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Analysis of narrowband emission observed in the Saturn
magnetosphere
J. D. Menietti,
1
S.-Y. Ye,
1
P. H. Yoon,
2
O. Santolik,
3,4
A. M. Rymer,
5
D. A. Gurnett,
1
and A. J. Coates
6
Received 9 December 2008; revised 30 January 2009; accepted 27 February 2009; published 10 June 2009.
[1]Narrowband emission is observed at Saturn centered near 5 kHz and 20 kHz and
harmonics of 20 kHz. This emission appears to be in many ways similar to Jovian
narrowband emission observed at higher frequencies. We analyze one example of this
emission near a possible source region. In situ electron distributions suggest narrowband
emission has a source region associated with electrostatic cyclotron harmonic and upper
hybrid emission. Linear growth rate calculations indicate that the observed plasma
distributions are unstable to the growth of electrostatic harmonic emissions. In addition, it
is found that when the local upper hybrid frequency is close to 2 f
ce
or 3 f
ce
(f
ce
is the
electron cyclotron frequency), electromagnetic Zmode and weak ordinary (Omode)
emission can be directly generated by the cyclotron maser instability. In the presence of
density gradients, Zmode emission can mode-convert into Omode emission, and this
might explain the narrowband emission observed by the Cassini spacecraft.
Citation: Menietti, J. D., S.-Y. Ye, P. H. Yoon, O. Santolik, A. M. Rymer, D. A. Gurnett, and A. J. Coates (2009), Analysis of
narrowband emission observed in the Saturn magnetosphere, J. Geophys. Res.,114 , A06206, doi:10.1029/2008JA013982.
1. Introduction
[2] Our knowledge of planetary plasma waves and radio
emission is filtered by our knowledge of terrestrial emis-
sions. Earth orbiting satellites have revealed two general
types of nonthermal emission, directly generated emission
and mode-converted (indirect) emission. Auroral kilometric
radiation (AKR) is one of the most intense terrestrial radio
emissions and is directly generated by the cyclotron maser
instability [Gurnett, 1974; Wu and Lee, 1979]. Terrestrial
continuum emission and narrowband radio emissions are
believed to be generated indirectly by mode conversion
from intense electrostatic waves [Gurnett,1975;Jones,
1976; Melrose, 1981]. Jovian decametric emission and
Saturn kilometric radiation are believed to be directly
generated by the cyclotron maser instability and are there-
fore counterparts of terrestrial AKR. Similarly, narrowband
radio emissions are present at Jupiter (narrowband kilo-
metric emission or nKOM) and at Saturn (narrowband
emission) with similar characteristics to terrestrial narrow-
band continuum emission and are believed to have a similar
source mechanism.
[3] Narrowband emission observed at Saturn has many
similarities to terrestrial narrow-banded nonthermal contin-
uum emission. Brown [1973] and Gurnett and Shaw [1973]
first reported terrestrial nonthermal continuum emission in a
broad frequency range extending from 5 kHz to <100 kHz.
Gurnett and Shaw [1973] and Gurnett [1975] proposed a
source near the dawnside plasmapause, with a source mech-
anism associated with intense upper hybrid waves. Kurth et
al. [1981] and Kurth [1982] described the details of the
narrow-banded escaping component of continuum emission
providing clear evidence of its narrow-bandedness associated
with intense upper hybrid (UH) resonance emissions. These
emissions are also believed to have a low-latitude source in
the outer plasmasphere and in the magnetopause [Morgan
and Gurnett, 1991]. The source mechanism of this contin-
uum emission and planetary nonthermal continuum emis-
sion has been proposed to be a mode conversion process
occurring near the dayside magnetopause and/or the night-
side plasmapause near the equator. Both linear [e.g., Jones,
1976, 1988; Budden, 1980] and nonlinear [cf. Melrose,
1981; Barbosa, 1982; Fung and Papadopoulos, 1987;
Ronnmark, 1983b, 1989] classes of mode conversion have
been suggested as summarized by Kurth [1992]. All of
these mechanisms involve electrostatic upper hybrid waves.
In the linear mechanism upper hybrid waves refract (in a
steep density gradient) to Zmode waves at a wave normal
angle near 90°.Zmode waves can mode convert to Omode
waves [cf. Horne, 1989, 1990]. The nonlinear mechanisms
are described by the authors as more efficient than the
linear conversion mechanism [Ronnmark, 1989]. For these
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 114, A06206, doi:10.1029/2008JA013982, 2009
Click
Here
for
Full
A
rticl
e
1
Department of Physics and Astronomy, University of Iowa, Iowa City,
Iowa, USA.
