Weak Double Layers in the Solar Wind and their Relation to
the Interplanetary Electric Field
C. Salem , C. Lacombe †, A. Mangeney†, P. J. Kellogg and J.-L. Bougeret†
Space Sciences Laboratory, University of California, Berkeley, USA
†
LESIA, Observatoire de Paris-Meudon, Meudon, France
School of Physics and Astronomy, University of Minnesota, Minneapolis, USA
Abstract. In the solar wind at 1 AU, coherent electrostatic waveforms in the ion acoustic frequency range (between the ion
and electron plasma frequencies) have been recently observed by the WAVES/TDS instrument on WIND. Many of these
structures have been interpreted in terms of Weak Double Layers (WDL), since they sustain a net potential drop of roughly
1 mV directed towards the Earth. The TDS data are compared to the continuous measurements of thermal and non thermal
electric spectra above 4 kHz obtained by the WAVES/TNR instrument : this allows us to determine the frequency of occurrence
of the WDL at the L1 Lagrange point. Extrapolating this result provides a total potential drop of about 300 to 1000 Volts on
the Sun-Earth distance, compatible with the potential needed to maintain the global charge neutrality in the solar wind. This
suggests that the interplanetary electrostatic potential is not continuous but results from a succession of WDL, distributed
intermittently between the Sun and the Earth. We also find that the energy of the non thermal fluctuations on TNR between
4 and 6 kHz is correlated to the interplanetary electrostatic field, parallel to the spiral magnetic field, calculated with a twofluid model, thus providing further evidence of a relation between the interplanetary electrostatic field and the electrostatic
fluctuations in the ion acoustic range.
1. INTRODUCTION
in this respect, electrostatic waves in the Doppler-shifted
ion acoustic frequency range, i.e. with frequencies f between the proton and the electron plasma frequencies
( f pi f < f pe ), have been observed by several spacecraft
in the solar wind. This broadband ion acoustic activity is
an intermittent but almost permanent feature of the solar
wind [5, 6, 7]. Neither the wave mode nor the source of
these waves have yet been unambiguously identified [5].
Recently, high-time resolution data from the WAVES
experiment on WIND have led to a major contribution
to our understanding of this ion-acoustic-like wave activity in the solar wind, by revealing for the first time its
highly coherent nature [7, 8]. Indeed, Coherent Electrostatic Waves (CEW hereafter) have been observed, as a
mixture of quasi-sinusoidal wave trains and solitary like
structures with scales of tens of Debye lengths [7]. The
latter appear to be Weak Double Layers (WDL hereafter)
with a net potential difference ∆φ 1 mV across the
structure. The observed potentials usually drop towards
the Earth, in the same sense as the interplanetary electrostatic potential Φ IP . It is then tempting to speculate that
ΦIP is actually the result of a succession of small potential drops in WDL, due to small charge separations between the protons and the escaping electrons [8]. In this
paper, we propose to check this hypothesis by estimating the rate of occurrence of the WDL in the solar wind.
We also check whether the waves play a role in the solar
The solar wind is the outward extension of the milliondegree hot solar corona. It is a weakly collisional,
strongly turbulent plasma in a supersonic and superAlfvénic spherical expansion. Since the electrons are less
gravitationally bounded by the Sun than the protons, they
tend to be displaced outward with respect to the protons.
To maintain the global charge neutrality of the solar wind
plasma, an interplanetary electrostatic potential difference ∆ΦIP sets in between the solar corona and infinity.
The corresponding electric field EIP is directed antisunward and plays a key role in the solar wind expansion.
Values of ∆ΦIP can be obtained from different models for
solar wind expansion, for example, in a two-fluid model
(where E is related to the electron pressure) or in an exospheric model [1, 2] (where E is such that the flux of
the escaping electrons is equal to the proton flux). These
models predict a potential difference ∆Φ IP of the order
of 400 to 1000 Volts between the solar corona and the
Earth orbit. Such large-scale potentials can of course not
be measured directly in-situ.
