GEOPHYSICAL RESEARCH LETTERS, VOL. 10, NO. 8, PAGES 623-626, AUGUST 1983
OBSERVATIONS ON GEOS-1 OF WHISTLER MODE TURBULENCE GENERATED BY A GROUND-BASED VLF TRANSMITTER
T. Neubert
Danish Space Research Institute, Lundtoftevej 7• DK-2800 Lyngby• Denmark
F. Lefeuvre• M. Parrot
LPCE/CNRS• 45045 Cedex• Orleans, France
N. Cornilleau-Wehrlin
CRPE/CNET•921311ssy-les-Moulineaux• France
Abstract. Signals launched by the NLK Jim
Creektransmitter in Alaska on 18.60 and 18.65 kHz
have been observed on GEOS-1. Data for one pass
over Alaska on June 11, 1977, are presented
here. The peak amplitude of the signals is ~5
pT (0.6 mV/m), which is received when the satellite
is close to exact conjugacy at 7500 km altitude.
While the weaker signals received at some distance
from conjugacy behave as expected from linear
theory, the stronger signals received closer
to conjugacy have features which indicate that
some non-linear process is active. These features
are: 1) a turbulent electric frequency spectrum
2) an increased electrostatic character of the
waves. The threshold field amplitude of the
supposed (but unidentified) non-linear interaction
is ~1 pT.
Introduction
Turbulence of ground based VLF transmitter
signals received by low altitude satellites
at conjugacy in the opposite hemisphere has
been analyzed in Edgar [1976] . Here the
observations are interpreted in terms of linear
propagation effects, where large wave normal
angles produce large Doppler shifts induced
by the satellite motion. In the present case,
the satellite and the transmitter are in the
same hemisphere.
The observations are presented in a preliminary
report by Cornilleau- Wehrlin et al. [1978].
They observe a puzzling feature, namely a
depression in the cB/E ratio, where c is the
velocity of light in vacuum, and B, E the magnetic
and electric field amplitudes of the whistler
waves. This occurs for high field values in
the part of the orbit where the satellite is
close to conjugacy with the transmitter. The
depression is rather abrupt, the ratio falling
to 1/3 of the values found in the border regions.
It is the purpose of the present paper to
extend the analysis and discussion of Cornilleau-
Wehrlin et al. [1978]. First the experimental
set up is described, and the turbulent nature
of the electric signal in the part of the orbit
coinciding with the depression in the cB/E ratio
is demonstrated. Then calculations of the
polarization, ellipticity, and wave normal
direction are presented. Finally the refractive
index and the propagation characteristics are
discussed along with the amplitude calibration
of the wave experiment. It is concluded that
linear theory is inadequate for describing the
observations. Some suggestions are made for
further studies.
The Set Up
The Jim Creek signals are recorded by the
Swept Frequency Analyzer system (SFA) on GEOS-1.
Six SFA's operate as heterodyne systems controlled
by a single frequency synthesizer. The analyzers
select bands of 300 Hz in the frequency range
150 Hz to 77 kHz in 256 steps of 300 Hz, thus
giving a complete coverage. The sampling frequency
is 1488 Hz, and the bandwidth is determined
by a highpass filter at 150 Hz and a low pass
filter at 450 Hz. When recording the Jim Creek
signals the SFA's were connected to three magnetic
and three electric sensors. The sensors are
parallel to the axis of a cartesian coordinate
system with x, y in the spin plane and z along
the spin axis. A more detailed description of
the GEOS wave experiment is found in S-300
Experimenters [1978].
The SFA swept 4 steps around the transmitted
frequencies, recording 0.69 s on each step (1024
samples). This scheme was followed in order
to enable the detection of triggered emissions.
Such emissions were, however, not observed,
and the present paper uses SFA data from one
step only, covering the frequency range 18.5
to 18.8 kHz.
The Jim Creek transmitter emits coded
information switching between 18.60 and 18.65 kHz.
The minimum duration on either frequency is
10 ms.