2
Institute for Physical Science and Technology, University of
Maryland, College Park, Maryland, USA.
3
Faculty of Mathematics and Physics, Charles University, Prague,
Czech Republic.
4
Institute of Atmospheric Physics, Prague, Czech Republic.
5
Applied Physics Laboratory, Johns Hopkins University, Laurel,
Maryland, USA.
6
Mullard Space Science Laboratory, University College London,
Dorking, UK.
Copyright 2009 by the American Geophysical Union.
0148-0227/09/2008JA013982$09.00
A06206 1of13
processes electrostatic upper hybrid waves coalesce with
lower-frequency waves.
[4] Electrostatic (n+ 1/2) f
ce
waves near the upper hybrid
frequency, f
UH
, are frequently observed in space plasmas
and are often found to be associated with the observation of
loss cone electron distributions at the source [Kurth et al.,
1979a, 1979b]. Ronnmark et al. [1978] have shown that
wave growth rate maximizes when (n+ 1/2) f
ce
f
UH
due to
the nonconvective nature of the instability. Auroral roar
emission is left-hand ordinary (L-O) mode emission ob-
served by ground-based receivers at frequencies from
0.03–30 MHz. These are narrow-banded emissions that
are interpreted as emissions near the first and second
harmonics of f
ce
. In explaining the generation of terrestrial
auroral roar, Yoon et al. [1996, 1998] have shown that the
growth rates of Zmode are greatly enhanced when f
UH
2
=f
ce
2
+
f
pe
2
=(nf
ce
)
2
, where n= 2 and 3. This Zmode can escape into
free space by a linear mode conversion into ordinary (O)or
whistler mode [e.g., Ellis, 1956]. Willes et al. [1998] inves-
tigated a competing theory of nonlinear coalescence to
explain the conversion of Zmode to a freely propagating
mode (cf. Melrose [1991] applied to solar radio emission).
[5] Jovian narrow-band kilometric (nKOM) radio emis-
sion was first reported from the Voyager radio emission data
[Warwick et al., 1979; Kaiser and Desch, 1980]. The
emission is characterized by its obvious narrow band
(50 kHz) and its relatively smooth morphology at fre-
quencies centered typically near 100 –300 kHz. Daigne and
Leblanc [1986] reported the emission to be polarized in the
left-hand circular (LHC) mode when observed by Voyager
from the northern magnetic hemisphere and RH polarized
when observed from the southern. Thus it is consistent with
Omode emission and similar to terrestrial continuum
emission [Gurnett, 1975]. A number of theoretical models
for the generation of nKOM currently exist [cf. Jones, 1987,
1988; Fung and Papadopoulos, 1987].
[6] The first detections of narrowband radio emission
from Saturn were made by Voyager [Gurnett et al., 1981;
Scarf et al., 1982]. Voyager 1 observed a band of emission
near 5 kHz observed between about 3.25 R
S
and 58 R
S
. The
inferred polarization of the emission was L-O mode. Ye et
al. [2009] have recently presented an extensive survey of
narrowband emissions observed in the Saturn magneto-
sphere by the Cassini RPWS instrument, primarily at
frequencies near 5 kHz and near 20 kHz and sometimes
harmonics separated by the local cyclotron frequency. The
emission is observed most intensely associated with storms
of Saturn kilometric radiation and then is seen each rotation.
The typical bandwidth is 1–3 kHz. Ye et al. [2009] have
identified the electromagnetic emission as ordinary (O)
mode. They present direction finding results supported with
observations that locate the sources of the emission off the
magnetic equator near the intersection of the surface of f
ce
and the surface of plasma frequency where (n+ 1/2) f
ce
f
UH
. The emissions originate from the northern and southern
edges of Saturn’s plasma torus at L7 to 10 for 5 kHz or
L4 to 7 for 20 kHz emission. These locations are
consistent with the hypothesis that the emission is similar
to continuum emission observed at Earth [cf. Gurnett and
Shaw, 1973; Morgan and Gurnett, 1991] and at Jupiter
[Gurnett et al., 1983]. Wang et al. [2008] summarize the
observations of narrowband radio emissions by Cassini and
examine the possible association of narrowband radio emis-
sions with a revolving plasma cloud detected by the Mag-
netospheric Imaging/Ion and Neutral Camera (MIMI/INCA)
instrument on board Cassini.