Since the solar wind is a weakly collisional plasma, it
is usually argued that wave-particle interactions replace
binary collisions in order to restore the fluid character
of the flow by regulating the energy transport and dissipation [3, 4]. Among the waves that can play a role
CP679, Solar Wind Ten: Proceedings of the Tenth International Solar Wind Conference,
edited by M. Velli, R. Bruno, and F. Malara
© 2003 American Institute of Physics 0-7354-0148-9/03/$20.00
513
wind energy transport by looking for a relation between
the energy of the waves and the solar wind properties.
2. THE WAVE MEASUREMENTS
The WAVES experiment on WIND measures electric and
magnetic plasma waves over a large range of frequencies
[9]. In the present study, we consider the electric field
fluctuation measurements provided by two instruments,
the Thermal Noise Receiver (TNR) and the Time Domain Sampler (TDS), with the x antenna, a wire dipole
of physical length 2L x tip-to-tip (L x = 50 m), spinning in
the Ecliptic plane.
The TDS is a "snapshot" waveform sampler. It detects
all the electric signals above a programmable threshold
of 50 µ V/m, and generates 2048 point events. Due to
telemetry constraints, only a few waveforms are transmitted to the ground. During the period analyzed here in
1995, the transmitted event is not the most intense but
the most recently recorded, roughly every 10 min. In this
study, we consider only high bit rate events sampled at
120,000 samples per second, so that an event duration is
17.07 ms. The electric field E is obtained by dividing the
measured potential difference at the antenna terminals by
the length L x [7].
The TNR is a very sensitive digital spectrum analyzer
designed to do thermal noise spectroscopy in the ambient solar wind plasma [4, 10]. In its lowest frequency
band (4-16 kHz), it measures continuously electric power
spectra V 2 in V2 /Hz every 4.5 s with an integration time
of 1.472 s. The square electric field E 2 (V2 m 2 Hz 1 ) is
obtained by dividing V 2 by L2x [11].
We also use here hourly averages of the magnetic
field components (MFI experiment [12]), the solar wind
speed Vsw and the electron and proton temperature, Te
and Tp (3D-Plasma experiment [13]), the electron density
Ne from electron thermal noise [10]. Detailed electron
distribution functions [13] have been integrated to give
hourly averages of the components of the heat flux vector
Qe and of the parallel to perpendicular temperature ratio
Tek =Te? [10].
FIGURE 1. Typical weak double layer detected in the solar
wind : (a) the measured electric field smoothed over 10 points
(positive if directed towards the Earth) ; (b) the corresponding
electric potential profile, normalized to k B Te .
and non-sinusoidal isolated spikes lasting less than 1 ms.
These solitary like structures are found to be Weak Double Layers (WDL hereafter), with a net potential difference across the structure implying a non-zero average
electric field almost always directed towards the Earth
[7, 8]. Figure 1 shows an example of WDL observed in
the solar wind. Figure 1a displays the electric field E k
parallel to B (in mV/m, and smoothed over 10 points
in order to eliminate the high frequency noise) during
a time interval of 4 ms. The corresponding electric potential, normalized to the local electron temperature Te is
shown in Figure 1b. About 30% of the CEW in our sample are WDL. A statistical study indicates that a typical
spatial size of the WDL is 25λ D and a typical value
for the potential drop across the WDL is ∆φ 1 mV, or
e∆φ =kB Te 10 4 10 3 [7].
TDS observations strongly suggest that these structures are one-dimensional, varying only along the magnetic field B, and that they are convected by the solar
wind since their velocity in the plasma frame is much
smaller than the solar wind speed [7]. These WDL probably manifest small-scale charge separation due to a partial decoupling between electrons and protons on distances comparable to a Debye length scale.
TDS observations are not continuous so that the rate
3. SUMMARY OF OBSERVATIONS
Our observations were taken in the ambient solar wind,
at the Lagrange point L1, from May 20 to June 26, 1995.
