ARTICLE IN PRESS
Journal of Atmospheric and Solar-Terrestrial Physics 69 (2007) 1739–1746
www.elsevier.com/locate/jastp
Upstream whistler-mode waves at planetary bow shocks:
A brief review
C.T. Russell
Institute of Geophysics and Planetary Physics and Department of Earth and Space Sciences, University of California,
Los Angeles, CA 90095-1567, USA
Received 9 August 2006; received in revised form 15 November 2006; accepted 2 February 2007
Available online 4 July 2007
Abstract
Upstream whistler-mode waves appear to be present in front of all collisionless shocks. Because the whistler-mode group
velocity exceeds its phase velocity over the frequency range in which the phase velocity increases with frequency, interesting
alterations of polarization and frequency spectrum occur in the observer’s reference frame. Landau resonance also plays a
role in the wave properties. The source of these waves is the shock but the mechanism for wave generation is not yet
understood.
r 2007 Elsevier Ltd. All rights reserved.
Keywords: Upstream waves; Planetary bow shocks; Whistler-mode waves
1. Introduction
Upstream whistler-mode waves on magnetic field
lines connected to the bow shock were discovered by
OGO-5, one of the first spacecraft to obtain high
cadence magnetometer data upstream of the Earth’s
bow shock (Russell et al., 1971). At 1 AU these
waves are close to 1 Hz in the satellite (and Earth’s)
reference frame, i.e. the Pc-1 frequency band. They
are often called simply 1 Hz waves. However, as we
will see in this review, these narrow-band waves
do not pass through the Earth’s magnetosheath and
do not enter the magnetosphere. Thus they do
not contribute to the complex morphology of Pc-1
waves as observed in the magnetosphere and on the
Tel.: +1 310 8253188; fax: +1 310 2063051.
E-mail address: ctrussell@igpp.ucla.edu
1364-6826/$ - see front matter r 2007 Elsevier Ltd. All rights reserved.
doi:10.1016/j.jastp.2006.11.004
ground. Instead magnetospheric Pc-1 waves appear
to be associated with ion cyclotron resonance with
magnetospheric ions. As we shall see, the upstream
whistlers are clearly right-handed waves, generated
at the bow shock, damping as they propagate
upstream in the solar wind.
Since they were discovered there have been
several proposed hypotheses for their generation.
Fairfield (1974) was one of the first to undertake a
comprehensive study of these waves. He demonstrated that the waves propagated in the oblique
whistler mode, and that Doppler shifting significantly affected the observed frequency of the waves,
their polarizations and their spectral densities. He
hypothesized that the waves were generated at the
bow shock by some unspecified mechanism. Later
studies by Rodriguez and Gurnett (1975) and
Greenstadt et al. (1981) suggested that these waves
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C.T. Russell / Journal of Atmospheric and Solar-Terrestrial Physics 69 (2007) 1739–1746
1740
Bz
-20
By
10
0
-10
0
Bx
Venus
July 12, 1980
Bz
By
Bx
Mercury
March 29, 1974
20
-9.0
-10.5
6.0
4.5
3.0
0
10.5
0
|B|
|B|
6.0
20
3.0
0
2102:00
2103:00
-0.8
-2.4
Bx
5.6
By
1139:00
0.2
0.0
-0.2
0.8
0
0.2
|B|
5.6
|B|
1138:00
Saturn
August 30, 1981
0.0
4.0
4.0
2.4
0
2126:00
1137:00
Bz
By
Bx
Earth
November 7, 1977
Bz
0
2104:00
0.0
0.2
0.0
2127:00
2128:00
20:55
21:45
Fig. 1. Time series of components, Bx, By, Bz and jBj in solar orbital coordinates with X toward the Sun, Y in the direction opposite
planetary motion and Z along the (northern) orbital pole illustrating the occurrence of upstream whistler mode waves at Mercury, Venus,
Earth and Saturn.
are subject to strong damping in the shock foot
and unlikely to reach deep into the foreshock
where they are observed. Sentman et al. (1983)
addressed this problem by proposing that large
pitch-angle elections backstreaming from the
shock could amplify the waves in the solar wind.
