Annales Geophysicae, 24, 275–289, 2006
SRef-ID: 1432-0576/ag/2006-24-275
© European Geosciences Union 2006
Annales
Geophysicae
Electric field measurements on Cluster: comparing the
double-probe and electron drift techniques
A. I. Eriksson1 , M. André1 , B. Klecker2 , H. Laakso3 , P.-A. Lindqvist4 , F. Mozer5 , G. Paschmann2,6 , A. Pedersen7 ,
J. Quinn8 , R. Torbert8 , K. Torkar9 , and H. Vaith2,8
1 Swedish
Institute of Space Physics, Uppsala, Sweden
für Extraterrestrische Physik, Garching, Germany
3 Solar System Division, ESA/ESTEC, Noordwijk, Netherlands
4 Alfvén laboratory, Royal Institute of Technology, Stockholm, Sweden
5 Space Sciences Laboratory, University of California, Berkeley, CA, USA
6 International Space Science Institute, Bern, Switzerland
7 Department of Physics, Oslo University, Norway
8 Space Science Center, University of New Hampshire, Durham, NH, USA
9 Space Research Institute, Austrian Academy of Sciences, Graz, Austria
2 Max-Planck-Institut
Received: 16 June 2004 – Revised: 29 November 2005 – Accepted: 14 December 2005 – Published: 7 March 2006
Abstract. The four Cluster satellites each carry two instruments designed for measuring the electric field: a doubleprobe instrument (EFW) and an electron drift instrument
(EDI). We compare data from the two instruments in a representative sample of plasma regions. The complementary
merits and weaknesses of the two techniques are illustrated.
EDI operations are confined to regions of magnetic fields
above 30 nT and where wave activity and keV electron fluxes
are not too high, while EFW can provide data everywhere,
and can go far higher in sampling frequency than EDI. On
the other hand, the EDI technique is immune to variations
in the low energy plasma, while EFW sometimes detects
significant nongeophysical electric fields, particularly in regions with drifting plasma, with ion energy (in eV) below the
spacecraft potential (in volts). We show that the polar cap
is a particularly intricate region for the double-probe technique, where large nongeophysical fields regularly contaminate EFW measurments of the DC electric field. We present
a model explaining this in terms of enhanced cold plasma
wake effects appearing when the ion flow energy is higher
than the thermal energy but below the spacecraft potential
multiplied by the ion charge. We suggest that these conditions, which are typical of the polar wind and occur sporadically in other regions containing a significant low energy ion
population, cause a large cold plasma wake behind the spacecraft, resulting in spurious electric fields in EFW data. This
interpretation is supported by an analysis of the direction of
the spurious electric field, and by showing that use of active
potential control alleviates the situation.
Correspondence to: A. I. Eriksson
(anders.eriksson@irfu.se)
Keywords. Magnetospheric physics (Electric fields; Instruments and techniques) – Space plasma physics (Spacecraft
sheaths, wakes, charging)
1
Introduction
The electric field is a key parameter for determining and
modelling various space plasma physics processes, for example, reconnection and particle acceleration. Modern spacecraft for in-situ studies of space plasma physics, therefore,
usually carry instruments for observing the electric field,
from zero frequency up to frequencies well above the highest characteristic frequencies in the plasma. For measurement of low frequency and quasi-static fields in low density plasmas, the two main measurement techniques employ
double probes and electron drift instruments. Descriptions
of these techniques are provided by Pedersen et al. (1998)
and Maynard (1998) for double probes, and by Paschmann
et al. (1998) for electron drift instruments. In brief, the operational principle of a double probe instrument is to measure
the voltage difference between two usually spherical probes,
which, for magnetospheric conditions, must be forced to stay
close to the potential of the unperturbed plasma at their respective positions by use of a suitably chosen bias current
(Fig. 1). The electron drift technique is based on the fact
that to zeroth order, gyrating charged particles drift at a velocity E×B/B 2 . This drift velocity can be determined using
two properly directed electron beams which must be detected
upon their return to the spacecraft (Fig. 2). The equivalent
electric field can then be calculated from the drift and from
magnetic field data.
2
Comparing electric field measurements
276
Ib
Rp
s/c
U
Ib
Rp
~
Φ
Fig. 1. The operational principle of a double probe instrument. Two
Fig.
1. The operational
principle
of a double
probeidentical
instrument.
Two
boom-mounted
probes (solid
circles)
are fed with
bias curboom-mounted
(solidRcircles)
are
fed
with
identical
bias
currents Ib . If the probes
resistances
over
the
probe
sheaths
(dashed
cirp
rents
the resistances
the probe
sheaths
cirp over
b . If
cles) Iare
equal,
the voltageRU
measured
on board
the(dashed
spacecraft
cles)
are
equal,
the
voltage
U
measured
onboard
the
spacecraft
will
will be equal to the potential difference 8 in the plasma between
be
the potential
difference
Φ field
in the
plasma
the
theequal
probetolocations.
Unwanted
electric
signals
canbetween
arise either
probe
Unwanted
electric
field signals
arise either
from alocations.
difference in
Rp between
the probes,
or fromcan
an asymmetric
from
a difference
Rp between
the probes,
from an
asymmetric
potential
structureinaround
the spacecraft
andorbooms
adding
to the
potential
structure
around
the Currents
spacecraft
andthrough
booms the
adding
to the
unperturbed
8 in the
plasma.
close
spacecraft
unperturbed
Φ in theFor
plasma.
Currents
close
through the
sheath (not shown).
a more
complete
description,
seespacecraft
Pedersen
sheath
(not shown). For a more complete description, see Pedersen
et al. (1998).
et al. (1998).
Each technique has its own merits and weaknesses. Double probe instruments have relative advantages in terms of
conceptual simplicity, regular and essentially unlimited sampling frequency, the possibility to measure rapidly varying fields at arbitrarily high amplitudes, and an operational
principle independent of the magnetic field. On the other
hand, as the measurement principle depends on the electrostatic coupling of the probe to the plasma surrounding it,
the technique is sensitive to perturbations from the spacecraft or the wire booms supporting the probes. Though there
are many ways to reduce such perturbations, including design symmetry, biasing of probes and bootstrapping of adjacent boom elements, their possible influence always constitutes an uncertainty which only comparison to other measurements can eliminate. In contrast, electron drift instruments are quite insensitive to the details of the spacecraft
environment, as the keV energy typical for electrons emitted by EDI is much higher than any potentials arising on a
well-designed scientifc spacecraft (normally less than 50 V).
In the weak magnetic fields typical for Cluster, the emitted electrons also spend most of their time in an orbit far
away from the spacecraft, further diminishing any influence
of the spacecraft-plasma interaction. In addition, the electron drift technique does not depend on spacecraft orientaFig.
The double
operational
principle
of the at
EDI
electron
driftshorter
instrution,2.while
probe
instruments
best
can have
ment
on along
Cluster,the
using
gun-detector
units (GDU1
andtoGDU2)
booms
spintwoaxis
and are often
confined
meaemitting
twoinbeams
of keV
electrons
and detecting
theirtechnique
drift upon
surements
the spin
plane.
A strength
of the EDI
return. For any given magnetic field B and drift velocity v, here
is that the measurement relies upon simple geometry; thus,
assumed to be solely due to an electric field E, only one orbit exist
when beam tracking is successful the absolute measurement
that connects each gun with the opposite detector, enabling a unique
is relatively reliable and does not require calibration or offset
determination of v and hence of E. The drawing is not to scale: in
However,
as the
electron
driftelectrons
methodreach
relies2 km
on
acorrection.
100 nT magnetic
field, the
orbits
of the EDI
observing
electrons
returned
to
the
spacecraft
by
the
ambient
from the spacecraft. For details see Paschmann et al. (2001).
magnetic and electric fields, the magnetic field has to be sufficiently strong for the emitted beam not to disperse too much
for detection. Rapid variations in the magnetic or electric
field will also complicate the beam tracking, so the method
works best in regions where the field variations are less rapid
than the tracking bandwidth (∼100 Hz), and the angular step-
higher than any potentials arising on a well-designed scienA. I.spacecraft
Eriksson et
al.: Electric
Cluster
tifc
(normally
lessfield
thanmeasurements
50 V). In the on
weak
magnetic fields typical for Cluster, the emitted electrons also
spend most of their time in orbit far away from the spacecraft,
further diminishing any influence of the spacecraft-plasma
interaction. In addition, the electron drift technique does not
depend on spacecraft orientation, while double probe instruments at best can have shorter booms along the spin axis
and often are confined to measurements in the spin plane. A
strength of the EDI technique is that the measurement relies
upon simple geometry; thus, when beam tracking is successful the absolute measurement is relatively reliable and does
not require calibration or offset correction. However, as the
electron drift method relies on observing electrons returned
to the spacecraft by the ambient magnetic and electric fields,
the magnetic field has to be sufficiently strong for the emitted beam not to disperse too much for detection. Rapid variations in magnetic or electric field will also complicate the
beam tracking, so the method works best in regions where
the field variations are less rapid than the tracking bandwidth
(∼ 100 Hz), and the angular stepping rate of the beam. Furthermore,
strong ambient
electron
fluxes
the
Fig.
2. Thesufficiently
operational principle
of the EDI
electron
driftnear
instruFig.ment
2. The
operational
of can
the units
EDI
electron
drift
instrubeam
(typically
keV)
swamp
the beam
signal
onenergy
Cluster,
using principle
two 1gun-detector
(GDU1
and
GDU2)
ment
on prevent
Cluster,
usingoftwo
gun-detector
(GDU1
and
emitting
two beams
keVTable
electrons
and units
detecting
their
driftGDU2)
upon
and
detection.
1 summarizes
the
performance
emitting
two
beams
of
keV
electrons
and
detecting
their
upon
return.
For any
given magnetic field B and drift velocitydrift
v, here
of the two
techniques.
return.
