,showingthepickupioncycloidal
plasma. From Huddleston et al. .
COWEE ET AL.: HYBRID SIMULATION OF ION PICKUP WAVES
2 of 9
to the amount of energy given up by the ring to the waves.
They assumed that the ring gives half of its energy to the
waves, but if the value is less, then the mass loading rates are
 Warm plasma linear dispersion analysis of the electro-
in the Io plasma torus has been previously carried out by
Huddleston et al. [1997, 1998], and we use their dispersion
solver for this study. Because of an error in their original
dispersion solver, in which the electron density was not set
consider a wave mode to have real wave vector k and
complex frequency w = wr+ ig where wrand g are the real
frequency and growth rate, respectively. The maximum
growth rate over all wave numbers is gm. For propagation
parallel to the ambient magnetic field, B0= B0^ x, the wave
vector k = kx^ x and wave number, k = kx.
 For both the dispersion analysis and simulation runs,
ion species (same mass and charge state) with one or more
components, j, and electrons, e. Each ion species component
has a distinct velocity distribution function, such as a zero-
drift maxwellian (core), c, or ring, r. The electron density is
equal to the total ion density, n0= Sjnj(all ions singly
charged). Each component has a mass, mj(in units of proton
mass, mp), and charge state, Zj= 1 (in units of proton charge,
ep). Component parallel and perpendicular thermal velocities
are vkj = (2kBTkj/mj)
important plasma parameters are defined as follows: plasma
frequency is wpi
inertial length is c/wpi. Subscript i refers to the arbitrary ion
species whose plasma parameters were used for normal-
ization of the results; here it is either S+or SO2
wish to compare to those of Huddleston et al.  use S+
normalization, consistent with their analysis. Other results
which consider SO2
simulation use SO2
simulation technique defines input parameters Alfven speed
as vA= B0/
 The ring velocity, vr, is the perpendicular velocity
of a ‘‘ring’’-type velocity distribution. It is the ion pickup
(or injection) velocity and nominally defined in at Io as
vr= vco? vIo, where vcois the plasma corotation velocity
at Io (?74 km/s) and vIois Io’s orbital velocity (?17 km/s).
The pickup process can produce a range of ring velocities
Io’s orbital velocity. However, for simplicity we consider the
newborn ion populations to all have the same ring velocity.
We use a ring velocity distribution function with little or no
thermal spread about the ring in the perpendicular and
parallel directions (in the results the spread is indicated by
theringT?jand Tkj). We assume here, for simplicity, that the
ionization process results in newborn ion rings with very
little initial velocity spread away from a cold ring.
1=2and v?j = (2kBT?j/mj)
2/(?0mi); gyrofrequency is Wi= epB0/mi;
+. Results we
+or OH+as the only ion species in the
+or OH+normalization, respectively. The
, plasma beta as bj= 2m0n0Tkj/B0
anisotropy Aj= T?j/Tkj.
 The velocity distribution function for each compo-
nent is then assumed as
exp ? v?? vr
p3=2r erfc ?r
ðÞ þ exp ?r2
where r = vr/v?j. A maxwellian velocity distribution is
obtained by setting vr= 0 and a cold, delta-function ring
would be obtained by keeping nonzero vrand setting vkj=
v?j= 0. Electrons are assumed to have a cold maxwellian
 The dispersion relation for L-mode waves at parallel
propagation is then
?z0Z z ð Þ þZ0z ð Þ
1 þ r2
ð Þ þ exp ?r2
where z0= w/kvkjand z = (w ? Wj)/kvkj. Z(z) is the plasma
dispersion function [Fried and Conte, 1961] and Z0(z) =
 The electromagnetic hybrid simulation code used in
this study is that of Winske and Omidi  and treats ions
kinetically and electrons as a massless, charge-neutralizing
fluid. Since electrons do not play a role in the growth of the
instability and thus can be treated as an inertialess fluid,
saving computation time. Ions, however, interact resonantly
with the waves and cannot therefore be considered as a
fluid. Electromagnetic fields and ion velocities are calcu-
lated in three dimensions, but particle position is determined
in one dimension. While simulations in two or three
dimensions would allow a broader range of wave modes,
the one-dimensional code can accurately reproduce the
physics of the interaction but without the excessive com-
putational run time. We would expect our results to be
somewhat modified if done in higher dimensions; for
example, the wave amplitudes may not be as high and
wave power may decay faster since the free energy can be
distributed along more than one wave vector. However, we
still expect wave modes at parallel propagation to dominate
over all other directions and the relation between relative
changes in wave amplitudes and growth rates due to
changing plasma conditions to be the same.