This interval is typical of the solar wind close to the last
minimum of solar activity, because Wind has explored
high-speed as well as low-speed streams [7, 14]. During this interval, the TDS detected about 2160 Coherent
Electrostatic Waves (CEW hereafter). These CEW display two main typical shapes : sinusoidal wave packets
514
FIGURE 2. Time profile of the spectral power of the electric
potential at two frequencies on TNR during 6 hours (sampling
time : 4.5 s).
of occurrence of WDL in the solar wind can only be estimated if we combine wave observations from both TDS
and TNR instruments. The TNR instrument is sensitive
enough to measure both the thermal and the non-thermal
fluctuations. This can be seen on Figure 2 which displays
the temporal profile of the electrostatic fluctuations (in
V2 /Hz) measured on TNR at 4.09 kHz (upper panel) and
5.78 kHz ( f pe ' 23 25 kHz). The thermal fluctuations,
or Quasi-Thermal Noise (QTN) [15], depend on Ne , Te ,
Vsw , and Tp [16] and their intensity distribution is Gaussian. The non-thermal high intensity fluctuations are very
sporadic, with a more or less power law intensity distribution [11]. Their intensity and rate of occurrence decrease when the frequency increases. These nonthermal
fluctuations are the spectral counterparts of the waveforms seen on TDS[11].
FIGURE 3. (a) The different average TDS and TNR spectra
(see text below) ; (b) the rate of occurrence in s 1 of CEW in
the solar wind at 1 AU as a function of the frequency (Eq. 1).
thermal fluctuations averaged over the sample of thermal
spectra, and the dashed line T NR NT the spectrum of
the non-thermal fluctuations averaged over the sample
of non-thermal spectra during 38 days. The solid line
spectrum T NR M is the average of the non-thermal
TNR spectral energy over the total number of spectra,
thermal plus non-thermal ; it is thus a time average of
the non-thermal energy in the ambient solar wind. So the
average number of CEW in the solar wind per second
will be given by a comparison of VT2DS with VT2NR M . If
there is only one TDS event during the TNR integration
time τ , then its TNR intensity at a given frequency will
be VT2NR = VT2DS =β , β = 1:472=0:01707 = 86 being the
ratio between the TNR and the TDS integration times.
Thus, the number of CEW observed in the solar wind
during 1 s above 4 kHz is
4. RATE OF OCCURRENCE OF WDL
We estimate the rate of occurrence of the CEW and of
the WDL in the solar wind by comparing the average
spectral densities on TDS and on TNR in their common
frequency range, i.e. between 4 and 6 kHz. The upper
line of Figure 3a gives the spectral density VT2DS ( f ) of the
CEW averaged over the 2160 waveform spectra. Most
of these spectra have a peak power around 2 kHz [7,
11]. However, the measured frequencies over the whole
sample vary between 0.2 and 8 kHz, and about 11%
of the CEW have significant power above 4 kHz [11].
The dashed line T NR T is the spectrum of the purely
NCEW ( f ) = β VT2NR
2
M =(τ VT DS ):
(1)
NCEW ( f ) is plotted in Figure 3b. Above 4 kHz, the average number of CEW per second in the solar wind is
NCEW 0:36.
Since only 11% of the observed CEW contribute to
the frequency range above 4 kHz, and 30% are WDL, we
conclude that an estimate of the number of WDL drifting
past the Wind spacecraft per second is
NW DL 1 s
515
1
(2)
Assuming (i) an average travel time of 3 10 5 s for a
solar wind plasma element between the solar corona and
the Wind orbit, (ii) that N WDL and the average potential
difference ∆φ across a WDL remain both constant from
the solar corona to the Earth, one may estimate the total
potential difference at 1 AU [11] :
300 ∆Φ1AU 1000 Volts:
(3)
This range of values for ∆Φ 1AU is the one needed
to maintain charge neutrality in the solar wind [17].
So these results suggest that the interplanetary electric
potential is not continuous but is actually established
through a succession of WDL, distributed intermittently
along the radial direction.
5. ENERGY OF THE WAVES
We look here for correlations between the electric field
of the ion acoustic like waves and some properties of
the solar wind plasma, as those found in Helios data
[18]. For that, we consider hourly averages of the square
electric field E 2 of the TNR non-thermal fluctuations
between 4 and 6 kHz [11]. We find no correlation of
logE 2 with Te =Tp , nor with Vsw or Qe , in contrast to the
Helios results. However, weak correlations (0.31 or 0.32)
are found between logE 2 and Te , Tek Te? , and cos χ =
cos(Vsw ; B). One possible interpretation is that these
parameters to which logE 2 seems to be related play a role
in the interplanetary electrostatic potential. According to
Pilipp et al. [19] the interplanetary electrostatic potential
ΦPG due to the electron pressure gradient, in a two-fluid
model, can be written as a function of Te , Tek Te? and
cos2 χ for a spiral magnetic field in the ecliptic plane
FIGURE 4. The interplanetary electric field parallel to the
spiral magnetic field in a two-fluid model (Eqs 4 to 7) as a
function of the hourly energy E 2 of the nonthermal emissions
between 4 and 6 kHz : (a) scatter plot, (b) average and standard
deviation in equal bins of logE 2 .