Two types of spectral analysis have been
performed. One is a Fourier transform of the
1024 samples from each SFA, producing amplitude
spectra with 1.4 Hz frequency resolution for
each of the 6 wave field components. A spectrum
calculated from a 0.69 s interval will then
contain both frequency components including
some sidebands. However, the strongest component
in a spectrum will be on either 18.60 or 18.65 kHz
if the rays reaching the satellite behave linearly,
and the Doppler shift induced by the satellite
motion is negligible.
The other method consists of the construction
Copyright 1985 by the American Geophysical Union. of 3 x 3 spectral matrices of the magnetic field
components, calculated from time averaged modified
Paper number 5L0571. periodograms [Welch, 1967]. Depending on the
0094-8276/85/005L-0871505.00 time stationarity of the signal, intervals of
623
624 Neubert et al.' Observation of Whistler Mode Turbulence
0.52 to 0.60 s have been analyzed with a 23 Hz
frequency resolution. This makes it impossible
to discriminate between the two emitted
frequencies. Since analysis with a better frequency
resolution gives a poorer signal to noise ratio,
it seems safer to assume that the waves on the
two frequencies have the same propagation
characteristics allowing them to mix in the
analysis.
Observations
The rms values of the magnetic and electric
field amplitudes can be calculated from the
amplitude spectra. They are shown versus time
in Figures la and lb. At 7.30 UT the satellite
is approaching the Earth at 10.000 km altitude,
and at 7.55 UT it is located at 5.000 km altitude,
still descending (see Figure 1 of Cornilleau-
Wehrlin et al., 1978). At 7.45 UT the satellite
is at almost exact conjugacy at 7.500 km altitude
as calculated from an Olson-Pfitzer model [Kosik,
1978 ].
While the electric signal varies relatively
smoothly, the magnetic signal has large amplitude
variations with conspicuous peaks around 7.36
and 7.42 UT. Figure lc shows the ratio cB/E
as function of time. The ratio increases between
7.33 and 7.37 UT as the Jim Creek signal rises
out of the noise. However, the ratio drops abruptly
at 7.37 UT from ~4.5 to •2 and decreases further
until 7.52 UT where it suddenly rises from ~1
to •3. An exception is the peak at 7.42 UT.
For parallel propagating whistler mode waves
the refractive index is given by cB/E. The values
shown in Figure lc are, within the depression
region, a factor 4-6 times lower than expected
from theory (see Discussion).
The occurrence of the frequency of the maximum
amplitude component in each of the ~700 spectra
calculated from 7.25 to 8.00 UT is shown in
5.0
0.0
I I I ..I. . I I
-
-
I , I I J I
- cB/E -
_ _
I , I , I I
o.o
0.6
E
E
8.0
c}
o.o
7.30 7.40 7.50 8.00
UNIVERSAL TIME (hr)
Figure 1. a) Amplitude of the magnetic field
b) amplitude of the electric field c) cB/E.
18.70
..• 18.65
:• 18.60
18.55
18.70
,--, 18.65
:• 18.60
18.55
i ' i , i
Bx
I i I 4 I I •
7.30 7. 0 7.50 8.00
UNIVERSAL TIME (hr)
Figure 2. Occurrence of strongest frequency component
Figure 2. From 7.37 to 7.52 UT a few spectral
points on Bx appear in between the transmitted
frequencies, signifying a modest state of
turbulence.
The signal on Ey behaves different from that
on Bx in the period 7.37 to 7.52 UT, which
coincides exactly with the period of depression
in cB/E. The signal is very turbulent, the maximum
spectral component appearing anywhere from 20 Hz
below the lower to 30 Hz above the upper of
the two transmitted frequencies.
The noisy nature of the signals is illustrated
further in Figure 3. Spectra averaged over 5
min are shown for three time intervals: 7.32
- 7.37 UT (not noisy), 7.47 - 7.52 UT (noisy),
and 7.53 - 7.58 UT (not noisy). The spectra
from Bx and Ey are similar in the periods that
are not noisy, and resemble spectra calculated
from simulated signals. In the noisy period,
the Bx spectrum is slightly changed, while the
Ey spectrum is very turbulent.
The double peaks on Bx and Ey with a ~5 Hz
frequency separation seen on the spectra from
7.32 - 7.37 UT are believed to be an effect
caused by two raypaths leading to the satellite
in the 5 min period. The wave normal angle of
the rays at the location of the satellite differ
and the rays experience different Doppler shifts.