For
any
given
magnetic
field
B
and
drift
velocity
v,
here
assumed
to
be
solely
due
to
an
electric
field
E,
only
one
orbit
exists
As the strengths and limitations of the two techniques
that
connects
each
gun
with
the
opposite
detector,
enabling
a
unique
assumed
to
be
solely
due
to
an
electric
field
E,
only
one
orbit
exist
are so different, they complement each other. Each of the
ofgun
v and
hence
of
E. Thedetector,
drawing isenabling
not to scale:
in
thatdetermination
connects
each
with
the
opposite
a unique
four
Cluster
spacecraft
(Escoubet
et al., 2001)
therefore
cara 100-nT magnetic
field,
the orbits
of
thedrawing
EDI electrons
reach
2 km in
determination
of
v
and
hence
of
E.
The
is
not
to
scale:
ries the
onespacecraft.
instrument
of
eachsee
type:
the double-probe
instrufrom
Forthe
details,
et al. (2001).
a 100
nT magnetic
field,
orbitsand
ofPaschmann
the
EDI electrons
reachet2 al.,
km
ment
EFW (Electric
Fields
Waves,
Gustafsson
from1997;
the spacecraft.
For
details
see
Paschmann
et
al.
(2001).
Gustafsson
et al.,Furthermore,
2001) and the
Electron Drift
ping rate
of the beam.
sufficiently
strongInstruamment
(EDI,
Paschmann
et
al.,
1997;
Paschmann
et
al.,1 2001).
bient electron fluxes near the beam energy (typically
keV)
Since
the start
nominal
operations
in February
2001,
EFW
can
swamp
the of
beam
signal
and prevent
detection.
Table
1
has
operated
on
all
four
spacecraft
essentially
all
the
time.
summarizes the performance of the two techniques.
Though
operations
are restricted
regions
with suffiAs the EDI
strengths
and limitations
of thetotwo
techniques
are
ciently
intense
magnetic
field, and
operational
so
different,
they
complement
eachwas
other.
Each ofon
theCluster
four
spacecraft
four (Tango)
onlyetbriefly,
theretherefore,
is a large carries
amount
Cluster
spacecraft
(Escoubet
al., 2001),
of
simultaneous
data
from
the
two
instruments
available
for
one instrument of each type: the double-probe instrument
comparison.
In
addition,
the
EDI
implementation
flying
EFW (Electric Fields and Waves, Gustafsson et al., 1997,on
Clusterand
is of
a design
very
much
improved(EDI,
over previous
mis2001)
the
Electron
Drift
Instrument
Paschmann
sions,
so
there
are
unprecedented
possibilities
to
compare
the
et al., 1997, 2001). Since the start of nominal operations in
performances.
Finally,
data
obtained
by
both
techniques
are
February 2001, EFW has operated on all four spacecraft esmade widely
to theEDI
scientific
community
through
sentially
all theavailable
time. Though
operations
are restricted
to
the Cluster
Dataintense
System
(Daly, 2002),
sowere
thereinis
regions
with aScience
sufficiently
magnetic
field, and
alsoonanCluster
unprecedented
compare
data in
order
use
spacecraftneed
fourto
(Tango)
onlythe
briefly,
there
is ato
provide
a background
for users
of from
Cluster
field data.
large
amount
of simultaneous
data
theelectric
two instruments
This is the
of the present
study.the
WeEDI
cannot
exhaust
available
forscope
comparison.
In addition,
implemenall pitfalls
in improved
one single
tation
flyingand
on limitations
Cluster is ofofaeither
designtechnique
very much
paper,
but we missions,
aim at illustrating
the unprecedented
general features,
particuover
previous
so there are
possibillarlytopointing
particularly
overby
the
ities
compareout
thediscrepancies
performances.arising
Finally,
data obtained
polartechniques
caps.
both
are made widely available to the scientific
It shouldthrough
be noted
in this
paperData
we System
concentrate
community
thethat
Cluster
Science
(Daly,on
the twosoCluster
instruments
specifically designed
obtain2002),
there is
also an unprecedented
need to for
compare
ingdata
electric
field to
measurements,
i.e. EDI and
One
may
the
in order
provide a background
for EFW.
users of
Clusalso
construct
electric
estimate
velocity
moter
electric
fieldandata.
Thisfield
is the
scope from
of thethe
present
study.
ment
v i from
the Cluster
ion spectrometers
(CIS,
Rèmetechet al.,
We
cannot
exhaust
all pitfalls
and limitations
of either
2001)inand
magnetic
FGM fluxgate
magnique
onethesingle
paper,field
but B
wefrom
aim the
at illustrating
the general features, particularly pointing out discrepancies arising
especially over the polar caps.
and
of th
A
are s
four
ries
men
1997
men
Sinc
has
Tho
cien
spac
of si
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Clus
sion
perf
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also
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2001
A. I. Eriksson et al.: Electric field measurements on Cluster
277
Table 1. Summary of merits and drawbacks of the double-probe and electron drift techniques for magnetospheric electric field measurments. The implementations on Cluster, EFW and EDI, provide 2-D measurements. Extending the EDI technique to three-dimensional
measurements will require a significant advance over the current state of the art.
Ambient B
Frequency range
Dimensionality
Sensitivity to thermal/cold plasma
Sensitivity to s/c-plasma interactions
Sensitivity to ambient keV electrons
Sensitivity to B-field variations
Additional data products
Alternative data products
Double-probes (EFW)
Electron drift (EDI)
no limitations
DC to MHz
2-D (spin plane) or 3-D (if axial booms)
Yes
Yes
Low
No
S/c potential, plasma density, waves
Density and temperature
from use as Langmuir probe
&30 nT on Cluster
.10 Hz (depending on beam returns)
2-D (⊥B) or 3-D (in principle)
No
No
May swamp signal
Yes
B-field magnitude
keV electron measurements
at high time resolution
It should be noted that in this paper we concentrate on
the two Cluster instruments specifically designed for obtaining electric field measurements, i.e. EDI and EFW. One may
also construct an electric field estimate from the velocity moment v i from the Cluster ion spectrometers (CIS, Rème et al.,
2001) and the magnetic field B from the FGM fluxgate magnetometers (Balogh et al., 2001), assuming E+v i ×B=0. We
will use this to obtain a “third opinion” on the electric field
in cases where EFW and EDI disagree, and we will also include some CIS and FGM data for establishing the geophysical context of the data we show, but a complete CIS-EFW
comparison, also in regions where there are no EDI data, is
outside the scope of the present study, as is any details of
measurement errors in the CIS data.
While the Cluster data set for comparison of the two techniques surpasses what is available from previous missions,
we should note that some comparative studies have been
made before. Bauer et al. (1983) and Pedersen et al. (1984)
compared data from the two instrument types on the GEOS
satellites, finding some effects that we will also see in Cluster data. Kletzing et al. (1994) showed data from the F1
(double probes) and F6 (electron drift) instruments on the
Freja satellite in the topside ionosphere. Finally, the Geotail satellite carries instruments of both kinds, allowing Tsuruda et al. (1994) to compare their initial results.
2
EDI–EFW comparison in various plasma regions
2.1
2.1.1
Example 1: Solar wind-magnetosheath-plasma mantle
Geophysical setting
Our first example spans 12 h, from 12:00 to 24:00 UT, on
13 February 2001. The orbit of Cluster during this time interval is illustrated in Fig. 3. As can be seen from the model
boundaries and field lines in this figure, Cluster should move
from the solar wind through the magnetosheath and into the
magnetosphere during this time interval. The entry into the
magnetosphere occurs duskward of the southern cusp, so that
Cluster at the end of the interval is on field lines reaching the
duskside plasma mantle or low-latitude boundary layer.
Figure 4 shows 12 h of data from Cluster SC3. The top
three panels (a–c) show the electric field measurements that
are our real topic here and to which we will return after describing the geophysical setting. The lower three panels (d–
f) are auxilliary data for illustration of the plasma environments. As expected from Fig. 3, the spacecraft was in the
solar wind at the start of the interval (13 February 2001,
12:00 UT), with weak magnetic field (FGM data, bottom
panel f) and a density around 10 cm−3 (CIS HIA density moment, panel e). The first bow shock crossing can be seen
around 14:40 UT, with an increase in density and magnetic
field. The increasing density causes the electrostatic potential
of the spacecraft with respect to the surrounding plasma, Vsc ,
to decrease, as more plasma electrons become available for
compensating the emission of photoelectrons. This is seen as
a small increase in the EFW probe-to-plasma potential, Vps ,
which essentially is the negative of Vsc and thus will covary
with the density. One may therefore use Vps as a proxy for the
plasma density. How to convert from Vps to plasma density
has been reported for Cluster by Pedersen et al. (2001).
The magnetopause is crossed around 20:10 UT, after
which the magnetic field (panel (f) of Fig. 4) increases as
the spacecraft comes closer to the Earth. In the plasma mantle, the density as reported from CIS HIA (panel e) and EFW
Vps decreases monotonically to reach the limit of the HIA instrument sensitivity just after 22:00 UT. After this time, the
Vps data indicate a density increase not noted by the HIA
ion spectrometer, which is the expected behaviour if the ion
energy is below the spacecraft potential, so that the ions cannot reach the particle instrument.1 The Vps data suggest a
density increase towards 1 cm−3 at the end of the interval
at 24:00 UT. As the impact of this population is seen in the
spacecraft potential but not in the ion detector, the ion energy
1 For convenience, we implicitly assume normalization to the elementary charge e whenever comparing energies and potentials.
4
278
4
4
A. I. Eriksson
et al.: Electric
field
measurements
on Cluster
Comparing
electric
field
measurements
Comparing
electric
field
measurements
Comparing
electric
field
measurements
Fig.
3. (red)
Cluster
orbit
(red)
for
February
13, 2001,
the data
in
Figurein
4, viewed
from
GSE
YZ(left)
and
Z (right)
3.for
Cluster
orbit13,
(red)
February
13,corresponding
2001,
to4,the
viewed
from
GSE
Y directions.
(left)
and directions.
Zdirections.
(right) directions.
Fig. 3. Cluster
orbit
February
2001,
corresponding
to thecorresponding
data intotoFigure
viewed
GSE4,from
Y
(left)
and
(right)
Fig.