 The simulation code uses a particle-in-cell technique
which represents the ions as a collection of ‘‘superparticles’’
on an imposed spatial grid. Field quantities are determined
by Maxwell’s equations solved using the weighted densities
and velocities of the superparticles in each grid cell. All ion
components in the simulation are represented by an equal
number of superparticles, and the collected densities and
velocities of the superparticles of each component are then
weighted by the relative density of each component before
being used to solve for the fields. This technique allows us
COWEE ET AL.: HYBRID SIMULATION OF ION PICKUP WAVES
3 of 9
to model small ion densities because it avoids the statistical
problems inherent in small sample size.
 Because linear dispersion theory predicts maximum
growth of the instability at parallel propagation [Huddleston
et al., 1997], the simulation axis, x, is aligned with the
ambient magnetic field. This field is assumed to be constant
and uniform throughout the run, which is appropriate for
distances further than several Io radii from Io that are outside
the interaction region where the corotating plasma flow is
diverted aroundthemoon [Kivelson etal.,2001].Thesystem
has periodic boundary conditions and all particle positions
and velocities are declared at the start of the simulation. In
order to resolve the full range of wavelengths excited, all
simulation runs consider a system oflength 30–50 c/wpiwith
512 grid cells.
 Initial tests of the code revealed several numerical
problems in simulating a zero-drift anisotropy instability in a
with b < 10?4). First, because the growth of anisotropy
noise would artificially inflate the parallel temperature.
Because instability in the torus can be relatively weak (wave
energies between 10?6< (dB/B0)2< 10?3), these simulations
are particularly susceptible to numerical heating effects, as a
temperature increase of less than several eV significantly
decreases the growth rate. To reduce the numerical heating to
an acceptable level, we used between 50,000 and 800,000
superparticles to allow the weaker instabilities to grow.
 Second, we found that the parallel and antiparallel
propagating waves had amplitudes and growth rates which
differed by as much as a factor of two. The ring particles
wouldsubsequently scatterasymmetrically invelocity space.
For instability growth at k ? B0= 0, this should not occur, as
linear theory predicts the same properties for both parallel
and antiparallel propagating modes. This proved to be due to
a very small net current across the simulation box produced
when the particle velocities were initially collected on the
spatial grid. This effect is also enhanced by the very low ion
in a quiet start configuration, that is mirroring in position and
velocity across the simulation axis, there was no initial net
current and the wave modes grew similarly at both parallel
and antiparallel propagation.
5.1. Predictions of Linear Theory
 Analytic study of the growth of the ion cyclotron
waves observed at Io using warm plasma and magnetic field
conditions observed by Galileo has shown that wave growth
maximizesatparallel propagation andisindeeddrivenbythe
temperature anisotropy of newborn ions. The presence of a
thermalized component of the ion in the torus damps wave
growth. Since the plasma torus is mainly composed of
thermalized atomic O+and S+, waves near these gyrofre-
quencies are not expected to form. For molecular sulfur ions
which dissociate quickly, there is insufficient time for a
thermalized component to form and thus SO2
cyclotron waves may grow relatively undamped [Warnecke
et al., 1997; Huddleston et al., 1997, 1998; Blanco-Cano et
 In an exactly perpendicular pickup geometry the
newborn ion ring is cold (Tk= T?= 0); however, wave-
particle interactions early on during instability growth will
increase the temperature spread about the ring. Huddleston
et al.  considered instability driven by an SO2
with vr= 57 km/s and a temperature spread of 5 eV in a
plasma composed primarily of S+and O+thermal ions of
T= 100 eV. Solutions of the warm plasma dispersion relation
for the parameters listed in Table 1 are shown in Figure 2.