[7] In this paper we examine in some detail an example of
narrowband emission observed by Cassini at Saturn with
center frequency near 10 kHz. The example is associated
with electrostatic cyclotron harmonic (ECH) emission and
probable upper hybrid waves. We determine nonlinear fits
to in situ particle observations and use a linear dispersion
solver to calculate the growth rate of the ECH emissions.
We then apply the cyclotron maser instability to calculate
the growth rates for both the Zmode and Omode. The
results indicate that the Zmode growth rate is many orders
of magnitude higher than the Omode. We speculate on how
Omode narrowband emission may be generated by mode
conversion.
2. Instrumentation
2.1. RPWS
[8] The Cassini Radio and Plasma Wave Science (RPWS)
instrument measures oscillating electric fields over the
frequency range 1 Hz to 16 MHZ and magnetic fields in
the range 1Hz to 12 kHz [cf. Gurnett et al., 2004]. The
instrument uses 3 nearly orthogonal electric field antennas
and 3 orthogonal magnetic search coil antennas, providing a
direction-finding capability. There are 5 receiver systems:
the high-frequency receiver (HFR) covering 3.5 kHz to
16 MHZ; the medium frequency receiver (MFR) covering
24 Hz to 12 kHz; a low-frequency receiver (LFR) covering
1Hzto26Hz;a5-channelwaveformreceiverwhich
operates in either a 1 –26 Hz or 3 Hz–2.5 kHz mode; and
a high-resolution wideband receiver (WBR) that covers two
frequency bands, 60 Hz to 10.5 kHz and 800 Hz to 74 kHz.
The data presented in this study are measured by the HFR
and MFR.
2.2. ELS
[9] The Cassini Plasma Spectrometer (CAPS) is com-
posed of three sensors: the electron spectrometer (ELS), the
ion beam spectrometer (IBS), and the ion mass spectrometer
(IMS). Of importance in this study is the ELS which
contains an 8-detector fan array in a single plane. Each
detector has a 5.2°20°field of view for a total in-plane
field of view of 160°. The instrument measures electron
energy from 0.6 eV to 28,250 eV over a period of 2 seconds
with a resolution of DE/E = 0.17 [cf. Young et al., 2004].
3. Analysis
3.1. Observations and Wave Growth Rate Analysis
[10] As explained by Ye et al. [2009] the Saturn NB
emissions observed most frequently near 20 kHz have
source regions that probably lie on the northern and south-
ern edges of the plasma density torus at Saturn. These are
best observed during Cassini orbits that extend to higher
latitudes. We have isolated an example of this type of
emission near a fortuitous encounter by Cassini of the
probable source region on 24 April (DOY 114) 2007. At
the time, the spacecraft was in a high-inclination orbit,
having crossed the magnetic equator proceeding southward
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at a radial distance of about 6 R
s
and local time of about 3
hours. In Figure 1a we show a plot of a portion of the orbit
in the x-y plane (Saturn solar equatorial coordinates) where
+x is toward the sun in the Saturn-sun plane, and +z is along
the northward spin axis of Saturn. Figure 1b shows this
portion of the orbit in the r-z plane, where r=(x
2
+y
2
)1
=
2.
Figure 1a. A portion of the Cassini trajectory is shown in Saturn solar equatorial (SSQ) coordinates in
the x-y plane.
Figure 1b. The same portion of the Cassini trajectory is shown in the r-z plane.
A06206 MENIETTI ET AL.: NARROWBAND EMISSION AT SATURN
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[11] In Figure 1c we display the wave spectrogram for day
114 of 2007 for the time interval 1500 to 2100 UT. The
frequency axis is linear ranging from 0 to 35 kHz. The white
line near the bottom of the plot indicates f
ce
, while the more
jagged white line above depicts f
UH
. The sharply decreasing
value of f
UH
indicates the proximity of a steep density
gradient. Narrowband emission (NB) is seen indicated by
the arrows. A possible source region of the narrowband
emission is identified near 1745 –1840 over the frequency
range 10 < f<12 kHz. For reasons that will become clear
later we believe this emission is a mixture of Z and Omode.