3. Fig.
Cluster
orbit
(red)
for
13 for
February
2001,
corresponding
the data
indata
Fig. from
4,Figure
viewed
GSE
Y (left)
and
Z colour
(right)
Model
magnetosheath
(light
shading)
and
magnetosphere
(dark
shading)
are
shown,
as
are
some
magnetic
field
lines
coded
forcoded for
Model
magnetosheath
(light
shading)
and
magnetosphere
(dark
shading)
are
shown,
as
are
some
magnetic
field
lines
colour
Model magnetosheath
(light
shading)
and
magnetosphere
(dark
shading)
are
shown,
as
are
some
magnetic
field
lines
colour
coded
for
Model
magnetosheath
(light
shading)
and
magnetosphere
(dark
shading)
are shown, as are
some
magnetic
field
lines
colour coded
for
magnetic
field
intensity.
Cluster
moves
inbound,
from
the
solar
wind
to
the
magnetosphere.
Plot
prepared
using
the
Orbit
Visualization
Tool,
magnetic
field
intensity.
Cluster
moves
inbound,
solar
to the
Plot
prepared
Orbit Visualization
magnetic fieldmagnetic
intensity.
Cluster
moves
inbound,
from
the solar
wind
tosolar
thethe
magnetosphere.
Plotmagnetosphere.
prepared
using
the Orbit
Visualization
Tool,
field
intensity.
Cluster
moves
inbound,
from
thefrom
wind
to wind
the magnetosphere.
Plot
prepared
using
theusing
Orbitthe
Visualization
Tool, Tool,
http://ovt.irfu.se.
http://ovt.irfu.se.
http://ovt.irfu.se.
http://ovt.irfu.se.
(a)
(b)
(c)
(d)
(e)
(a)
(b)
(c)
(d)
(e)
(f)
(f)
(a)
(b)
(c)
(d)
(e)
(f)
Fig.
the magnetosheath
magnetosheath into
into the
the magnetosphere.
magnetosphere. Panels
Panelsfrom
fromtop
toptoto
Fig.4.4. Comparison
ComparisonofofEFW
EFWand
and EDI
EDI data
data from
from the
the solar
solar wind
wind through
through the
bottom:
(a)
EExxininDSI
coordinates
(almost
GSE,
see
text)
in
an
inertial
frame. Red
Red is
is EFW
EFW data
data based
based on
onspin
spinfits
fitsfrom
fromprobe
probepair
pair12,
12,blue
blue
bottom:
(a)
DSI
coordinates
(almost
GSE,
see
text)
in
an
inertial
frame.
Fig.
4. Comparison
of EFW
and
EDI data
from
the solar
wind through into
the magnetosheath
into the
magnetosphere.
Panels from
top to
Fig. 4. Comparison
of EFW
andx EDI
data
from
the solar
wind
through
the magnetosheath
themagnetic
magnetosphere.
Panels
from
top
toCIS
+
isisEDI,
black
is
the
component
of
−v×B
from
CIS
HIA
velocity
moment
and
FGM
field,
green
is
the
same
for
CODIF
EDI,
black is(a)
xE
component
of −v × B(almost
from CIS
HIAsee
velocity
and frame.
FGM magnetic
field,data
green
is theonsame
for
CIS
CODIF
bottom:
in DSI coordinates
GSE,
text) inmoment
an is
inertial
Red on
is EFW
based
spin
fits
from
probe O
pair 12, blue
x (almost
bottom: (a) EOx+indata.
DSI
coordinates
GSE,
see
text)
in
an
inertial
frame.
Red
EFW
data
based
spin
fits
from
probe
pair
12,
blue
(b,Ec) E
in same
format.
EFW
probe-to-spacecraft
potential
(e)Density
Densitymoments
momentsfrom
fromCIS:
CIS:HIA
HIA(green,
(green,
data. (b,c)
and
Ez E
inz same
format.
(d)(d)
EFW
probe-to-spacecraft
potential
VpsV≈
−Vscsc. .(e)
y and
ps ≈−V
+
is EDI, yblack
is x×component
of −v
B frommoment
CIS HIA
velocity
moment
and
magnetic
field,for
green
the same
is EDI, blackassuming
is x component
of −v
B from CIS
HIA×velocity
and
FGMmagnitude.
magnetic
field,FGM
green
is the same
CIS is
CODIF
O +for CIS CODIF O
assumingprotons
protonsonly)
only)and
andCODIF
CODIFOO++ (black).
(black). (f)
(f) FGM
FGM magnetic field magnitude.
data.
sameprobe-to-spacecraft
format. (d) EFW probe-to-spacecraft
Vps ≈ moments
−Vsc . (e)from
Density
from CIS: HIA (green,
y and E
z in
data. (b,c) Ey and E
sameEformat.
(d)
EFW
potential Vps ≈ −Vpotential
CIS:moments
HIA (green,
z in (b,c)
sc . (e) Density
+
+
assuming
protonsOonly)
and CODIF
(black).field
(f) FGM
magnetic field magnitude.
assuming protons only)
and CODIF
(black).
(f) FGMOmagnetic
magnitude.
A. I. Eriksson et al.: Electric field measurements on Cluster
must stay at least below 25 eV after 22:00 UT, and below
10 eV close to midnight. One may also note that this cold
plasma shows quite a lot of structure.
The top three panels in Fig. 4 show the electric field measurements by EFW (red) and EDI (blue), and the electric field
inferred from the FGM magnetic field measurements and the
velocity moments v i from the CIS HIA (green) or CODIF
(oxygen ions, black) detectors, assuming E+v i ×B=0. The
EFW data shown are deduced by fitting a sinusoidal function
to the voltage between probes 1 and 2. We have not corrected
the EFW data for any well-known effects in double-probe instruments, like sunward offsets or partial shielding (Pedersen
et al., 1998; Maynard, 1998). The impact of such corrections
will instead be discussed as data are presented.
To transform CIS velocity moments, we assume that
E+v i ×B=0. We have chosen to include only EFW measurements from the plane in which these are made, i.e. the
spin plane, though, in principle, the third component could
be derived using magnetometer data and E×B=0 as an assumption. All data are therefore given in a reference frame
known as despun inverted, or DSI, coordinates, which is
a close approximation to GSE but with the Z axis along
the spacecraft spin axis. If the spacecraft spin was exactly
aligned with the GSE Z axis, the DSI and GSE systems
would be identical: for Cluster they differ only by a few degrees.
It should be noted that all the methods used to determine the electric field signals in this plot, in fact, are twodimensional, either by being utilized in the spin plane (EFW)
or in the plane perpendicular to B (EDI), or by assuming
E+v i ×B=0 (CIS). Three-dimensional double-probe electric field measurements have been implemented on other
spacecraft, for example, on the Polar EFI instrument (Harvey et al., 1995), using shorter axial booms, and could, in
principle, also be implemented by an EDI technique.
2.1.2
Solar wind
In the weak magnetic field in the solar wind, i.e. before
14:40 UT in Fig. 4, EDI cannot provide data, but it is clear
that EFW and CIS agree to well within a mV/m. While comparison of EFW and CIS data is not a prime topic in this
paper, we may note in passing that this agreement is typical for spin resolution data in the solar wind, though velocity
wakes may at times contaminate the sunward component in
higher resolution EFW data, as may be expected in the supersonically flowing solar wind. A detailed scrutiny will show
some tendency, seen most clearly in the EY data in panel (b),
for the EFW electric field, to show slightly lower magnitude
than expected from CIS velocity. This can be attributed to the
effective antenna length being slightly shorter than the physical probe separation, due to the effect of the conductive wire
booms on the real electric field. In effect, the booms partially short-circuit or shield away the ambient electric field.
This effect is well-known (e.g. Mozer, 1973; Pedersen et
al., 1998) and results in underestimates of the E-field magnitude of some 20% for Cluster EFW in tenuous plasmas. In
279
panel (a), showing the sunward component EX , the effect is
partially masked by a close-to-constant sunward offset field
of 0.5 mV/m. The sunward offset is due to the inevitable
photoemission asymmetry between probes on booms pointing toward and away from the Sun (Pedersen et al., 1998). In
the following discussion of other events, we will not further
comment on the sunward offset or the partial shielding, but
the reader should be aware that these effects always influence
double-probe electric field data to some extent.
2.1.3
Magnetosheath
After having entered the magnetosheath, the first time close
to 14:40 UT (Fig. 4), EDI data starts appearing intermittently
when the magnetic field strength is sufficiently high, the limit
typically being around 30 nT. When present, EDI data agrees
well with EFW and CIS in this region, despite EDI obviously
operating close to and sometimes below its low-B-field limit.
An exception is the large EX just before 20:00 UT, occurring
in a region of enhanced magnetic activity (not shown) which
complicates the interpretation of EDI data. CIS shows deviations from EDI and EFW, particularly in EX , around 15:00
and 17:00 UT, where the differing values derived from CIS
HIA are due to instrumental reasons outside the scope of this
paper. For EFW, the magnetosheath usually is a relatively
benign region, as the Debye length normally is well below
the boom length and the plasma flow is subsonic, thus not
creating appreciable wakes.
2.1.4
Plasma mantle
Following the spacecraft into the magnetosphere from
20:10 UT onwards (Fig. 4), we expect the conditions to become more suited to the EDI measurement technique as the
background magnetic field becomes stronger and less variable than in the magnetosheath. This is confirmed by the
good agreement we find between EDI and CIS ion data. For
the CIS data, the velocity moment after about 21:00 UT must
be calculated from the mass-separated data from the CODIF
sensor because of the increased relative abundance of oxygen. One should note that even though the behaviour of the
spacecraft potential shows that the ion detectors only capture a fraction of the ion population, the ion velocity moment should still be reasonably reliably determined as long
as there is a sufficient count rate, particularly when using
mass-separated data. We thus conclude that EDI works well
in this region of the magnetosphere.
While EDI and CIS agree well in the mantle, i.e. after
20:10 UT, we start seeing some hints of EFW slightly deviating. The discrepancy is small in this example, around a
mV/m, except for the spike in EX at 22:00 UT. We believe
the cause of the deviation is to be found in the effects of the
cold plasma component discussed above in Sect. 2.1.1. Similar discrepancies will be encountered in some other environments presented below, but are most pronounced in the polar
cap region. We will discuss them in detail in Sect. 3.
2806
6
Comparing
electric on
field
measurements
A. I. Eriksson
et al.: Electric
measurements
Cluster
Comparing
electric field
field
measurements
Comparing
electric
field measurements
Fig. 5. Cluster orbit (red) for July 4, 2001, corresponding to the data in Figure 6, viewed from GSE Y (left) and Z (right) directions. Model
magnetosheath
(light
shading)
magnetosphere
(darkinshading)
are
shown,
as
some6,
magnetic
field
lines
colour
coded
field
Fig.