However, this mechanism could not predict all the
properties of the upstream whistlers. In a series of
papers, D. Orlowski and co-workers (Orlowski
et al., 1990, 1993; Orlowski and Russell, 1991)
reopened the study of these waves and concluded
that the Fairfield hypothesis was indeed correct.
An intriguing feature of the upstream whistlers is
their variable spectral shape and polarization.
Sometimes the waves have an extremely sharp
upper cutoff frequency. Orlowski et al. (1993)
proposed that the observed spectral shape could
be explained by a large Doppler shift and the
dispersive properties of a broadband (Do/oE1)
whistler-mode wave. Orlowski et al. (1995) followed
this suggestion with a detailed analysis of the
spectral properties of the waves and the nature of
the growth and damping that various particles
distributions would produce. They found that the
wave properties were inconsistent with those predicted by the Sentman et al. (1983) hypothesis and
that the waves damped with distance from the shock
rather than growing as Sentman et al. (1983)
predicted. The end result of this analysis was that
the waves must be generated at the shock and
propagate upstream but they did not identify the
instability that generates the whistler-mode waves.
This problem is yet unsolved today.
Our instruments have progressed much in the last
decade and we now have new missions that could
contribute to the solution of this problem such as
Cluster, THEMIS, STEREO (in interplanetary
space), Venus Express (at Venus) and in the
more distant future the Magnetosphere Multiscale
Mission. In this brief review, we present an overview
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C.T. Russell / Journal of Atmospheric and Solar-Terrestrial Physics 69 (2007) 1739–1746
of the observations and analysis that are the
underpinning of our present understanding of this
phenomenon.
Upstream whistlers appear to be a universal
phenomenon at collisionless shocks. They have
been observed at Mercury (Fairfield and Behannon,
1976; Orlowski et al., 1990); Venus (Orlowski and
Russell, 1991; Orlowski et al., 1993); Saturn
(Orlowski et al., 1992); as well as by many authors
at Earth, including Russell et al. (1971), Fairfield
(1974), and Orlowski et al. (1995). Fig. 1 shows the
time series of these small amplitude waves at four
planets: Mercury, Venus, Earth and Saturn. In this
figure, the upstream whistlers are the highest
frequency waves displayed. Since these four bodies
have bow shocks of varying strengths and form the
obstacle to the flow in different ways, we conclude
that the creation of these whistler-mode waves is a
generic shock process and is not specific to a small
range of boundary conditions. We see from Fig. 1
102
Mercury
Venus
Trace Power (nT2/Hz)
100
Earth
10-2
Saturn
10-4
10-2
100
Frequency (Hz)
102
Fig. 2. Trace of the power spectral matrix as a function of
frequency for upstream whistlers at Mercury, Venus, Earth and
Saturn.
4
Frequency (Hz)
2. Observations
1741
3
f (Hz) = 0.196 BT(nT)
2
Mercury
Venus
Earth
1
0
0
5
10
15
Magnetic Field (nT)
20
25
Fig. 3. The frequency of upstream whistler mode waves at
Mercury, Venus and Earth as a function of the magnetic field
strength at the time of observation.
that the wave amplitude is modulated during an
occurrence, forming wave packets.
The spectrum in the spacecraft frame is similar at
the different planets as demonstrated in Fig. 2, but
the frequency does vary with distance from the Sun.
Three of the 4 power spectra shown in Fig. 2 exhibit
the steep upper frequency cutoff that is often
present in these waves. The Saturn spectrum is
weak here and the sample rate is low so the waves
appear close to the Nyquist frequency. Thus, it is
not possible to judge the sharpness of the upper
frequency cutoff. The frequency of the waves is in
part controlled by the interplanetary magnetic field.