The emission just above f
ce
is electrostatic electron cyclotron
emission and probably a harmonic emission (indicated with
arrows). We show a close up of the region near a probable
source region of narrowband emission in Figure 2, now
with color bar indicating calibrated electric field spectral
density. Zmode emission has an upper cutoff near f
UH
and O
mode has a lower cutoff near the plasma frequency (f
p
). A
feature identified as upper hybrid emission is indicated in
Figure 2 near 1830 with an upper cutoff near 11.8 kHz. We
estimate a slightly smaller value of f
UH
=11.6kHzat
1834:30, where growth rate analysis will be conducted as
discussed below. At this time f
c
= 3640 Hz, so we calculate
f
p
= 11.03 kHz and f
z
= 9357 Hz, where the latter is the
low-frequency cutoff of Zmode, f
z
=1
2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
f2
cþ4f2
p
qfc
.
These values are consistent with independent determinations
of f
p
using plasma wave sounder data (P. Canu, private
communication, 2008). A shift of f
p
by ±1 kHz has almost
no effect on the growth rate analysis discussed below.
[12] To confirm these wave identifications we show in
Figure 3a the apparent circular polarization measurements
for this emission as calculated from the RPWS instrument,
over a time interval from 17.0 hours to 20.0 hours on day
114. In Figure 3a we show the region identified as Zmode
and Omode narrowband emission. Apparent polarization
recorded by RPWS in the 2-antenna mode refers to the
polarization relative to the antenna plane, and assumes a
direction of arrival perpendicular to the antenna plane (see
Fischer et al. [2008] and Ye et al. [2009] for details). We
note that the emission labeled Zmode and Omode changes
apparent circular polarization from red to blue near 1830 UT.
The polarization of Omode emission is left handed, while
the Zmode in the cold plasma approximation for f
p
/f
c
>1
and f>f
p
is extraordinary and propagation at wave normal
angle of q= 0 is not possible [cf. Gurnett and Bhattacharjee,
2005; Benson et al., 2006]. For f
z
<f<f
p
the polarization of
the mode is LHC at q= 0, and the wave is extraordinary at
q=90°. Since the Saturn Kilometric Radiation (SKR) is
known to be generated as right-hand circular polarization
(RCP), and at this time appears strongly red (+1 on the
Figure 1c. A frequency versus time wave spectrogram for day 114 of 2007 for the time interval 1500 to
2100 UT. The frequency axis is linear, ranging from 0 to 35 kHz. The white line near the bottom of the
plot indicates f
ce
, while the more jagged white line above is f
UH
. Narrowband (NB) emission and
electrostatic cyclotron harmonics (ECH) are indicated.
A06206 MENIETTI ET AL.: NARROWBAND EMISSION AT SATURN
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A06206
color bar; data not shown here), we expect the left-hand
circular polarization of Omode to appear blue on the
spectrogram. We interpret the transition from red to blue
to indicate that the Cassini spacecraft travels through the
source region thus experiencing wave vectors, k,that
reverse direction relative to the local magnetic field pro-
ducing a reversal of the apparent polarization, even though
the actual polarization remains LCP. This is schematically
shown in Figure 3b, where kB< 0 before the spacecraft
encounters the source region, and kB> 0 after. The
Figure 2. A calibrated wave spectrogram showing a close-up of the region near a probable source
region of narrowband emission.
Figure 3a. Apparent circular polarization measurements as calculated from the RPWS instrument over
a time interval from 17.0 h to 20.0 h on day 114. We show the region identified as Zmode and Omode
narrowband emission.
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A06206
apparent reversal of polarization is interpreted, then, as
evidence that the spacecraft traverses the source region.
[13] To investigate the generation mechanism of these
waves we require the electron phase space density (PSD)
distribution. At this time the ELS instrument was only
viewing in one hemisphere covering an approximate range
of pitch angles 100.7°<a< 176.34°. Since the spacecraft is
located at low L-shells (L< 7) and most probably closed
field lines [Connerney et al., 1983], we have assumed that
the data are gyrotropic and can also be mirror-reflected
to the supplemental range of pitch angles, 180°a.In
Figure 4 we show a contour of the electron PSD for the time
interval 1834:28–1834:30 UT, assuming the reflection of
the data as described. The plot includes data for pitch
angles within about 3.7 degrees of the magnetic field line,
and we observe a loss cone for pitch angles less than
about 20 degrees for jV
k
j>110
7
m/s. In Figure 5 we
plot the electron PSD for E< 568 eV, showing a distinctive
electron beam with a center near jV
k
j=410
6
m/s.
[14] We have fitted the observed ELS electron distribu-
tion function contours using a sum of bi-Maxwellians as
follows
fsv?;vk
¼X
S
ns
p3
2w2
?swks
!