5.for
Cluster
orbit
(red)
for
July
4, 2001,
in
Figure
viewed
from
GSE
Y
andfor
Zmagnetic
(right) directions.
Model
. 5. Cluster orbit
(red)
July
4,
2001,
corresponding
to thecorresponding
data
Figure
6, the
viewed
GSE
Y
(left)
and
(right)
directions.
Model
Fig.
5.
Cluster
orbit
(red)
for
4and
July
2001,
corresponding
to the to
data
indata
Fig.from
6,are
viewed
from
GSE
YZ(left)
and
Z(left)
(right)
directions.
Model
intensity.
The
Cluster
motion
is
upward
in
both
projections.
Plot
prepared
using
the
Orbit
Visualization
Tool,
http://ovt.irfu.se.
magnetosheath
(light
shading)
and
magnetosphere
(dark
shading)
are
shown,
as
are
some
magnetic
field
lines
colour
coded
for
magnetic
field
gnetosheath (light
shading)
and
magnetosphere
(dark
shading)
are
shown,
as
are
some
magnetic
field
lines
colour
coded
for
magnetic
field
magnetosheath (light shading) and magnetosphere (dark shading) are shown, as are some magnetic field lines colour coded for magnetic field
intensity.
Cluster
is upward
inprojections.
both
projections.
PlotOrbit
prepared
Orbithttp://ovt.irfu.se.
Visualization
Tool, http://ovt.irfu.se.
ensity. The Cluster
motion
is upward
inmotion
both
projections.
prepared
using
the
Visualization
Tool,
intensity.
The The
Cluster
motion
is upward
in bothPlot
Plot
prepared
using
theusing
Orbitthe
Visualization
Tool, http://ovt.irfu.se.
(a)
(a)
(a)
(b)
(b)
(c)
(c)
(b)
(c)
(d)
(d)
(e)
(e)
(f)
(f)
(d)
(e)
(f)
Fig.6.6.Comparison
ComparisonofofEFW
EFWand
andEDI
EDIdata
data from
from the
the plasmasphere
plasmasphere through
Fig.
through the
the cusp/cleft
cusp/cleft into
intothe
thepolar
polarcap.
cap.Format
FormatasasininFigure
Fig. 4.4.
. 6. Comparison of EFW and EDI data from the plasmasphere through the cusp/cleft into the polar cap. Format as in Figure 4.
Fig. 6. Comparison of EFW and EDI data from the plasmasphere through the cusp/cleft into the polar cap. Format as in Figure 4.
A. I. Eriksson et al.: Electric field measurements on Cluster
2.2
2.2.1
Geophysical setting
Inner magnetosphere
In the plasmasphere and trough regions, i.e. 12:00–13:00 UT
in Fig. 6, EFW and EDI are seen in panels (a) and (b) to
agree to better than a mV/m in this example, with the largest
deviations seen in the plasmasphere (before 12:15 UT). A
blowup of part of the trough region is seen in Fig. 7, showing
detailed agreement to within 0.1 mV/m in the observation of
pulsations, with periods around a minute. The EDI data have
been filtered by a boxcar averager, but otherwise no corrections or filtering of any kind have been applied to the data.
Such good agreement is commonly found in the trough
and subauroral regions, which generally are favourable to
EDI and EFW alike. In the plasmasphere, there can sometimes be discrepancies due to the formation of plasma wakes
(Bauer et al., 1983). However, we find a region of significant difference between EDI and EFW electric field measurements between 13:00 and 13:20 UT in Fig. 6. This will
be discussed further in Sect. 3.
2.2.3
281
Example 2: Plasmasphere-boundary layer-polar cap
Our second example is from 4 July 2001, between 12:00
and 17:30 UT. From the orbit plots in Fig. 5, we may expect Cluster to pass from the plasmasphere across boundary
layer field lines into the polar cap. Data from Cluster SC1 are
presented in Fig. 6, in a format similar to Fig. 4. Panel (d)
at first shows Vps values close to zero, corresponding to a
plasmaspheric density above 100 cm−3 . The plasmapause is
crossed in a few minutes just before 12:15 UT, when the density as inferred from Vps drops to ∼30 cm−3 in a region we
may identify as the trough. The density decreases continuously to around 15 cm−3 at 13:00 UT, where another density
drop signals a brief encounter with a part of the plasma sheet
extending into the afternoon sector. The increased variations
in the electric field, starting around 13:20 UT and continuing
until after 14:00 UT, are consistent with the expectation that
Cluster here should encounter boundary layer plasmas. Finally, the drop in hot plasma density, as seen by the CIS ion
detectors (panel e) around 14:20 UT, signals the start of the
open field line region of the polar cap, where the spacecraft
remains for the rest of the time interval plotted.
2.2.2
Comparing electric field measurements
Plasma sheet and boundary layer
Let us first look at the time interval when Cluster encountered boundary layer field lines, i.e. around 13:20–14:00 UT
in Fig. 6, as indicated by the higher level of electric field fluctuations. Here, the agreement between EDI and EFW as seen
on this time scale again is very good. However, the boundary
layer is a very dynamic region, and all dynamics certainly do
not show up in this spin-resolution plot. Figure 8 again shows
a blowup, with EFW data at full time resolution, which for
this case was 25 samples/s. As is to be expected, EDI cannot adequately cover this dynamical situtation, though the
data points actually acquired agrees well with EFW. As for
Fig. 7. Detail of part of the data in Fig. 6, showing agreement beFig. 7.
Detail
partEDI
of the
datatoin
6, ashowing
tween
EFW
(red)ofand
(blue)
theFigure
level of
fractionagreement
of a mV/m
(red) and EDI (blue) to the level of a fraction of a
inbetween
the innerEFW
magnetosphere.
mV/m in the inner magnetosphere.
EFW, the good quality of the data shown here is common not
crossed
in a few layer
minutes
just before
when the in
denonly
for boundary
plasmas
but is 12:15,
also dominating
the
sity as inferred from Vps drops to ∼ 30 cm−3 in a region
plasma sheet and auroral zone, and essentially always in the
we may identify as the trough. The density decreases concentral plasma sheet (not shown).
However, spurious fields
tinuously to around 15 cm−3 at 13:00, where another density
can sometimes show up in double-probe data, as is illustrated
drop signals a brief encounter with a part of the plasma sheet
byextending
the largeinto
EDI-EFW
discrepancy seen in the plasma sheet
the afternoon sector. The increased variations
(Fig.
6,
13:00–13:20
UT).
As was13:20
the case
in the regions
in the electric field starting around
and continuing
unwith
some
EDI-EFW
discrepancy
in
Example
(Fig.Cluster
4), the
til after 14:00 are consistent with the expectation1 that
plasma
density
indicated
by the layer
CIS instrument
in thisthe
rehere should
encounter
boundary
plasmas. Finally,
−3 ) is much lower than what is expected
gion
(below
0.1
cm
drop in hot plasma density as seen by the CIS ion detectors
from
thee)EFW
Vps14:20
valuesignals
(around
cm−3
hinting
that line
cold
(panel
around
the 1start
of),the
open field
plasma
may
be
the
source
of
the
problem.
For
the
moment,
region of the polar cap, where the spacecraft remains for the
we
only
notetime
the interval
existence
of this kind of problem, which we
rest
of the
plotted.
will discuss in more detail in the following sections.
2.2.2 Inner magnetosphere
2.2.4 Polar cap
In the plasmasphere and trough regions, i.e. 12:00 - 13:00 in
After
leaving
theand
boundary
field
lines(a)around
UT
Figure
6, EFW
EDI arelayer
seen in
panels
and (b)14:20
to agree
to better
thansatellite
a mV/menters
in this the
example,
largest
devi(Fig.
6), the
polar with
cap.theThe
probe-toations seen
in the plasmasphere
(before
blowup
spacecraft
potential
Vps of panel (d)
stays 12:15).
betweenA–20
V and
of V
part
the remainder
trough region
is seen
in Figure
7, showing
de–30
forofthe
of the
interval,
indicating
densities
−3 , mV/m
tailed agreement
to within
observation
of
between
1 cm−3 and
0.3 cm0.1
except inforthe
a brief
excursion
with periods
around
a minute.
data haveto
topulsations
–40 V (around
0.1 cm−3
) around
15:35The
UT.EDI
Comparing
been
bydensity
a boxcarmoment
averager,
otherwise
correcthe
CISfiltered
CODIF
in but
panel
(e), it isnoclear
that
tions
or filtering
ofthe
anyion
kind
have been
applied
to the
data. of
the
density
seen by
detector
is only
a small
fraction
Suchdensity,
good agreement
is commonly
found inminimum
the trough
the total
except possibly
at the density
inand subauroral
regions,
favourable
to
dicated
by the EFW
Vps atwhich
15:35 generally
UT. In theare
polar
cap region,
EDI
and EFW
alike. In
thethe
plasmasphere,
there can
somethe
plasma
component
from
CIS data is readily
identified
times be discrepancies due to formation of plasma wakes
as the polar wind, a cold plasma flow known to fill these re(Bauer et al., 1983). However, we find a region of signifgions in number densities comparable to those indicated by
icant difference between EDI and EFW electric field meaVps . By using artificial potential control, the Polar spacecraft
surements between 13:00 and 13:20 in Figure 6. This will be
could
be brought down to close to zero values of Vps , endiscussed further in Section 3.
abling the ions to reach the spacecraft and consequently allowing Moore et al. (1997) and Su et al. (1998) to determine
Fig. 8. D
EDI (blue
layer.