This is illustrated in Fig. 3 that shows the wave
frequency in the satellite frame versus the interplanetary magnetic field strength. To our knowledge
no such study has been done on the frequency in the
plasma frame. In fact such a study would be quite
difficult, if only because, as will be shown below, the
Doppler shifting of these signals by the solar wind is
quite complex and hard to deconvolve.
The sensitivity to Doppler shifting by the solar
wind flow is illustrated by Fig. 4. Our reference to
these waves as upstream whistlers clearly indicates
that the waves are right-hand polarized in the
plasma rest frame. However, in Fig. 4 the waves are
left-hand polarized for all directions of propagation
that are within 501 of the direction of the solar wind
flow. These are the directions of propagation that
are most greatly Doppler-shifted by the solar wind.
As mentioned in the Introduction, if the waves
are generated at the shock we expect them to be
damped by Landau resonance. When a whistler
mode wave travels obliquely to the magnetic field it
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50
0
Left
Frequency (Hz)
1
-1
-2
0
30
60
90
Fig. 4. The frequency (with sign) of upstream whistlers as the
angle between the wave normal and the solar wind direction
changes.
Mercury (Mariner 10)
Number of Wave Events Normalized by Anglular Area of Bin
Right
2
40
30
20
10
Venus (PVO)
Wave Amplitude (nT)
1.0
Earth (ISEE-1)
Saturn (Voyager)
0
0
20
40
60
80
Fig. 6. The number of wave events in 101 bins of the angle
between the magnetic field and the wave normal. The rate is
normalized for the solid angle subtended by the bin. The narrow
distribution of wave normal angles about the field direction is
consistent with Landau damping that attenuates the wave more
as the angle to the field increases.
0.1
0.01
10000 20000 30000 40000 50000 60000 70000
Distance from the Shock (km)
Fig. 5. The amplitude of upstream whistlers at Mercury, Venus,
Earth and Saturn as a function of distance from the bow shock.
has an electric field parallel to the magnetic field
that can resonate with the drift of thermal electrons
along the magnetic field. Unless there is a bump on
the tail of the electron distribution, the usual solar
wind distribution (Maxwellian) damps the wave.
We can easily test this prediction.
Fig. 5 shows the amplitude of upstream whistlers
versus distance from the shock for Mercury, Venus,
Earth and Saturn. Perhaps surprisingly the wave
amplitudes do not exhibit differences that we can
attribute to each planet. Rather there is one single
curve that fits all the data, albeit it is a semilog plot.
Fig. 6 supports the Landau damping hypothesis by
showing that most events propagate along the
magnetic field and fewer events propagate at a large
angle. Here we have binned the data in 101 bins and
normalized the rate for the solid angle subtended by
the bin. Fig. 7 shows yet a third test. Here we show
the wave amplitude versus the propagation angle to
the field at two distances from the shock. Closer to
the shock the waves are stronger and have a broader
angular range of propagation. The waves clearly
damp with distance from the shock and damp more
strongly at greater angles of propagation to the
magnetic field as predicted by Landau resonance
theory. Thus, the concerns of Rodriguez and
Gurnett (1975) and Greenstadt et al. (1981) were
partially correct. Landau damping does affect any
waves propagating at an angle to the magnetic field.
However, the waves that propagate parallel to the
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C.T. Russell / Journal of Atmospheric and Solar-Terrestrial Physics 69 (2007) 1739–1746
field are not affected by Landau damping and
penetrate deep into the foreshock.
3. The effects of Doppler shifting
As illustrated in Fig. 4, the polarization of
the wave in the spacecraft frame depends strongly
on the direction of propagation relative to the
solar wind flow. However, this is not the only
effect on the waves. Fig. 8 shows a time series and a
power spectrum of upstream whistlers about 3.5
Wave Amplitude (nT)
3.0
d<0.3 R v
1<d<10 R v
2.0
1.0
0
0
30
60
Propagation Angle (deg.)