EIPk is displayed in Figure 4 as a function of logE 2 . Note
that EIPk is expressed in nV/m, not in mV/m. EIPk refers
to the large-scale interplanetary electric field, calculated
in the framework of a two-fluid model (Eqs. 6 and 7),
while the electric field E in Figure 1 or in the abscissae
of Figure 4 refers to the local electric field fluctuations
measured by TDS and/or TNR with an antenna (see
section 2). The correlation between logE 2 and EIPk ,
shown in Figure 4 is better ( 0:45) than the individual
correlations (0.31 or 0.32) between logE 2 and Tek Te? ,
Te , or cos χ , providing further evidence of a relation
between the small-scale coherent electrostatic waves and
the large-scale interplanetary electric field.
i
d h
pe? + ( pek pe?) cos2 χ +
dr
1
2
2
(2 cos χ sin χ )( pek
pe? )
(4)
r
where pek;? = Ne kB Tek;? is the electron pressure parallel
and perpendicular to the B field. Using the relation
eNe
dΦPG
dr
=
cos2 χ
2
2
2 2
= Vsw =(Vsw + Ω r )
(5)
6. CONCLUSION
where Ω is the angular frequency of the Sun rotation,
and assuming that Te ∝ r α , the radial component of the
interplanetary electric field at 1 AU is
dΦPG h
= (2 + α )Te? + (Tek Te? )
dr
2
4
11
[1 + (1 + α ) cos χ 2 cos χ ] =1:5 10
Observations made by the Time Domain Sampler, an
electric waveform analyzer onboard WIND, have shed
a new light on the nature of the "ion acoustic" electrostatic turbulence in the solar wind. We showed that this
turbulence consists of small amplitude coherent waves
and solitary like structures, many of which are very Weak
Double Layers (WDL) with small potential drops of
roughly 1mV over a few tens of Debye lengths, directed
towards the Earth [7]. This coherent electrostatic wave
activity seems to be a common feature of collisionless
Er (V =m) =
(6)
where the temperatures are in eV ; and the component of
this electric field along the magnetic field is
EIPk (V =m) = j cos χ j Er :
(7)
516
space plasmas. Indeed, electrostatic solitary structures
have been observed almost everywhere in the Earth’s environment. Most of the observations available, in the auroral terrestrial regions, in the Earth’s magnetotail as well
as in the solar wind, have been rewiewed by Salem et al.
[8]. The properties of these waves depend on the region
of observation which determines the plasma regime.
WIND observations have allowed for the determination of the rate of occurrence of WDL in the solar wind,
NWDL 1s 1 . We show that extrapolating this result
leads to a total potential difference of 300 to 1000 Volts
between the solar corona and 1 AU, which is in the range
of values needed to maintain charge neutrality in the solar wind plasma [17]. This gives the first observational
indication of the existence of the large-scale electric field
in the interplanetary medium, which plays a fundamental
role in the expansion of the solar wind [20]. Furthermore,
a correlation is found between the energy of the coherent
ion acoustic waves and the amplitude of the interplanetary electric field expected in a two-fluid model, with a
spiral magnetic field.
These results suggest that the observation of weak
double layers in the solar wind is related to the existence of the interplanetary electric field. The corresponding electric potential difference between the solar corona
and the Earth orbit would actually be established through
a succession of small potential drops across a multitude
of WDL, distributed intermittently along the radial direction.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
ACKNOWLEDGMENTS
Work at UC Berkeley is supported by NASA grant FDNAG511804 to the University of California. The french contribution
is supported by the Centre National d’Etudes Spatiales and the
Centre National de la Recherche Scientifique.
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