2.2.3 P
Let us fi
tered bou
Figure 6
tuations.
on this ti
layer is a
not show
a blowup
this case
not adeq
data poin
EFW, the
only for b
plasma s
central p
can some
by the la
(Figure 6
with som
the plasm
gion (bel
from the
plasma m
we only
will disc
2.2.4 P
After lea
(Figure 6
spacecra
agreement
ction of a
the dena region
ases conr density
ma sheet
ariations
nuing unt Cluster
nally, the
detectors
field line
ns for the
13:00 in
) to agree
gest deviA blowup
wing devation of
data have
o correce data.
e trough
urable to
an somema wakes
of signifeld meais will be
282
7
A. I. Eriksson et al.: Electric field measurements on Cluster
though the electric field estimates are usually good when
present, particularly inside the magnetopause. In the plasmasphere and trough, the two instruments generally agree well,
though EFW may sometimes pick up spurious signals, the
nature of which we will return to in Sect. 3. This also happens at times in the auroral zone, though this region is usually more problematic for EDI than for EFW, as the strong
and rapid electric field variations and the presence of intense
auroral electrons may result in an EDI data loss. On the
other hand, EDI provides very good data in the polar caps, at
least sufficiently close to the Earth to keep the magnetic field
above the EDI threshold of about 30 nT, where the EFW data
often are severly contaminated or even dominated by spurious electric fields.
3
Fig. 8. Detail of part of the data in Fig. 6, with EFW (red) and
EDI
data of
at part
full time
in the6,plasma
sheet(red)
boundary
Fig.(blue)
8. Detail
of theresolution
data in Figure
with EFW
and
layer.
EDI (blue) data at full time resolution in the plasma sheet boundary
layer.
that the cold polar wind flow can be seen all the way out to
2.2.3
the
PolarPlasma
apogeesheet
at 9and
RE .boundary
Since thelayer
thermal energy, as well
as the bulk flow energy of the ions in the polar wind, are beLetthe
us typically
first look observed
at the time
interval when
Cluster
low
spacecraft
potential
−Vpsencoun, we see
tered
boundary
layer
field
lines,
i.e.
around
13:20
14:00
in
why this plasma cannot reach the CIS detectors–and
hence
Figure
6
as
indicated
by
the
higher
level
of
electric
field
flucescapes detection.
tuations. Here, the agreement between EDI and EFW as seen
Differences between the electric field signals from EFW
on this timescale again is very good. However, the boundary
and
EDI can be seen in panels (a) and (b) of Fig. 6. Allayer is a very dynamic region, and all dynamics certainly do
though
seen
Y component,plot.
the Figure
X component
most
not show
in in
thisthespin-resolution
8 again is
shows
significantly
affected.
EDI atworks
wellresolution,
in this region,
asfor
can
a blowup, with
EFW data
full time
which
bethis
seen
bywas
comparing
to the As
E-field
from
thecanCIS
case
25 samples/s.
is to estimated
be expected,
EDI
oxygen
velocity cover
moment
this is situtation,
computable.
At times,
not adequately
thiswhen
dynamical
though
the
particularly
around
15:30
UT,
the
data
suggests
some
covaridata points actually acquired agrees well with EFW. As
for
ance
between
thequality
EFW-EDI
and V
. EDI, using
EFW,
the good
of thediscrepancy
data shown here
ispscommon
not
keV
should
insensitive
to potentialalso
variations
onlyelectrons,
for boundary
layerbe
plasmas
but is dominating
in the
ofplasma
the 10sheet
V order,
but
this
is
certainly
not
the
case
forinEFW.
and auroral zone, and essentially always
the
The
indications
thus point
to the dominant
ercentral
plasma sheet
(not shown).
However,measurement
spurious fields
canoriginating
sometimes from
show EFW
up in double-probe
data, EDI.
as is illustrated
ror
rather than from
The event
by the large
EDI-EFW
seen inexamples
the plasmalike
sheet
presented
here
is not andiscrepancy
isolated artifact:
this
(Figure
6, 13:00
– 13:20).
As wascomparisons
the case in the
regions
are
commonly
found
in EFW-EDI
in the
polar
with
some and
EDI-EFW
discrepancy
in Example
1 (Figure
4),
cap
region,
in preceeding
sections
in this paper
we have
the plasma
indicatedfor
by briefer
the CIS intervals
instrumentininother
this reseen
similardensity
discrepancies
re−3
gion (below
) is muchimportant
lower than
is expected
gions,
as well.0.1Itcm
is obviously
towhat
understand
why:
−3
from
thebeEFW
Vps value
(around
this
will
the topic
of Sect.
3. 1 cm ), hinting that cold
plasma may be the source of the problem. For the moment,
we only
note theofexistence
2.3
Summary
events of this kind of problem, which we
will discuss in more detail in the following sections.
Summarizing what can be learned from the discussion
2.2.4 Polar cap
around Figs. 4 and 6, we conclude that EFW produces good
quality
electricthe
field
data inlayer
the field
solarlines
windaround
and the
magneAfter leaving
boundary
14:20
UT
tosheath,
with
some
spurious
components
on
the
order
of a
(Figure 6), the satellite enters the polar cap. The probe-tomV/m
often
appearing
in
regions
with
a
tenuous
cold
plasma
spacecraft potential Vps of panel (d) stays between -20 V and
component in the mantle. EDI produces no data at all in
the solar wind and only intermittently in the magnetosheath,
3.1
Polar cap discrepancies
Spurious field and spacecraft potential
Figure 9 shows a detailed view of 1 h of data from Fig. 6.
Panel (a) shows Vps , approximately equal to the negative of
the spacecraft potential Vsc . During this hour, this quantity stays between –20 V and –30 V, corresponding to plasma
densities between about 1 cm−3 and 0.3 cm−3 (Pedersen et
al., 2001), except for an excursion to –15 V, or 1.5 cm−3 , at
around 800 s. Panels (b) and (c) show the X and Y components of the electric field from EDI (magenta) and EFW
(red/black). The EFW data plotted are spin fits from probe
pair 12 (red) and 34 (black). The data from the two probe
pairs coincide nearly exactly, so that the black trace is hard
to discern.
It can be seen in these panels (b) and (c) of Fig. 9, that
EFW and EDI electric field measurements differ by several
mV/m during most of this interval. It is interesting to note
that this discrepancy is the same regardless of the EFW probe
pair used, as the red (P12) and black (P34) curves coincide.
If it is the EDI field which is the more accurate representation
of the unperturbed electric field in the plasma, the source of
the perturbed field seen by EFW must be quite stable. That
the field seen by EFW cannot only be the unperturbed electric field in the plasma should be clear from the EDI–CIS
agreement shown previously in Fig. 6. A further indication
is that the EFW E-field varies with the probe-to-spacecraft
potential, Vps . This can be seen more clearly in panel (d),
displaying the DSI X (solid) and Y (dashed) components of
the difference between the instruments,
E spur = E EFW − E EDI .
(1)
Comparing panel (d) to panel (a), we can immediately see
that the difference between the instruments almost disappears at the temporary increases in Vps at 800 and 3100 s, and
hints of a partial, albeit imperfect, covariation which can be
seen during a large part of the plotted interval. As it is hard to
conceive of a mechanism by which the EDI instrument, using
electrons of keV energy, should be sensitive to potential variations of a few volts, this dependence on Vps is independent
A.
I. Eriksson
et al.: field
Electric
field measurements on Cluster
Comparing
electric
measurements
2839
Cluster SC1 2001−07−04
(a)
−20
−30
5
Angle in spin plane [deg]
Espur [mV/m] Ey [mV/m]
Ex [mV/m]
Vps [V]
−10
16:05
16:10
16:15
16:20
16:25
16:30
16:35
0
−5
5
16:40
16:45
16:50
EDI Ex
16:55
(b)
EFW Ex
16:05
16:10
16:15
16:20
16:25
16:30
16:35
16:40
16:45
16:50
EDI Ey
16:55
(c)
0
−5
5
EFW Ey
16:05
16:10
16:15
16:20
16:25
16:30
16:35
16:50
16:55
(d)
Spurious Ex
16:05
16:10
16:15
16:20
16:25
180
16:30
16:35
16:40Projection
16:45of −B
16:50
16:55
(e)
Spurious E
90° = duskward
90
Projection of v
⊥
°
0
−90
16:45
Spurious Ey
0
−5
270
16:40
0 = sunward
16:05
16:10
16:15
16:20
16:25 16:30 16:35 16:40
Time [UT] on 2001−07−04
16:45
16:50
16:55
Fig. 9. Comparison of EFW and EDI data for an event with a spurious electric field in the EFW data. Panels from top to bottom: (a) EFW
Fig. 9. Comparisonpotential
of EFW and
data
a spurioussee
electric
field
the EFW reference
data. Panels
fromRed
top and
to bottom:
(a) EFW
probe-to-spacecraft
Vps EDI
≈ −V
(b)an
EXevent
(DSIwith
coordinates,
text) in
theinspacecraft
frame.
black represent
sc . for
probe-to-spacecraft
potential
Vps ≈
−Vscpairs
. (b)12
EXand
(DSI
text)
in the(c)
spacecraft
reference
frame.
Red and field
blackinisEFW
EFWdata,
data
EFW
data based on spin
fits from
probe
34,coordinates,
respectively,see
blue
is EDI.
EY in same
format.
(d) Spurious
based on spin
from probe
pairs
34, respectively,
blue is of
EDI.
(c) projected
EY in same
format.
(d)plane,
Spurious
field from
in EFW
assuming
assuming
EDI fits
is correct.
Black
is E12
magenta
is EY . (e) Angles
fields
onto
the spin
counted
the data,
Sun direction,
X , and
EDI
is correct.
is Eis
magenta
is E−E
Angles
of the
fields
projectedofonto
spin plane, counted
from the
sunisdirection,
as shown
in
10. Red
, blue is
projection
EDIthe
perpendicular
drift velocity,
green
the projection
of the
as
shown
in Fig.Black
X ,E
y . (e)
spur =E EFW
EDI
Figure 10.
is Espur = E
− the
E EDI
, blue isalong
the projection
EDI from
perpendicular
drift
green
is the projection
of the
negative
negative
of Red
the geomagnetic
field
(i.e.
direction
B pointingofaway
the Earth).
Thevelocity,
spike-like
excursions
(e.g. around
16:10
UT)
EFW
of the geomagnetic
fieldin(i.e.
thewhich
direction
along
B pointing
originate
from glitches
EDI,
are of
no interest
here.away from Earth). The spike-like excursions (e.g. around 16:10) originates from
glitches in EDI of no interest here.
evidence that the problem indeed is with the double-probe
in panel (e)
Figure
9. Thethat
directions
areofexplained
in Figmethod.