90
Fig. 7. The amplitude of upstream whistlers as a function of the
propagation angle to the magnetic field direction at two distances
from the shock. The solid lines show least square fits to the data
points. The different amplitudes and slopes are consistent with
Landau damping as the waves propagate away from the shock.
1743
Venus radii (Rv) upstream from the shock as
observed by Pioneer Venus on July 12, 1980
(Orlowski and Russell, 1991). The power spectrum
shows a very distinct peak with an intensity of
0.7 nT2/Hz and a frequency of 1.4 Hz. The waves are
left-hand elliptically polarized with an ellipticity of
0.97 and are propagating at an angle of 361 to the
magnetic field. The wave normal is 201 from the
solar wind flow direction. A remarkable feature of
this spectrum is the strong decrease in power
spectral density near 1.5 Hz with a falloff of about
160 dB/decade.
In contrast to the July 12 waves, Fig. 9 shows
upstream whistlers observed on July 3, 1980 about
1 Rv upstream of the Venus shock. As would be
expected for this closer distance the waves are
stronger. However, they are right-hand polarized
and have a much different spectrum. In fact, there is
no sharp break in the spectrum here and the highfrequency right-handed whistler power joins
smoothly with the more linear low-frequency
power. The whistler waves here are propagating at
341 to the magnetic field, similar to the 361, in the
previous example, but their propagation angle to
the solar wind flow is 641, much larger than the
previous 201. Thus, these whistler waves are not
subject to as much Doppler shift as in Fig. 8. The
weakness of the Doppler shifting can explain both
the different polarization and the difference in the
spectral shape.
Fig. 8. Upstream whistlers seen 3.5 Rv upstream from the Venus shock. (Left) Time series in VSO coordinates. (Right) Trace of the power
spectrum for these waves. These waves were strongly Doppler shifted, propagating at about 201 to the solar wind flow direction.
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1744
102
Bx
(nT)
8
Orbit 576
July 3, 1980
1427:26-1428:44 UT
Trace Power (nT2/Hz)
0
By
(nT)
-8
8
0
Bz
(nT)
0
BT
(nT)
-8
8
-8
8
0
1427:26
:45
1428:05
Universal Time
:25
1428:44
100
10-2
10-4
10-2
100
Frequency (Hz)
Fig. 9. Upstream whistlers seen 1 Rv from the Venus bow shock. (Left) Time series in VSO coordinates. (Right) Trace of the power
spectrum for these waves. These waves were only weakly Doppler shifted, propagating at 641 to the solar wind flow direction.
105
Waves Swept
Downstream
Velocity [km/s]
104
Waves Propagate
Upstream
Polarization
Reversal
103
No Polarization
Change
Vph
Vg
102
101
Vg
Vph
f1
VSW k
RH Branch
(Whistlers)
f2
LH
Branch
100
0.001 0.01
0.1
1
10
100
1000 10.000
Frequency [Hz]
Fig. 10. The phase and group velocities for right-handed
(whistler) and left-handed waves in a cold plasma for parallel
propagation in a 5 nT magnetic field and a 5 cm3 proton–electron plasma. The horizontal line shows the Doppler-shift velocity
imposed by the solar-wind flow.
We can best explain the effects we see with a plot
of the phase and group velocities of whistler mode
waves versus frequency in the plasma frame.