1Ds
ðÞev2
?
w2
?sþDs
1bs
ðÞ
"
ev2
?
w2
?sev2
?
bsw2
?s
!#
evkvds
ðÞ
2
w2
ks
ð1Þ
where v
k
and v
?
are the particle velocities parallel and
perpendicular to the magnetic field, respectively; w
k
and w
?
are the parallel and perpendicular thermal velocities,
respectively; v
d
is the parallel drift velocity. The parameters
Dand bdescribe the depth and width of the model loss
cone, respectively, and subscript ‘‘s’’ refers to the plasma
populations or species, such as cold, energetic, etc.
[15] The nonlinear least squares fit to the electron PSD of
Figures 4 and 5 using the functional form of equation (1)
assumes seven populations of plasma: six electron distribu-
tions and a cold plasma ion distribution. The observed
electron distribution warrants these model populations.
The electron populations include a dominant (density) core
plasma, a mid-energy warm plasma, an energetic warm
plasma, a low-density, cool, electron beam traveling both
directions along the magnetic field line, and a very cold
isotropic electron background plasma. The ions are assumed
to be a cold plasma background.
[16] The total density of the plasma was fixed by obser-
vations of the local upper hybrid resonance at the time, f
UH
=
11.6 kHz. In Table 1 we present the fitting parameters
determined for 24 April 2007, 1834:28–1834:30 UT. An
overplot of contours of PSD determined from the data and
from the model is presented in Figure 6.
[17] To determine roots of the dispersion equation and to
calculate the growth rate of the electrostatic plasma waves
resulting from the model distribution function, we have used
a modification of a warm plasma dispersion solver [cf.
Santolik and Parrot, 1996], based on the susceptibility
tensor calculated by the ‘‘waves in homogeneous, anisotropic
multicomponent plasmas’’ (WHAMP) code [cf. Ronnmark,
1983a]. The solver also includes a cold plasma susceptibility
tensor, which we used for the background ion component.
[18] Roots of the dispersion equation and growth rate
calculations of the plasma waves obtained from the
model distribution function using this code are presented
in Figure 7. Growth is seen for fundamental emission
Figure 3b. A schematic diagram depicting the spacecraft at position 1 receiving emission from an NB
source region with apparent left-hand circular polarization (kB< 0). After the spacecraft passes through
the source region the apparent polarization changes to right-hand circular (kB> 0) even though the
actual polarization of the NB emission does not change.
A06206 MENIETTI ET AL.: NARROWBAND EMISSION AT SATURN
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A06206
Figure 4. Contour of the electron distribution for the time interval 1834:28 to 1834:30 UT. The data
have been reflected about a pitch angle of 90 degrees as described in the text. The contour levels are in
units of s
3
/m
6
.
Figure 5. A close-up of the inner region of Figure 4 showing the electron phase space density for
E<568 eV and a distinctive electron beam with a center near V
k
=±410
6
m/s.
A06206 MENIETTI ET AL.: NARROWBAND EMISSION AT SATURN
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A06206
(Figure 7a) and harmonic near 9 kHz (Figure 7b) at the
approximate frequencies and bandwidths of the observa-
tions. For the fundamental emission we show results for
emission near peak wave growth which occurred at a wave
normal angle, q=87.5°(solid). We also show wave
growth at near minimum wave normal angle q= 55.5°
(dotted), which produces a weaker but a more broad-
banded emission. Figure 7b shows the results for emission
near peak growth centered around 9 kHz for q= 88.0°.A
weak growth for upper hybrid/Zmode emission is also
found but not shown, and will be discussed in detail using
a semirelativistic code in the next section. Although an
intense narrow-banded emission is observed centered near
5500 Hz (see Figure 1), no wave growth for this frequency
range was found in the linear dispersion analysis. We
hypothesize that this emission, which falls between har-
monics of f
c
, may be propagating from a nearby source
region. The calculated and model bandwidths of the
emission are listed in Table 2. The bandwidths can be
extended at reduced growth rate by extending the range of
wave normal angles (Dq) in the calculations as seen in
row 2 of Table 2. The loss cone of the mid-energy plasma
is the free energy source for the EC fundamental emission,
harmonic, and Zmode/UH emission. Absence of the
counterstreaming beams has almost no effect on any of
these emissions.
[19] As mentioned above, for this time period we are also
fortunate to have polarization measurements from the RPWS
instrument, so that Zmode and Omode emission can be
better identified. Growth rate calculations of these emissions
require a semi-relativistic treatment, which is beyond the
limitations of a linear nonrelativistic code. In the next section
we treat these emissions using an analytical approach based
on the work of Yoon et al. [1996, 1998].