Weofthus
conclude
the type
EFW-EDI
disure
10:
note
that
all
angles
are
referring
to
projections
in the
crepancy encountered in the polar cap is due to a spurious
spin plane,
from
solarfield
direction
≈ XGSE )
field,
E spur ,counted
adding to
the the
natural
in the(X
EFW
DSI data.
positive towards dusk (YDSI ≈ YGSE ). The green line shows
the angle of the projection of −B onto the spin plane: in the
3.2 Direction of spurious field
northern hemisphere, −B is the direction away from Earth
along the field lines. The angle of the projection of the EDI
To
obtain
further
information
theplane
spurious
field, we
will
flow
velocity,
v EDI
, onto theon
spin
is shown
in blue.
now
study
its
direction
by
plotting
a
set
of
angles
in
the
spin
Note that while the full EDI flow velocity vector is necessarplane
in panel (e)toofBFig.
9. The
are explained
in
ily perpendicular
because
of directions
the EDI operational
princiFig.
10:
note
that
all
angles
are
referring
to
projections
in
the
ple (Section 1), the projections of v EDI and B onto the spin
spin
the solar direction (XDSI ≈XGSE )
planeplane,
do notcounted
need to from
be perpendicular.
positive towards dusk (YDSI ≈YGSE ). The green line shows
theThe
angle
of plane
the projection
onto the E-field
spin plane:
in
spin
direction of
of −B
the spurious
seen by
the
Northern
Hemisphere,
−B
is
the
direction
away
from
the
EFW is shown in red. We can see that throughout the in◦ of the projection of the
Earth
the field
lines.
The180
angle
terval,along
this angle
stays
around
, superficially suggesting
EDI
flow
velocity,
v
,
onto
the
spin
plane is shown
in blue.
EDI may be antisunward.
that the spurious field
However,
we
Note
that
while
the
full
EDI
flow
velocity
vector
is
necessarmay note that the direction of E spur depends on the direcily
to B because
thedrift
EDIvelocity
operational
printionperpendicular
of the perpendicular
part ofofthe
v ⊥ deterciple
(Sect.
1),
the
projections
of
v
and
B
onto
the
spin
EDIthe spurious field (red)
mined by EDI, shown in blue. In fact,
plane
do
not
need
to
be
perpendicular.
always stays between v ⊥ (blue) and −B (green). To deter-
The spin plane direction of the spurious E-field seen by
mine is
which
direction
thecan
important,
show data
EFW
shown
in red. isWe
see thatwe
throughout
thefrom
in◦
a
northern
hemisphere
dawn-dusk
orbit
in
Figure
11,
in the
terval, this angle stays at around 180 , superficially suggestsame
format
as in Figure
Jumping
directly to However,
panel (e),
ing
that
the spurious
field 9.may
be antisunward.
we
see
that
the
spurious
field
stays
between
the
−B
we may note that the direction of E spur depends on and
the v
di⊥
on
this
orbit
as
well,
while
it
does
not
at
all
align
with
the
rection of the perpendicular part of the drift velocity v ⊥ desolar direction.
is exactly
expectfield
for
termined
by EDI,This
shown
in blue.the
In direction
fact, the we
spurious
the
polar
wind
plasma
flow
that
can
be
expected
in
this
re(red) always stays between v ⊥ (blue) and −B (green). To
gion
of
space:
EDI
should
correctly
pick
up
its
perpendicdetermine which direction is more important, we show data
ular component
observe the
parallel
from
a Northern vHemisphere
dawn-dusk
orbit
in Fig.velocity
11, in
⊥ but cannot
component
v k . as
Asinthe
polar
wind is an
outflow
along (e),
the
the
same format
Fig.
9. Jumping
directly
to panel
geomagnetic
lines, field
the unobservable
should
be
anwe
see that thefield
spurious
stays betweenvthe
−B
and
v
k
⊥
tiparallell
the geomagnetic
field,
toward
also
on thistoorbit,
while it does
notwhich
at all here
alignpoints
with the
soEarth.
The polar
velocity
v ⊥ we
+ vexpect
lar
direction.
Thiswind
is exactly
thevector
direction
forthus
the
k should
lie between
−B and
v ⊥that
, precisely
observed
spurious
polar
wind plasma
flow
is typicalasinthe
this
region of
space:
electric
fieldcorrectly
does. This
suggests that E
EDI
should
pickstrongly
up its perpendicular
component
spur is reto
the
plasma
flow.
In
the
following
section,
we will
vlated
but
cannot
observe
the
parallel
velocity
component
vk.
⊥
discuss
how wind
such aisspurious
fieldalong
may the
arise.
As
the polar
an outflow
geomagnetic field
lines, the unobservable v k should be antiparallel to the geomagnetic field, which here points toward the Earth. The
polar wind velocity vector v ⊥ +v k should thus lie between
perpendicular as well as antiparallel to the magnetic field would
thus be directed between the v perp and −B vectors, i.e. where we
find E spur .
10
284
electric
field measurements
A. I. Eriksson et al.:Comparing
Electric field
measurements
on Cluster
3.3 Electrostatic wake model
Y
Cluster SC1 2001−04−28
X (sunward)
Espur
−B
Fig. 10. Directions of various quantities projected onto the spin
Fig. 10.
Directions
ofcoordinate
various quantities
ontoGSE
the axes,
spin
plane.
X and
Y are DSI
axes, veryprojected
close to the
plane.
Y aredirection
DSI coordinate
very close
to angles
the GSE
so
that XXisand
the solar
which isaxes,
a reference
for the
in
axes,9.soBthat
X ambient
is the solar
direction which
is reference
anFig.
is the
magnetospheric
magnetic
field, for
andthe
E spur
Figure 9.electric
B is the
ambient
magnetospheric
field,
isgles
theinspurious
field.
The projection
of themagnetic
perpendicular
and E spur of
is the
electric
field. The
of the percomponent
the spurious
plasma flow
is denoted
by vprojection
.
The
projection
in
⊥
pendicular
the plasma
is denotedperpendicular,
by v ⊥ . The
this
plane ofcomponent
a 3-D flowof
velocity
v withflow
components
projection
in this plane
3D flow field,
velocity
v with
as
well as antiparallel
to of
theamagnetic
would
thuscomponents
be directed
perpendicular
as
well
as
antiparallel
to
the
magnetic
would
between the v perp and −B vectors, i.e. where we find Efield
spur .
thus be directed between the v perp and −B vectors, i.e. where we
find E spur .
(a)
−20
Electrostatic
wake model
22:30
Ex [mV/m]
3.3
Vps [V]
−B and v ⊥ , precisely as is the case of the observed spurious
electric field. This strongly suggests that E spur is related to
Cluster SC1 2001−04−28
the plasma flow. In the following section, we will discuss
how such −10
a spurious field may arise.
22:35
22:40
Angle in spin plane [deg] Espur [mV/m] Ey [mV/m]
10
To understand
the EFW
double-probe
measurements, it is necesEx
EDI Ex
(b)
5
sary to consider the potential in space around the space0
craft. Initially neglecting any background electric field, i.e.
22:30
22:40
the field that we would
like to22:35
measure,
the
poEFWelectrostatic
Ey
10
tential field 58 in the vicinity of the spacecraft will be
deter(c)
mined by the
0 spacecraft potential, Vsc , and by any potentials
EDI Ey of the satellite.
induced in the plasma because of the presence
22:30
22:35 the 22:40
In the following
we
will
consider
possible
contribution
Spurious Ey
10
8wake arising
from
a
wake
behind
the
spacecraft
in a(d)
flowing
5
plasma.
0
Spurious Ex
A wake is expected
to form22:35
behind 22:40
any object in a super22:30
of −B
sonic flow. In aProjection
plasma,
where the thermal speed is usually
90 for electrons than for ions, wakes are(e)usually
much higher
negatively charged, as thermal motion will carry more elecSpurious E
0 Projection
v
trons than ions
into theofwake.
If the
characteristic wake size
⊥
L, which should be chosen to be in the direction where the
−90
wake is the
thinnest, is around or exceeding the Debye length
λD in the surrounding plasma, negative potentials on the order of the thermal potential
KTe /e may appear,
22:30 equivalent
22:35
22:40
Time [UT] on 2001−04−28
8wake ∼ −
KTe
,
e
L & λD .
(2)
Fig. 11. Comparison of EFW and EDI data for an event with a
spurious electric field in the EFW data, this time from a dawn-dusk
Values much above this cannot be reached, as electrons then
orbit, in the same format as in Figure 9.
cannot enter the wake, and consequently, charge accumulation stops. For LλD , a simple solution of Poisson’s equa-
Angle in spin plane [deg] Espur [mV/m] Ey [mV/m]
B
v
Ex [mV/m]
Vps [V]
To understand
−10 the double-probe measurements, it is necessary to consider the potential in space around the(a)spacecraft. Initially
−20 neglecting any background electric field, i.e.
the field that we would like to measure, the electrostatic po22:35
22:40 will be detertential field10Φ in the22:30
vicinity of
the spacecraft
EFW
Ex
EDI Ex Vsc , and by any potentials
mined by the
(b)
5 spacecraft potential,
induced in the
0 plasma because of the presence of the satellite.
In the following we will consider the possible contribution
22:30
22:35
22:40
EFW Ey
Φwake arising
10 from a wake behind the spacecraft in a flowing
plasma.
(c)
5
A wake is0 expected to form behind any object in a superEDI Ey
sonic flow. In a plasma, where the thermal
speed usually is
22:30
22:35
22:40
much higher
wakesEyusually are
10 for electrons than for ions, Spurious
negatively charged,
as thermal motion will carry more
(d) elec5
0 into the wake. If the characteristic wake size
trons than ions
Ex
L, which should be chosen to be inSpurious
the direction
where the
22:30
22:35
22:40
Projection
of −B
wake is thinnest, is around or exceeding the Debye length λD
in the surrounding
plasma, negative potentials on the order
of
(e)
90
the thermal potential equivalent KTe /e may appear,
0
Projection of v
KTe
,
−90 e
Φwake ∼ −
⊥
Spurious E
L & λD .