Dispersion solutions exist for waves at each of the O+(dotted
line), S+(dashed line), and SO2
as the ring components are all potentially unstable to the
generation of waves near their gyrofrequency. For the waves
near the O+and S+gyrofrequencies, the dense core
component of those species damps wave growth, rendering
core ions present, the SO2
frequencies are just below the SO2
normalized wave numbers, kc/wpS+, between ?1 and 6
(equivalent to krSO2+ ?0.5–2.5, where rSO2+ = 22.4 km is the
is 78 km/s. The presence of protons does not affect wave
dispersion and that component is therefore not included.
+(solid line) gyrofrequencies,
+mode is dominant. Excited wave
+gyrofrequency and at
Table 1. Dispersion Calculation Parametersa
aTotal ion density is 3800/cc and B0 is 1700 nT. Normalization is
c/wpS+ = 48 km and WS+ = 0.81 Hz.
Figure 2. Dispersion solutions for the parameters listed in
Table 1. The real frequency and growth rate are normalized
to the S+gyrofrequency and the wave number is normalized
to the inverse S+plasma frequency. Wave modes are excited
rings. Corrected from Huddleston et al. .
COWEE ET AL.: HYBRID SIMULATION OF ION PICKUP WAVES
4 of 9
 The growth rate of the instability depends on the
amount of free energy in the ring which is a function of the
ion mass, ring density, ring velocity, and ring parallel
temperature. Huddleston et al.  found that the maxi-
mum growth rate increases with increasing ring density and
velocity but decreases with increasing ring temperature
(Figure 3). The effect of the ring parallel temperature on
growth rate is important because as the ring spreads, its
parallel temperature increases, thus reducing the instanta-
further address this behavior.
5.2. Simulation Results
 We simulate the growth of the zero-drift SO2
instability for simulation inputs given in Table 2, which are
similar to those in Table 1 except that we consider all the S+
and O+ions to be in the core component and we initialize the
contribute to the dispersion solutions for the SO2
can be removed for simplicity. Time histories of several
simulated quantities are shown in Figure 4. Growth of the
unstable electromagnetic waves is seen in the fluctuating
magnetic field energy density (Figure 4a). The instability
decays back to pregrowth levels (after WS+t = 6000, much
longer than shown here).
 Figures 4b and 4c show the simulated time history of
the ring velocity (calculated as hv?
and parallel temperatures about the ring. As the instability
grows, the ring ions scatter on the waves, losing perpendi-
cular energy (decreasing vr) and increasing the temperature
spread about the ring. The other components also interact
with the waves: O+core ions experience gradual heating and
cooling in the perpendicular and parallel directions, respec-
tively (Figure 4d), while the S+core ions experience
both perpendicular and parallel heating to a larger degree
(Figure 4e). Crary and Bagenal  predicted that large
S+corebutwouldnoteffect theO+core ions.Weseeastrong
increase in the S+core perpendicular temperature during
wave growth and a gradual decreases after wave energy
saturation, consistent with nonresonant behavior. After wave
activity has decayed, the ring anisotropy asymptotes to a
value of ?3, with Tk?250 eVand the O+and S+cores have
anisotropies of ?2 and ?0.5, respectively (not shown).
 Huddleston et al. [1997, 1998] used rings with 5 eV
temperature spreads in their dispersion calculations; how-
ever, we find that the rings experience greater heating in the
early stages of the simulation affecting the overall growth
rate. To better compare the simulated growth rates and
unstable wave modes with linear dispersion solutions, we
use the simulated plasma temperatures during the early
growth phase rather than the input plasma temperatures.