Table 1. Plasma Distribution Fitting Parameters
Density
a
(%) W
k
(eV) T
?
/T
k
(eV) V
d
(eV) Db
Cold background 2.0 0.063 1.0 0 1.0 0.0
Core 58.5 83.19 0.568 0 1.0 0.0
Mid-energy 22.0 386.2 1.23 0 1.0 0.0
Energetic 11.5 4677. 1.134 0 0.187 0.0167
Beam-dist. 3.0 6.079 0.464 42.42 1.0 0.0
Beam-dist. 3.0 6.079 0.464 42.42 1.0 0.0
Cold ions 100 — — — — —
a
Total density is 1.508 cm
3
.
Figure 6. An overplot of contours of PSD determined from the data and from the model described by
equation (1) with parameters from Table 1.
A06206 MENIETTI ET AL.: NARROWBAND EMISSION AT SATURN
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A06206
3.2. ZMode and OMode Growth Rate Calculations
[20] To determine the temporal growth/damping rates for
magnetoionic (cold-plasma) modes under weakly relativis-
tic formalism, we first discuss the dispersion relation for
cold-plasma high-frequency modes. The discussion is sim-
ilar to that given by Stix [1992] or by Benson et al. [2006].
The theoretical formulation is given as follows: First, the
indices of refraction for X/Zand O/Wmodes (Xis the
extraordinary mode and Wis the whistler mode) are given
by
N2
X¼1w2
p
wwþtW
ðÞ
;N2
O¼1tw2
p
wtwWcos2q
ðÞ
;ð2Þ
respectively, where
t¼sþffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
s2þcos2q
p
w2
pw2
w2
pw2
;s¼wWsin2q
2w2
pw2
;ð3Þ
and the frequency ranges for X/Z and O/W modes are
specified by
wX<wfast XmodeðÞ;wZ<w<wres
ZZmodeðÞ;
wp<wfast OmodeðÞ;0<w<wres
WWmodeðÞ:ð4Þ
Here the various cutoff and resonance frequencies are
defined by
wX¼1
2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
W2þ4w2
p
qþW
;wZ¼1
2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
W2þ4w2
p
qW
;
wres
Z¼1
ffiffiffi
2
pw2
pþW2þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
w2
pW2
2þ4w2
pW2sin2q
r
"#
1=2
;
wres
W¼1
ffiffiffi
2
pw2
pþW2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
w2
pW2
2þ4w2
pW2sin2q
r
"#
1=2
:
ð5Þ
We plot the square of the index of refraction versus
normalized frequency (w/W) for these modes for a range of
Figure 7. Real frequency (bottom plots) and growth rate (top plots) obtained from the linear dispersion
analysis for the (a) fundamental and (b) harmonic emission centered near 9 kHz. Fundamental emission
near peak growth at wave normal angle, q= 87.5°(solid), and weaker but more broadbanded emission for
q= 55.5°(dotted) are shown. Harmonic emission in Figure 7b is calculated for q= 88.0°.
Table 2. Comparison of Observed and Model Emissions
EC Fundamental (Hz) EC 1st Harmonic (Hz)
Observed bandwidth (Hz) 3650 – 4800 8500 – 9800
Calculated bandwidth (Hz) Dq3650 – 4045 (55.5°– 87.5°) 8315 – 9970 (88.0°– 89.5°)
A06206 MENIETTI ET AL.: NARROWBAND EMISSION AT SATURN
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wave normal angles q=5°,45°, and 85°in Figure 8 for
w
p
/W= 3.029 (as determined above). We do not explicitly
consider the W mode in this work. Note that the index of
refraction curve for the Zmode and Omode at q=5°are
nearly coincident at w=w
p
.
[21] Next, on the basis of the formalism described in the
past by Yoon et al. [1996, 1998], the growth rate for Xand O
modes are given, respectively, by
gX¼w2
p
w
p2
RXX
1
s¼0 QsWwðÞ
Z1
1
dmQX
suþ;mðÞ
þQwsWðÞQ1m2
s
Z1
ms
dmX
þ;
QX
su;mðÞ
!;
gO¼w2
p
w
p2
ROX
1
s¼0 QsWwðÞ
Z1
1
dmQO
suþ;mðÞ
þQwsWðÞQ1m2
s
Z1
ms
dmX
þ;
QO
su;mðÞ
!;
ð6Þ
where
QX
su;mðÞ¼ t2
t2þcos2q
u21m2
ðÞ
uNXmcos qjj
w
WKXsin qþcos q
tcos qNXumðÞ
JsbðÞ
bþJ0
sbðÞ
2
u@
@uþNXucos qmðÞ
@
@m
fu;mðÞ:
QO
su;mðÞ¼ 1
t2þcos2q
u21m2
ðÞ
uNOmcos q
jj
w
WKOsin qcos qtcos qNOumðÞ½
JsbðÞ
bþcos qJ0
sbðÞ
2
u@
@uþNOucos qmðÞ
@
@m
fu;mðÞ:
ð7Þ
and u=p
mecis normalized momentum and m=pz
pis the
cosine of the pitch angle.