We use the space physics education software
(Russell et al., 1995) that incorporates the cold
plasma dispersion relation of Stix (1962). Here we
chose typical upstream values and do not try to
precisely duplicate either event. Fig. 10 shows such a
plot for parallel propagation in a cold plasma with
a density of 5 protons and electrons per cubic
centimeter and a magnetic field of 5 nT. The
electron gyro frequency is 140 Hz and the proton
gyro frequency is 0.076 Hz. The solid lines show the
whistler mode and the left-hand mode phase
velocities in the plasma frame. The dashed lines
show the associated group velocities. In the portion
of the frequency range in which the phase velocity
increases with frequency, the group velocity exceeds
the phase velocity and vice versa. A horizontal line
marked Vsw k represents the speed of the solar
wind moving antiparallel to the wave normal. This
speed controls the Doppler shifting effects. As
the frequency increases from zero, eventually at
the plasma-frame frequency marked f1, the group
velocity exceeds the solar-wind Doppler-shift velocity along the wave normal and wave energy can
propagate upstream. However, at this frequency the
Doppler-shifting velocity still exceeds the phase
speed and the phase fronts are blown backwards
over the observer. Thus, the intrinsically righthanded waves appear left-handed in the spacecraft
frame. This situation continues until the plasmaframe frequency f2, which marks the point at which
the phase speed matches the Doppler-shifting
speed. Above this frequency, the group and
phase speed exceed the Doppler-shift speed until
close to the electron gyro frequency where we
might expect there to be much weaker signals if at
all. If the spacecraft is upstream from the shock
no energy will reach the spacecraft at frequencies
below f1. Between f1 and f2, waves will have their
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10 1
100
Power (nT2/Hz)
10-1
10-2
10-3
10-4
10-5
10-6
0.1
2
3 4 5 6
1
2
3 4 5 6
10
2
3
Frequency (Hz)
Fig. 11. Dark spectrum is the power spectral density of upstream
whistlers in the solar wind. Light spectrum is the power spectral
density of the same whistlers in the spacecraft frame.
polarizations reversed and at f2 the Doppler-shifted
frequency will be zero. Thus, f1 will be Doppler
shifted to the highest frequency in the spectrum
observed in the spacecraft frame. If this frequency is
f1*, then there is no wave energy above f1* except
energy arriving at much higher frequencies than f2
that reach the spacecraft with weaker Doppler
shifts, so that their polarization are not reversed
and their frequencies are only slightly altered. These
higher frequencies should have much weaker signal
strengths in most geophysical situations.
Fig. 11 illustrates the effect on the power
spectrum. Assume that the dark-shaded spectrum
between 2 and 5 Hz, say, is the natural power
spectrum in the solar-wind frame. The lower
frequency of this shaded power-law spectrum is
the lowest frequency whose energy can propagate
upstream. It Doppler-shifts to the uppermost
shaded frequency in the spacecraft frame (lightly
shaded spectrum). The upper end of the dark solar
wind frame spectrum maps to zero frequency,
creating between the two frequencies the characteristic, upward-sloping power with a sharp, upperfrequency cutoff. Any power below 2 Hz generated
at the shock is swept downstream and never reaches
the spacecraft. Any power above about 5 Hz in this
example does not have its polarization reversed and
can be found in the spacecraft frame at positive
frequencies, beginning at 0 Hz adding to the power
1745
from the negative frequency Doppler-shifted waves
because the power spectrum sums the contributions
from the negative frequencies and positive frequencies. As illustrated here we expect this power
originally at higher frequencies in the plasma frame
to be weaker than in the Doppler-shifted band.
Since the spectra we see do very much resemble our
hypothetical spectrum, we believe our assumption is
justified.
Finally, we can understand the dependence seen
for the frequency peak in Fig. 3. There are several
effects occurring simultaneously. The Alfven velocity decreases with distance from the Sun as does the
magnetic field so that the curves in Fig. 10 slip to the
left and down as one moves outward from the Sun.
The Doppler-shifted frequency of the peak amplitude depends on the wavelength and the phase
velocity at f1. The spiral angle of the interplanetary
magnetic field that guides the waves also affects
Doppler shifting. These several effects change the
frequency somewhat but not as much as simply the
overall shift to the left of both velocity curves with
decreasing field strength. The net result is a general
decrease of the frequency of the 1 Hz wave peak
with magnetic field strength but with some modification of the dependence at each planet due to the
specific conditions of its solar wind interaction.