For simulated quantities obtained at WS+t = 64 with ring
Tk= 14 eV we obtain the best fit dispersion solutions to the
simulated growth rate: gm/WS+ = 0.055 at kc/wpS+ = 1.4 and
wr/WS+ = 0.47 with unstable wave numbers between ?1–4
inertial lengths (Figure 5). The simulated wave spectrum
during WS+t = 0–80 is shown in Figure 6; waves are excited
just below the SO2
energy at kc/wpS+ ?1.25–1.5, in agreement with the linear
dispersion analysis predictions. The dominant wave modes
have vph?70–100 km/s. Waves are left-hand polarized and
propagate both parallel and antiparallel to B0with the same
dispersion and amplitudes.
 Instability is driven by the anisotropic ring, which
loses perpendicular kinetic energy and gains parallel kinetic
energy as the waves grow. This behavior is expected for
transverse electromagnetic waves, as they will scatter par-
the parallel direction by the v ? dB force. Kinetic energy and
momentum is conserved between the particles and waves,
and the particles scatter on characteristic surfaces defined by
their perpendicular velocity and the phase velocity of the
1=2) and the perpendicular
+cyclotron frequency and have peak
Figure 3. Dependence of the SO2+peak growth rate on
(a) the ring to background density ratio, (b) the ring parallel
temperature,and (c) theringvelocity.From Huddleston etal.
Table 2. Simulation Inputa
aHere c/vA= 499 and be= Sjbj.
2.44 ? 10?5
COWEE ET AL.: HYBRID SIMULATION OF ION PICKUP WAVES
5 of 9
Johnstone, 1992]. For a ring velocity of 57 km/s and a wave
phase velocity of 80 km/s, the ratio < = vph/vinj= 1.4, and the
particles will scatter along the characteristic surface shown
by the solid line in Figure 7. For < ? 1, particles undergo
pitch angle scattering (dashed line) while those with < ? 1
diffuseinenergy(dottedline), givingupmore oftheirkinetic
energy to the waves.
 Since a range of wave phase velocities is excited by
the instability as the system evolves, the particles will not
2is constant [Huddleston and
(top), S+core (middle), and SO2
during the simulation. While the O+and S+core components
do not show significant change over time, the SO2
clearly scattered. Ions lose energy in the perpendicular
direction, while gaining energy in the parallel direction.
The shape of the velocity space density contours are con-
trolled bytherange ofcharacteristic surfaces alongwhich the
particles may scatter.
 Previous studies of this instability showed that it is
driven by the anisotropy of the ring, and the growth rate
increases with ring velocity and density but decreases with
ring parallel temperature [Wu and Davidson, 1972; Convery
and Gary, 1997; Huddleston et al., 1998]. Indeed, we see in
the simulation that the instability acts to increase the temper-
aturespread aboutthering.Totestthedependenceon growth
rate of the ring parallel and perpendicular temperature,
velocity, and density, we ran an ensemble of simulations
for the range of parameters listed in Table 3.
 Figure 9 (top) shows the simulated growth rate of the
instability for varying initial ring Tkand nr/n0= 1.0. As
+ring (bottom) at five times
Figure 4. Time history of simulated quantities. Shown are
the (a) fluctuating magnetic field energy density, (b) ring
velocity, (c) ring parallel (dotted) and perpendicular (solid)
temperatures, (d) O+core, and (e) S+core parallel (dotted)
and perpendicular (solid) temperatures. Run parameters
given in Table 2.
Figure 5. Solutions to the dispersion relation given by
equation (1) at WS+t = 64. The O+core Tkand T?are 99.3 eV
and 100.4 eV, the S+core Tkand T?are 101.1 and 101.2 eV
and the SO2+the ring velocity is 56.4 km/s (1064.6 eV) and
ring Tkis 13.9 eV.
parallel and antiparallel to B0 with the same dispersion
properties. Run parameters given in Table 2.