[22] Various quantities that appear in (6) and (7) are
defined by
u¼Nsmcos qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
N2
sm2cos2qþ2sW
w1
s;
ms¼ffiffiffi
2
p
Ns
cos q1sW
w
1=2
;b¼w
WNssin qu1mðÞ
1=2;
KX¼w2
p
w2
pw2
Wsin q
wþtW;KO¼w2
p
w2
pw2
tWsin q
tw Wcos2q;
TX¼cos q
t;TO¼ t
cos q;
RX¼1þ
w2
pt2w2w2
pcos2q
w2wþtWðÞ
2sin2q
t2cos2q
t2þcos2q;
RO¼1þ
w2
pcot2qt
2w2
pw2
pcos2q
w2tw Wcos2qðÞ
2
t2cos2q
t2þcos2q:
ð8Þ
[23] In order to facilitate the analytical calculation of the
growth rate of Zmode and Omode we introduce a
functional form different from that of equation (1) for the
electron distribution function as follows:
fu;mðÞ¼
1
A"r0
p3=2a3
0
eu2=a2
0þrl
p3=2a3eu2=a2
1þDtanh u2m2
0
d2
þrb
p3=2a2
?ak
eu21m2
ðÞ
=a2
?eumu0
ðÞ
2=a2
kþeumu0
ðÞ
2=a2
k
#;
A¼rl1þDdZ
1=d
0
dx tanh x2x2
0
0
B
@1
C
Aþ1rl
r0¼1rlrb;x0¼m0
d
ð9Þ
where a
0
and aare the normalized thermal velocities of the
background and energetic populations, respectively. We
define m
0
= cos (q
L
) where q
L
is the loss cone. The
parameters dand Ddetermine the width and depth of the
loss cone. This functional form incorporates a core
distribution, r
0
, energetic or loss cone population, r
l
, and
beam components, r
b
.
[24] The parameters obtained for the functional form of
equation (1) can be translated into the dimensional parame-
ters of the model distribution function (9). The core electrons
are characterized by thermal velocity, v
T
= 4.63 10
6
m/s.
This is equivalent to a
0
0.0145. The loss cone electrons
have thermal speed 1.72 10
7
m/s, which gives a0.0573.
The number density of the energetic loss-cone electrons
versus the total electrons is about 0.223. The loss-cone angle
q
L
is about 20 degrees, which means m
0
= cos(q
L
)0.9397.
The loss-cone depth is characterized in the model distribu-
tion by D3. The beam drift speed is 3.727 10
6
m/s,
which means u
0
0.0124. The beam thermal speed
(defined in parallel direction) is 1.16 10
6
m/s, which makes
Figure 8. The square of the index of refraction versus
normalized frequency for the X(extraordinary), W(whistler),
O, and Zmodes for a range of wave normal angles (5°,45°,
and 85°). Note that the Oand Zmodes are nearly coincident
for small wave normal angles (q]5°).
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a
k
0.0039. The beam anisotropy factor is T
?
/T
k
0.529,
so that a
?
=ffiffiffiffiffiffiffiffiffiffiffi
0:529
pa
k
0.0028. Finally, the beam density
defined with respect to the total density is 6.445 10
3
times 2. In Figure 9 we plot the model electron distribution
without the core component, and in Figure 10 in 2-D we
plot contours of the distribution including the core
population, for direct comparison with Figure 4.
[25] Results of the growth rate calculations based upon
the model distribution and input parameters are shown in
Figures 11 and 12. Figure 11 shows the contours of Zand
Omode growth rates against the propagation angle q
(Figure 11, left) and normalized frequency w/W(Figure 11,
right).
[26] Figure 12 (left) is a combined plot of growth rate
contours for Zand Omodes. Note the Zmode emission is
narrowbanded. Figure 12 (right) shows the peak growth
rates for Oand Zmode versus w/W. The vertical axis is in
logarithmic scale, which shows that the Omode growth rate
is many orders of magnitude lower than that of the Zmode.