Inspection of individual spectra and Figure
2 indicate that the two ray paths exist
simultaneously.
As a final point in this section the
ellipticity, polarization, and wave normal
direction will be investigated. A detailed analysis
is not possible since measurements of the Earth
magnetic field Bo, and the plasma frequency
fp do not exist. Still, some indications can
be obtained from model estimates. Thus B_o is
estimated from a Magsat MGST(6/80) model [Langel
et al., 1980], while fp is taken from Chiu et
al. [ 1979].
The 4 step cycle of the SFA has a 2.75 s
period, while the satellite spin has a 5.7 s
period. The satellite then rotates 43.4 ø during
one step, while the orientation of the xy-antennas
is shifted 173.8 ø each 4 step cycle. For a signal
elliptically polarized in the xy plane, this
results in an amplitude modulation with a period
of 80 s.
Neubert eta!.' Observation of Whistler Mode Turbulence 625
The ellipticity of the magnetic wave field
in the xy plane at the upper transmitted frequency
is found from the rms amplitudes measured on
Bx and By in a 14 Hz band at 18.65 kHz. Using
the fact that the magnetic field of a plane
whistler mode wave is circularly polarized in
the plane perpendicular to the wave normal k,
the angle of k to the satellite spin axis can
be found. The result is the curve marked x,
shown in Figure 4a. The points connected with
dashed lines suffer from uncertainties due to
irregular fluctuations in Bx/By. The same procedure
can be used with the signals on Bx and Bz. The
result is the curve marked o in Figure 4a. The
analysis is confined to the time interval 7.33
to 7.55 UT where the Jim Creek signal is
predominant.
While the angle to the spin axis may be
calculated by the two methods outlined above,
the azimuth angle is still unknown. The discrepancy
shown in Figure 4b is then just an indication
of whether the wave field averaged over 40 s
may be considered as plane. This seems to be
the case around 7.42 UT and from 7.48 to 7.55 UT.
The results of Figure 4 are to be compared
with the angle of B_o to the spin axis of the
satellite At 7 30 UT the angle is 75 ø decreasing
to 71 ø at 7.51 UT. Thus, the smallest possible
wave normal angle to B_o for the periods of plane
waves can be estimated to be ~5 ø at 7.42 UT
and ~15 ø from 7.48 to 7.55 UT.
The polarization of the magnetic field changes
at 7.48 UT which is still in the period of
turbulence. This behaviour is different from
that of the electric field polarization as measured
in the xy plane which is well defined during
the whole period where the Jim Creek signal
is dominant. The average ellipticity is around
0.5 and unaffected by the degree of turbulence.
The polarization P and ellipticity E have
been estimated from 3 x 3 spectral matrices
of the magnetic field components [Samson and
Olson, 1980] at 66 time intervals in the period
7.32 to 7.53 UT. The wave field can be regarded
as that of one plane wave if P > 0.9, while
the ellipticity of plane whistler mode waves
is expected to be close to 1 [Lefeuvre et al.,
1982].
7.32-7.37 UT 7.47-7.52 UT ]'.53-7.58 UT
...... , '" ''" .... ,,,,,,,,,,,,,,,,,,,,,
i i .... , .... ! .... ' .... i .... , .... i ! .... , ........ , .... ! .... , .... i
18.5 18.6 18.7 18.5 18.6 18.7 18.5 18.6 18./' kHz
Figure 3. Averages of spectra (normalized relative to
peak amplitude).
Only 7 cases have P > 0.9. These are grouped
around 7.36, 7.42 and 7.48 UT, and coincide
with three of the peaks in the magnetic field
amplitude (Figure la). Note also that they fall
within the regions of well determined polarization
of Figure 4a (solid lines). Furthermore, in
16 cases the analysis shows that the wave field
is left hand polarized, in contradiction to
theory, which predicts right hand polarization.
In Lefeuvre et al. [1982] it was concluded
that the wave normal direction derived from
a spectral analysis is believable only for E > 0.6.
Just one case, at 7.36 UT, meets this requirement.