Frequency and wave number spectrum of
COWEE ET AL.: HYBRID SIMULATION OF ION PICKUP WAVES
6 of 9
predicted, an increase in the initial ring parallel temperature
reduces the growth rate but perpendicular temperature does
not (not shown). For vr= 60 km/s (1203 eV for SO2
increase of initial Tkgreater than 30 eV reduces the growth
rate by half because the anisotropy of the ring (and therefore
the free energy) is reduced. Thus although we see both the
ring parallel and perpendicular temperatures increasing
during the run (Figure 4c), it is the increasing parallel
temperature which returns the system to stability. Examina-
tion of the first 50 WS+?1shows that the ring parallel
temperature initially increases faster than the perpendicular
temperature, but eventually the perpendicular temperature
increase surpasses it, after which time vrstarts to decrease.
 Figure 9 (bottom) shows the simulated growth rate of
the instability for varying vrgiven initial Tk? 0 and nr/n0=
0.8 (circles) and 1.0 (squares). Also, as predicted by linear
theory, the growth rate of the instability is proportional to the
ring velocity and increases with ring relative density.
Consequently, larger-amplitude waves are generated since
these rings have more free energy to contribute. The
maximum wave energies generated for the ensemble of runs
are shown in Figure 10. Linear theory does not predict the
saturation energies of the waves generated by this instability;
however, Galileo detected SO2
energies of at most (dB/B0)2? 10?3, which the simulation
reproduces for the range of ring velocities and densities
 We next briefly consider ion cyclotron waves gener-
ated at Saturn’s magnetosphere. The Cassini spacecraft
detected ion cyclotron waves with peak energies of 5 ?
10?6< (dB/B0)2< 2 ? 10?4at gyrofrequencies near those
of water group ions (masses of 16–18 amu) on nearly all of
its passes. These waves are believed to originate from
unstable populations of newborn ions from the E-ring, which
the growth of these waves, we simulate the zero-drift ring
instability using the parameters given in Table 4, which are
appropriate for the E-ring (J.S. Leisner, personal communi-
cation, 2006). For simplicity, we consider the ion ring and
core of only one of the several water-group ions which may
be present. Simulation box length is 20 c/wpiwith 512 grid
cells and between 500,000 and 800,000 superparticles.
+ion cyclotron waves with
Figure 7. Characteristicsurfacesalongwithionsscatterfor
an injection velocity of 57 km/s and various phase velocities
equal to 29 km/s (dashed), 80 km/s (solid), and 114 km/s
(dotted). Particles scatter on circles centered on vphwhich
pass through vinj. The ±80 km/s wave phase velocities of the
parallel and antiparallel propagating waves are indicated by
Figure 8. Simulated velocity space density contours of the O+core (top), S+core (middle), and SO2+
ring (bottom) ions at five times during the run. Higher densities are indicated by darker lines. Run
parameters given in Table 2.
COWEE ET AL.: HYBRID SIMULATION OF ION PICKUP WAVES
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 Thesimulatedsaturation waveenergyandgrowthrate
for the varying are shown in Figure 11. As with the ring
instability at Io, the growth rate and wave saturation energy
increase with increasing ring density and ring velocity. The
simulated wave modes have peak frequencies at 0.95Wiand
wave numbers at kc/wpi? 0.6–1 (not shown), in agreement
wave energies and the wave frequencies are within the range
detected by Cassini.
6.Conclusions and Future Work
 In understanding wave generation resulting from
planetary ion pickup into the solar wind, the hybrid simu-
lation has already proved a very useful tool. As we have
shown, it can also be used to study the heavy ion and
perpendicular pickup geometry environments at Jupiter and
Saturn. The one-dimensional hybrid simulation results re-
produce the ion cyclotron waves generated by unstable
populations of newborn pickup ions for plasma and pickup
conditions like those in the Io plasma torus. While warm
plasma linear dispersion analysis has explained the genera-
tion of such waves, it cannot predict the amplitudes of the
waves. Thus the hybrid simulation is an important tool in
diagnosing the relation between wave characteristics and
plasma conditions in interpreting the observed waves.