However, Zmode is a trapped mode that cannot readily
escape the source region, unless it converts to Omode.
Therefore, satellite observation of Omode may be locally
generated Zmode that has converted to Omode [cf. Yoon et
al., 1998].
4. Discussion and Summary
[27] Next to Saturn kilometric radiation (SKR), Saturn
narrowband emission is perhaps the most common and
intense of the radio emissions observed at Saturn. In this
study we have isolated an example of this emission at
10 kHz near a fortuitous encounter by Cassini of a
probable source region, and we study the possible wave
generation mechanisms. For this case we have been fortu-
nate to obtain electron phase space densities with a suffi-
cient pitch angle distribution for analysis. The narrowband
emission is commonly associated with ECH and upper
hybrid (UH) emission. We perform a nonlinear least squares
fit of the observed electron distribution to a sum of
Maxwellians (equation (1)) and use the WHAMP dispersion
solver to show that a loss cone distribution is the free energy
source for the ECH emission. In order to estimate the
emission gain for the ECH emission we note that the
fundamental EC emission is 25 dB above background,
and the group velocity at the frequency of peak growth rate
is 1.1 10
6
m/s. The path length required to obtain this
gain is 350 km. These waves are propagating at oblique
angles with respect to the magnetic field (20°) at frequen-
cies near maximum growth.
[28] In addition to the analysis of growth of the ECH
and UH emission, we use the theory of the cyclotron
maser instability and a tractable analytic model of the
electron distribution function (equation (9) and Figures 9
and 10) to calculate the wave growth rate for both Zmode
and Omode narrowband emission. This is possible be-
cause, as discussed by Yoon et al. [1998], when the local
upper hybrid frequency is in close vicinity to 2 f
ce
or 3 f
ce
,
harmonic Zmode emission growth rate can be exceedingly
high. Our results indicate that the Zmode emission has a
peak growth rate that is many orders of magnitude larger
than the Omode (Figure 12). To account for the observed
Omode narrowband emission seen in Figures 1c and 2 we
postulate a mode conversion from Zmode to Omode near
the satellite location at 1835 UT. Using the measured
plasma parameters for this event we see from Figure 8 that
the dispersion curves for the Zmode and Omode are
nearly coincident for a wave normal angle of 5°for each
mode. These results therefore indicate that a likely source
of the observed narrowband emission is mode conversion
of Zmode to Omode near the density gradient (indicated
by the falling magnitude of f
UH
seen in Figures 1c and 2)
Figure 9. A 3-D plot of the model electron distribution
function that corresponds to the functional form of
equation (9) with the fitting parameters listed in the text.
Note the general characteristics of a loss cone and low-
energy counterstreaming beams.
Figure 10. A 2-D plot of the model distribution function
based on equation (9) for comparison to Figures 4 and 5.
The contour levels are again in units of s
3
/m
6
.
A06206 MENIETTI ET AL.: NARROWBAND EMISSION AT SATURN
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where the index of refraction of the two modes match.
Refraction of Zmode to small wave normal angles due to
the density gradient allows the index of refraction to
approach that of the Omode and facilitate mode conver-
sion to Omode (NB) emission.
5. Conclusions
[29] The generation of ECH and UH emissions observed
near source regions of narrowband emission can be
explained by loss-cone free energy directly observed in
the electron plasma pitch-angle distributions. Our results are
consistent with the indirect generation of electromagnetic
narrowband emission. The observed electron distribution is
unstable to the direct generation of Zmode emission, which
can then mode convert to Omode narrowband emission
near the strong density gradient [cf. Yoon et al., 1998]. The
Saturn narrowband emission is similar in morphology to
terrestrial continuum emission and to Jovian nKOM emis-
sion. The results of the analysis and theory presented
suggest its feasibility at other planets. It will be important
to test this scenario for other encounters with source regions
of narrowband emission, especially for conditions of vary-
ing ratios of f
p
/f
ce
.
[30]Acknowledgments. We thank J. Hospodarsky for clerical assis-
tance. We also thank P. Canu for RPWS Sounder data analysis. This work
was supported by Jet Propulsion Laboratory contract 1356500 to the
University of Iowa. P. H. Yoon acknowledges NSF grants 0535821,
0638638, and 0829309.
[31]Amitava Bhattacharjee thanks Jean-Louis Le Mouel for his assis-
tance in evaluating this paper.
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