4. Conclusions
A very simple model of bow shock generation of a
power-law spectrum of whistler waves can explain
all the observed properties of the upstream whistler
waves including their very odd spectral peak. This
model includes the effects of Doppler shifting on
whistler-mode signals, whose group velocity exceeds
their phase velocity, with Landau damping of the
propagating waves. Simply a segment of the powerlaw wave spectrum is cut and inverted in frequency
by the Doppler shifting. Some waves are carried
downstream toward the magnetosphere but are
broadband and probably do not contribute to the
Pc-1-wave spectrum seen in the magnetosphere This
phenomenon still has one important mystery, what
is the process at the shock that generates the
spectrum of whistler mode waves? Clues may be
found in the presently unknown dependence on the
shock normal angle and on the Mach number. We
encourage those groups of space plasma physicists
with the high-resolution shock data that are now
available from modern instrumentation to address
these questions.
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C.T. Russell / Journal of Atmospheric and Solar-Terrestrial Physics 69 (2007) 1739–1746
Acknowledgments
This work was supported by the National Science
Foundation under Grant ATM04-02213 and by the
National Aeronautics and Space Administration
under Grant NNG06GC62G.
References
Fairfield, D.H., 1974. Whistler waves observed upstream from
collisionless shocks. Journal of Geophysical Research 79,
1368–1378.
Fairfield, D.H., Behannon, K.W., 1976. Bow shock and
magnetosheath waves at Mercury. Journal of Geophysical
Research 81 (22), 3897–3906.
Greenstadt, E.W., Fredricks, R.W., Russell, C.T., Scarf, F.L.,
Anderson, R.R., Gurnett, D.A., 1981. Whistler mode wave
propagation in the solar wind near the bow shock. Journal of
Geophysical Research 86, 4511–4516.
Orlowski, D.S., Russell, C.T., 1991. ULF waves upstream of the
Venus bow shock: properties of one-Hertz waves. Journal of
Geophysical Research 96, 11,271–11,282.
Orlowski, D.S., Crawford, G.K., Russell, C.T., 1990. Upstream
waves at Mercury, Venus and Earth: comparison of the
properties of one Hertz waves. Geophysical Research Letters
17, 2293–2296.
Orlowski, D.S., Russell, C.T., Lepping, R.P., 1992. Wave
phenomena in the upstream region of Saturn. Journal of
Geophysical Research 97, 19,187–19,199.
Orlowski, D.S., Russell, C.T., Krauss-Varban, D., 1993. On the
source of upstream whistlers in the Venus foreshock. In:
Gombosi, T.I. (Ed.), Plasma Environments of Non-Magnetic
Planets. Pergamon Press, New York, pp. 217–227.
Orlowski, D.S., Russell, C.T., Krauss-Varban, D., Omidi, N.,
Thomsen, M.F., 1995. Damping and spectral formation of
broadband upstream whistlers. Journal of Geophysical
Research 100 (A9), 17,117–17,128.
Rodriguez, P., Gurnett, D.A., 1975. Electrostatic and electromagnetic turbulence associated with Earth’s bow shock.
Journal of Geophysical Research 80, 19–27.
Russell, C.T., Childers, D.D., Coleman, P.J., 1971. OGO-5
observations of upstream waves in the interplanetary medium:
discrete wave packets. Journal of Geophysical Research 76
(4), 845–861.
Russell, C.T., Le, G., Luhmann, J.G., Littlefield, B., 1995.
Educational software for the visualization of space plasma
processes. In: Szuszczewicz, E.P., Bredekamp, J.H. (Eds.),
Visualization Techniques in Space and Atmospheric Sciences.
NASA SP-519, Washington, DC, pp. 263–270.
Sentman, D.D., Thomsen, M.F., Gary, S.P., Feldman, W.C.,
Hoppe, M.M., 1983. The oblique whistler instability in the
Earth’s foreshock. Journal of Geophysical Research 88 (A3),
2048–2056.
Stix, T.H., 1962. The Theory of Plasma Waves. McGraw-Hill,
New York.