(2)
Values much above this cannot be reached, as electrons then
cannot enter the wake, and consequently charge accumula22:30
22:35
22:40
tion stops. For L solution of Poisson’s
D , aonsimple
Timeλ[UT]
2001−04−28
equation for a planar slab structure, void of ions but with
unperturbed
electron density, suggests a scaling
Fig. 11. Comparison of EFW and EDI data for an event with a
inofthe
2 EFWand
spurious
data,
thisdata
timefor
from
dawn-dusk
Fig.
11. electric
Comparison
EDI
an aevent
with a
L EFW
KTfield
e
orbit,
in
the
same
format
as in
9. L this
, Fig.data,
λtime
(3)
Φ
∼
−
spurious
electric
field
in
the
EFW
D . from a dawn-dusk
wake
e
λD
orbit, in the same format as in Figure 9.
A slab geometry is more appropriate for an ion wake caused
tionanforelongated
a planar slab
structure,
void of
ionsthan
but with
unperby
absorbing
physical
target
for the
returbed electron
a scaling
pelling
potentialdensity,
aroundsuggests
a positively
charged structure, for
which we wouldrather
2expect ion deflection in a classical
KT
L process.
e
Rutherford
scattering
Nevertheless,
an analogous
8wake ∼ −
,
L λD .
(3)
e
λrapid
scaling law, giving
increase with size, will apply also
D
in the deflection case. For Cluster, only in the cold and dense
A slab geometry is more appropriate for an ion wake caused
plasmasphere can the Debye length reach down to typical
by an elongated absorbing physical target than for the respacecraft dimensions, which can be taken to be the height
pelling potential around a positively charged structure, for
or radius of the cylindrical spacecraft, i.e. 1 – 1.5 m, and
which we would rather expect ion deflection in a classical
usually stays well above. The wakes forming behind a ClusRutherford scattering process. Nevertheless, an analogous
ter spacecraft in for example the solar wind could possibly
scaling law, providing a rapid increase with size, will also
be charged to a level of a volt or so, corresponding to some
apply in the deflection case. For Cluster, only in the cold
fraction of the solar wind electron temperature according to
and dense plasmasphere can the Debye length reach down to
(3), but the influence this wake with a width of a meter or so
typical spacecraft dimensions, which can be taken to be the
can have on the probes, 44 m away at the end of wire booms,
height or radius of the cylindrical spacecraft, i.e. 1–1.5 m,
must be small. Indeed, one can sometimes see a clear wake
and usually stays well above. The wakes forming behind a
in EFW data from the solar wind, appearing as a brief spike
Cluster
spacecraft,
for example
in the
posin
the data
from each
probe once
persolar
spin wind,
when could
the probe
sibly
be
charged
to
a
level
of
a
volt
or
so,
corresponding
to
crosses the narrow wake. Such wake signatures are easily
some
fraction
of
the
solar
wind
electron
temperature
accordidentifiable and cause little problem. The wire booms carrying to
(3), but
influence
that this wake,
with a width
of
ing
theEq.
probes
arethe
only
a few millimeters
in diameter,
so no
asignificant
meter or potentials
so, can have
on
the
probes,
44
m
away
at
the
end
can build up in a wake caused by them.
of wire
be small.
Indeed,
can should
sometimes
One
maybooms,
thus bemust
tempted
to conclude
thatone
wakes
not
see
a
clear
wake
in
EFW
data
from
the
solar
wind,
appearing
be much of a problem.
as a brief spike in the data from each probe, once per spin,
the the
Φwake
Values
cannot
tion st
equatio
unpert
Φwake
A slab
by an
pelling
which
Ruther
scaling
in the d
plasma
spacec
or rad
usually
ter spa
be cha
fractio
(3), bu
can ha
must b
in EFW
in the
crosse
identifi
ing the
signifi
One m
be muc
A. I. Eriksson et al.: Electric field measurements on Cluster
Comparing electric field measurements
when the probe crosses the narrow wake (not shown). Such
if the
is very tenuous,
spacecraft
powakeHowever,
signatures
are plasma
easily identifiable
and the
cause
few probtential
can
be
so
high
that
the
true
obstacle
to
the
ion
flow
lems. The wire booms carrying the probes are only a fewis
not the physical
structure
of significant
the spacecraft,
but thecan
potential
millimeters
in diameter,
so no
potentials
build
pattern
surrounding
it,
which
to
first
approximation
can to
be
up in a wake caused by them. One may thus be tempted
taken
to
be
the
vacuum
potential
arising
from
a
satellite
at
conclude that wakes should not be much of a problem.
potential Vsc . Thus, in case
However, if the plasma is very tenuous, the spacecraft potential can1be so2high that the true obstacle to the ion flow is
< eVscof, the spacecraft, but the potential
(4)
mi vflow
notKT
thei <
physical
structure
2
pattern surrounding it, which, to a first approximation, can
where T , mi and vflow are the ion temperature, mass and
be taken toi be the
vacuum potential arising from a satellite at
flow speed, e is the elementary charge and Vsc ≈ −Vps is
potential Vsc . Thus, in the case
the spacecraft potential, a wake will form whose characteristic size is determined not by the spacecraft or booms, but by
1
2
2
/e, as the ions (4)
will
KTthe
mi vflow
< surface
eVsc , Φ = 12 mi vflow
i <equipotential
deflect2 before reaching this equipotential. In the cases of interest,Tithe
length is much above the typical spacecraft
where
, mDebye
i and vflow are the ion temperature, mass and
scale
size
(a
few
meters),
so thecharge
spacecraft
is essenflow speed, e is the elementary
and Vpotential
sc ≈−Vps is the
tially
a
Coulomb
field.
For
a
spacecraft
potential
twice
the
spacecraft potential, a wake1 will2form whose characteristic
m
v
/e
equipotential
thus
will
ion
flow
energy,
the
Φ
=
i
flow
size is determined not by the2 spacecraft
or booms, but by the
be roughly one
spacecraft
away, increasing the effec2
equipotential
surface
8= 21 mradius
i vflow /e, as the ions will deflect
tive cross
section
ofequipotential.
the obstacle asIn
seen
the ion
flow by a
before
reaching
this
thebycases
of interest,
2
factor
around
2
=
4.
the Debye length is much above the typical spacecraft scale
The
formation
kind of enhanced
electrostatic
wake
size (a
few
meters), of
so this
the spacecraft
potential
is essentially
a
around
a
spacecraft
and
its
influence
on
the
double-probe
Coulomb field. For a spacecraft potential twice the ion flow
measurements on the
GEOS and ISEE spacecraft was dis2 /e
energy, the 8= 12 mi vflow
equipotential will thus be roughly
cussed by Bauer et al. (1983) and Pedersen et al. (1984). In
one spacecraft radius away, increasing the effective cross seccomparisons to electron drift measurements and ion drift motion of the obstacle, as seen by the ion flow, by a factor of
tion, they
found that the wake formed by the E × B drift
around 22 =4.
in a plasma caused perturbation of the measurement of E.
The formation
of this kind
enhanced
electrostatic
While
they considered
the of
increase
of effective
size wake
of the
around
a
spacecraft
and
its
influence
on
the
double-probe
spacecraft, we should note that the effect may be even more
measurements
on the
and ISEE
was disdramatic around
the GEOS
wire booms,
wherespacecraft
the logarithmic
pocussed
by
Bauer
et
al.
(1983)
and
Pedersen
et
al.
(1984).
tential decay applicable close to long booms can increase
the
In effective
comparisons
to electron
drift measurements
and to
ionmeters.
drift
obstacle
cross section
from millimeters
1
2 drift
motion,
that
the wake
formed
the E×B
In the they
case found
of very
tenuous
plasmas,
eVby
sc 2 mi vflow /e,
in this
a plasma
caused
perturbation
of
the
measurement
of
wire boom induced wake could be expected to be E.
the
While
considered
the increase
thespacecraft
effective size
of
morethey
important
contribution,
whileinthe
induced
1 may
2 be even
thewake
spacecraft,
notefor
that
effect
should we
stillshould
dominate
eVthe
sc & 2 mi vflow /e. The
more
dramatic
around
the
wire
booms,
where
the
logarithmic
situation is illustrated qualitatively in Figure 12b, where the
potential
close
to long charged
booms can
increase
shaded decay
regionapplicable
indicates the
negatively
wake
region,
theand
effective
obstacle
cross
section
from
millimeters
to mealso in Figure 8 of Pedersen et al. (1984).
2 /e,
ters. To
In the
casequantify
of very these
tenuous
plasmas,arguments
eVsc 12 mfor
i vflow
further
qualitative
the forthismation
wire-boom
induced
wake could
be expected
be the
of enhanced
electrostatic
wakes
and their to
effects
on
more
important measurements,
contribution, while
thenumerical
spacecraft-induced
double-probe
we need
simulations
1
2 /e. The situawake
should in
still
dominate
for eVSuch
mi vflow
of Cluster
a flowing
plasma.
simulasc & 2 particle-in-cell
tion
is illustrated
in Fig. 12b,
the shaded
tions
(Engwall etqualitatively
al., 2003, Engwall,
2004)where
are indeed
consisregion
indicates
the negatively
charged
wake region,
also
tent with
this hypothesis,
showing
a magnitude
andand
angular
in dependence
Fig. 8 of Pedersen
et al. (1984). electric field seen by EFW
of the wake-induced
agreeing
with our
observations.
similar wake
canforalso
To furtherwell
quantify
these
qualitative A
arguments
for the
be seen
the simulations
by Zinin
et al.
(2004).
mation
of in
enhanced
electrostatic
wakes
and
their effects on
double-probe measurements, we need numerical simulations
Effect
potential
control
of 3.4
Cluster
in aof
flowing
plasma.
Such particle-in-cell simulations (Engwall et al., 2004; Engwall, 2004) are indeed conEachwith
Cluster
carriesshowing
an instrument
for artificial
sistent
thissatellite
hypothesis,
a magnitude
and conantrol of the spacecraft potential by emission of ions, ASPOC
gular dependence of the wake-induced electric field seen by
(Torkar et al., 2001). If the model presented above is correct,
EFW, agreeing well with our observations. A similar wake
we expect the spurious electric field to depend on the spacecan also be seen in the simulations by Zinin et al. (2004).