Here a one peak Wave Distribution Function [Storey
and Lefeuvre, 1979] is found, and the angle
of k to the satellite spin axis determined by
Means method [Means, 1972] is 73 ø , in reasonable
agreement with the results in Figure 4a.
Two peak WDF's are obtained at 7.32 and 7.41 UT.
The solutions are acceptable since the angles
of the wave normal to the spin axis derived
from the measured matrices (by Means method)
are almost identical to the ones found from
the matrices reconstructed from the WDF solutions.
Also a two peak WDF is consistent with the low
value of P and E found in these cases.
Discussion
The refractive index p of whistler mode waves
may be expressed on the form: • - f /•f(f cose-f)
1- p c '
Here f is the wave frequency, fD,fc the electron
plasma and gyro frequencies,-and e the angle
k,B o. With model estimates of fc [Langel et
al., 1980] and fp [Chiu et al., 19791, refractive
index estimates are calculated and listed in
Table 1 for 8 = 0 ø and 60 ø at three times. In
the table is also listed the maximum expected
Doppler shift &fm = kVs/2•r' where v s is the
satellite velocity.
Outside the depression region, the measured
frequency shift is ~+5 Hz (Figure 3), which
is consistent with the model estimate of the
Doppler shift.
The refractive index P2 of electromagnetic
waves is given by: •2 = cB/E• where E• is the
component of the electric field perpendicular
to the wave normal k. For parallel propagating
waves (• = 0 ø) E• = E, and a plot like the one
in Figure lc would in this case be a direct
measure of the refractive index. In general
• • 0 ø and as E,,/E• = sin•/(cos•-f/f c), the
ratio cB/E will in general be smaller than the
refractive index.
The refractive index for parallel propagation
expected from the model is a factor 2 larger
626 Neubert et al.: Observation of Whistler Mode Turbulence
Table 1. Model estimates for three
satellite locations.
Time (UT) 7.35 7.45 7.55
Altitude (km) 9300 7200 5000
f (kHz) 260 300 370
•c(kHz) 80 120 200
•1 (9=0ø) 7.8 7.0 6.5
•1 (9=6øø) 13.1 10.9 9.6
v s (km/s) 7;7 8.9 10.1
Af.(8=O ø) (Hz) 3.6 3.7 3.9
n•(9=60 ø) (Hz) 6.1 5.8 5.8
than the ratio cB/E of Figure lc in the periods
bordering the depression, and a factor 4-6 larger
within that region. The model parameters are
thought to be reasonable since June 11 was in
a magnetically quiet period with Kp < 2 during
the previous 24 hours, and GEOS was inside the
plasmapause. Several possibilities are then
open: the amplitude measurements are erroneous,
the waves propagated with very oblique wave
normals, and/or the signals behave non - linearly.
The possibility of errors in the calibration
of the electric antennas is discussed in Neubert
et al. [1982], which concludes that the electric
field amplitudes may be overestimated by a factor
2 to 6, and in Lefeuvre et al. [1982], which
arrive at a factor 3.5.
A factor 2 larger cB/E ratio seems to be
consistent with refractive index estimates in
the regions bordering the depression and at
7.42 UT. With the results of the ellipticity
and polarization study it is then concluded
that the signals in these regions behave linearly.
Within the depression region the high degree
of turbulence and the electrostatic character
of the waves are consistent with waves propagating
with wave normals very close to the resonance
cone, the frequency being Doppler shifted by
the satellite motion (turbulent propagation
vector spectrum). However, it is not possible
to identify the responsible scattering mechanism
since the data set is rather limited. The wave
amplitudes are so large that even local non-linear
wave-wave interactions may be possible [Neubert,
1982•. If this is the case the threshold field
read from Figure 1 is ~1 pT.
We suggest that ISEE-1 and -2 VLF data for
passes near the Aldra Omega station be analyzed.
It should be possible to derive the refractive
index for the 10.2 kHz transmissions.
Acknowledgments. We wish to thank T. Bell
for his helpful suggestions and the information
on the plasma pause position. This work was
supported in part by the Danish Space Board,
Danish Natural Science Research Council, and
the Otto M•nsted Foundation.
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