 Simulated wave dispersion properties agree with the
prediction of linear dispersion theory. Waves are generated
at gyrofrequencies just below the pickup ion gyrofrequency
andatphasevelocities(70–100 km/s) slightlylargerthanthe
ring velocity (57 km/s). Also as predicted, the instability
growth rate increases with increasing ring relative density
and ring velocity but decreases with increasing ring parallel
temperature. As the instability grows, the increasing ring
parallel temperature eventually returns the system to stability
and the increasing perpendicular temperature does not play a
role. Linear dispersion theory cannot predict the saturation
with ring relative density and ring velocity. For a range of
possible pickup ion ring relative densities and velocities in
the Io plasma torus at Jupiter and the E-ring at Saturn, the
simulated waves have energies equivalent to those observed
by the Galileo and Cassini spacecraft.
 In the future we will examine how the generated wave
tobetter constrain theionpickup rates intheIotorus.Wewill
study the behavior of the instability at both parallel and
oblique propagation and examine the effects on the waves of
ionization and dissociation of pickup ions as well as how the
waves propagate away from their source. We will also
calculate the energy exchange rates, allowing us to compare
the role of waves and the efficiency of energy transfer from
newborn ions to background ions by instabilities at Io and at
Table 3. Ensemble Run Parametersa
aTotal ion density is 200/cc and B0is 1700 nT. Normalization is c/wpSO2+=
129 km and WSO2+= 0.40 Hz. Simulation units are c/vA= 114, bc= 0.0028.
Here br= 1.3–859 ? 10?6, Ar= 6541.3–58863.0.
Table 4. E-Ring Run Parametersa
aTotal ion density is 60/cc and B0is 195 nT. Normalization is c/wpOH+ =
121 km and WOH+ = 0.175 Hz. Simulation units are c/vA= 546, bc= 0.016.
Here br= 6.4 ? 10?6, Ar= 2000–3500.
Figure 9. Comparison of the simulated growth rates for
(top) varying initial ring Tkand nr/n0= 1.0 and (bottom)
varying initial ring velocity and density given initial Tk= 0
and nr/n0= 0.80 (circles) and 1.0 (squares). Run parameters
given in Table 3.
field energy densities for ring velocities between 30 and
90 km/s and ring relative densities of 0.8 (circles), 0.9
(diamonds), and 1.0 (squares). Run parameters given in
Simulated maximum fluctuations magnetic
COWEE ET AL.: HYBRID SIMULATION OF ION PICKUP WAVES
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we can better constrain the properties of the background
plasma and the newborn ions and the dynamics and associ-
ated timescales of ion pickup.
Yin, and Peter Gary at Los Alamos National Laboratory for their expertise
for Cassini data. The work was supported by the National Aeronautics and
Space Administration under research grant NAG 5-12022, by a grant from
the Jet Propulsion Laboratory for the analysis of data from the Cassini
Mission, and by summer student funding from the Institute of Geophysics
and Planetary Physics at Los Alamos National Laboratory.
 Amitava Bhattacharjee thanks the reviewers for their assistance in
evaluating this paper.
The authors wish to thank Dan Winske, Lin
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? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
M. M. Cowee, C. T. Russell, and R. J. Strangeway, Institute of
Geophysics and Planetary Physics, University of California, Los Angeles,
Los Angeles, CA 90095, USA. (firstname.lastname@example.org)
D. Winske, Los Alamos National Laboratory, Los Alamos, New Mexico,
Figure 11. Simulated maximum fluctuations magnetic
field energy densities for ring densities between 0.3 and
0.8 and ring velocities of 15 km/s (circles) and 20 km/s
(squares). Run parameters given in Table 4.
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