285
11
(a) mvi2/2 > KTi , mvi2/2 > eVsc
+
− Narrow wake
(b) KTi2 < mvi2/2 < eVsc
−
+
−
−
Enhanced wake
−
−
Fig. 12. Diagram illustrating ion wake formation behind a positive
Fig. 12. Cartoon illustrating ion wake formation behind a positive
body
centre body
body
bodysubject
subjecttotoaasupersonic
supersonicion
ion flow
flow from
from the
the left.
left. The
The centre
could
spacecraft
itself,orora acut
cutatatright
rightangles
anglesthrough
through aa wire
wire
couldbebethe
spacecraft
itself,
boom.
(a)
When
the
ion
drift
speed
is
higher
than
the
spacecraft
boom. (a) When the ion drift speed is higher than the spacecraft
potential,
geometric
potential,the
thewake
wakewidth
widthisisdetermined
determined by
by the
the spacecraft
spacecraft geometric
size.
ion flow
flow enensize. (b)
(b)When
When the
the potential
potential is
is much
much higher
higher than
than the
the ion
ergy,
the effective
effective
ergy,the
theions
ionsdeflect
deflectoff
offthe
the potential,
potential, so
so aa measure
measure of
of the
obstacle
to the
the
obstaclesize
sizeisisset
setby
bythe
theequipotential
equipotential surface
surface corresponding
corresponding to
ion
may thus
thus be
be
ionflow
flowenergy
energy (dashed).
(dashed). The
The wake
wake transverse
transverse size
size may
significantly
the body.
body. In
In
significantlylarger
largerthan
thanthe
the geometrical
geometrical dimensions
dimensions of
of the
both
cases,
the
wake
is
charged
negatively
by
the
random
motion
of
both cases, the wake is charged negatively by the random motion of
the
thesubsonic
subsonicelectrons.
electrons.
3.4
of potential
craft Effect
potential,
and thuscontrol
it should disappear or at least decrease in magnitude when ASPOC is used. Figure 13 shows
that this
is indeed
thecarries
case. The
figure shows
from contwo
Each
Cluster
satellite
an instrument
fordata
artificial
spacecraft,
SC1
(upper
three
panels),
on
which
ASPOC
was
trol of the spacecraft potential by the emission of ions, Active
not operational,
and Control
SC3 (lower
three panels),
an operaSpacecraft
Potential
(ASPOC)
(Torkarwith
et al.,
2001).
tional
ASPOC.
In
the
SC1
data,
we
find
EFW
(red)
If the model presented above is correct, we expect and
the EDI
spu(blue)
to disagree
field
after about
rious
electric
field tostrongly
depend on
on the
the electric
spacecraft
potential,
and
04:20,
indicating
spuriousorelectric
sometimes
exceedthus
it should
disappear,
at leastfields
decrease
in magnitude,
ing 5 ASPOC
mV/m. is
Between
04:20 and
04:24, that
a similar
when
used. Figure
13 shows
this isspurious
indeed
field
can be
to emerge
SC3two
data.spacecraft,
At 04:24, SC1
ASthe
case.
Theseen
figure
shows also
datainfrom
POC isthree
turned
on ononSC3,
which
is immediately
visible in
(upper
panels),
which
ASPOC
was not operational,
the SC3
Vps data
shown
in panels),
the bottom
panel
as a sudden ASPOC.
increase
and
(lower
three
with
an operational
a relatively
value
-7 V.and
At EDI
the same
Intothe
SC1 data,steady
we find
thataround
EFW (red)
(blue)time,
disthe spurious
field reduces
drastically,
particularly
its
agree
stronglyelectric
on the electric
field after
about 04:20
UT, indiX component.
Some difference
betweenexceeding
EDI and EFW
recating
spurious electric
fields sometimes
5 mV/m.
mains even
after
04:24,
butUT,
it isa clear
thatspurious
the disagreement
is
Between
04:20
and
04:24
similar
field can be
less to
pronounced
(around
mV/m)
thanAtwhat
weUT,
findASPOC
on SC1
seen
also emerge
in the1 SC3
data.
04:24
mV/m).
This isisclearly
the behaviour
expect
is(often
turned3 to
on5for
SC3, which
immediately
visible we
in the
Vps
from
the
wake
model:
the
wake
electric
field
should
decrease
data shown in the bottom panel, as a sudden increase to a
in amplitude
when
the spacecraft
it does
relatively
steady
value
around –7potential
V. At thedrops,
samebut
time,
the
not
have
to
disappear
completely,
as
even
when
ASPOC
is on
spurious electric field reduces drastically, particularly its
X
the spacecraft remains positive at more than 7 V (one should
component. Some difference between EDI and EFW remains
add the potential drop over the probe sheath of around 1 V to
even after 04:24 UT, but it is clear that the disagreement is
−Vps ). This is not an isolated example: the behaviour is conless pronounced (around 1 mV/m) than what we find on SC1
Comparing electric field measurements
286
13
A. I. Eriksson et al.: Electric field measurements on Cluster
Fig. 13. Comparison of EFW (red) and EDI (blue) electric field spin plane components (DSI coordinates, close to GSE) for an event with
a spurious electric field in the EFW data, for SC1 and SC3. On SC3, the artificial potential controller ASPOC is turned on at 04:24 UT,
immediately alleviating the spurious EX in the EFW data on this spacecraft.
Fig. 13. Comparison of EFW (red) and EDI (blue) electric field spin plane components (DSI coordinates, close to GSE) for an event with a
spurious electric field in the EFW data, for SC1 and SC3. On SC3, the artificial potential controller ASPOC is turned on at 04:24, immediately
alleviating the spurious EX in the EFW data on this spacecraft.
A. I. Eriksson et al.: Electric field measurements on Cluster
(often 3 to 5 mV/m). This is clearly the behaviour we expect from the wake model: the wake electric field should decrease in amplitude when the spacecraft potential drops, but
it does not have to disappear completely, since even when
ASPOC is on, the spacecraft remains positive at more than
7 V (one should add the potential drop over the probe sheath
of around 1 V to −Vps ). This is not an isolated example: the
behaviour is consistent in all cases examined. Together with
the directional considerations in Sect. 3.2, we interpret this
as evidence for the electrostatic wake model.
3.5
Implications for other regions
Up to now, all of Sect. 3 has considered the polar wind
plasma. However, the enhanced electrostatic wake mechanism outlined in Sect. 3.3, of course, works in other regions
with a cold plasma present. When considering the two example orbits in Sect. 2, we found several examples of EDI
and EFW electric field estimates deviating from each other,
and we also found that in these cases, the EFW Vps measurment indicates the presence of a significant or even dominant
component of cold plasma not seen by the ion instrument
CIS, and hence with an energy below eVsc . If this plasma is
flowing sufficiently fast, we will obtain exactly the situation
2 <eV , where an enhanced wake is expected
KTi < 12 mi vflow
sc
to develop, and significant spurious fields appear, explaining
why EFW-EDI discrepancies tend to turn up in regions where
there is a significant cold plasma population not seen by CIS.
The cold plasma of the polar wind does not stay close to
the Earth. Detailed observations from the Polar satellite established its properties at 9 RE (Moore et al., 1997; Su et
al., 1998). Recently, Sauvaud et al. (2004) have shown several examples of cold plasma in the tail out to 18 RE . The
polar wind is only one of the magnetospheric cold plasma
populations. Our example orbits (Sect. 2) show that cold
plasma can indeed turn up elsewhere, as has been also noted
in other studies. By using the ISEE-1 relaxation sounder,
Etcheto and Saint-Marc (1985) found a plasma component
below 30 eV sometimes dominating the plasma sheet boundary layer, reaching densities of 5 cm−3 . More recently, Seki
et al. (2003) found a similar plasma component in Geotail
data from the plasma sheet itself, where we clearly had spurious fields in our example (Sect. 2.2.3). Cold plasma originating from plasmaspheric detachments have been reported
in the magnetosphere in several studies (e.g. Chappell, 1974;
Elphic et al., 1996; Matsui et al., 1999; Foster et al., 2004),
mainly on the dayside, but it may also propagate to the tail
(Elphic et al., 1997). Of particular interest are the reports
from Cluster (Sauvaud et al., 2001) and Polar (Chen and
Moore, 2004) on cold plasmas with density ∼1 cm−3 and
temperature below 10 eV just inside the magnetopause. In
this region, densities are low and spacecraft potentials are
correspondingly high, often much above 10 V, but in the published cases, the ions nevertheless had sufficient energy to
reach the ion detectors on the spacecraft because of their high
flow speed, ∼150 km/s. In a situation with lower flow speed
and/or higher spacecraft potential, the ions may go unnoticed
287
and cause the type of wake effects we have discussed above
for the polar wind.
4
Conclusions
In this paper, we have reported on comparisons of EDI and
EFW instruments from different plasma regions, illustrating
them with some example events. A summary is given in
Sect. 2.3. Our main conclusions are as follows:
1. The general performance of both instruments is good,
with particular merits and drawbacks, as illustrated in
Table 1.
2. For Cluster, the limitations on EDI mainly show up as
periods when no E-field can be derived. When EDI data
are present, they are generally good, except in dynamic
regions like the auroral zone, where random aliasinglike effects may occur.
3. EFW, on the other hand, provides data in all environments and to high frequencies, but the DC electric fields
derived can, in some environments, be contaminated by
nongeophysical signals.
4. Double-probe electric field data can be contaminated by
local fields arising from enhanced electrostatic wakes in
2 <eV . On Cluster, this
regions where KTi < 12 mi vflow
sc
mainly happens in the polar wind but sometimes also in
other regions.
5. If the plasma density estimate from ion spectrometer
moments gives lower values than expected from spacecraft potential or plasma frequency measurements, this
can be an indication that there may be nongeophysical
electric fields in double-probe data caused by an enhanced cold plasma wake. A lower density in the ion
moments indicates plasma with energy below the s/c
potential, and hence a risk for wide wakes and wakeinduced electric fields.
6. On Cluster, the problem of enhanced electrostatic wakes
in flowing cold plasma is alleviated (but not eliminated)
by the use of artificial spacecraft potential control.
7. The double-probe and electron drift techniques for measuring the electric field are complementary to each
other. The Cluster spacecraft, carrying both kinds of
instruments, are well equipped to measure the electric
field in all regions.
Can electric field data from double-probe instruments like
EFW be cleaned from the effects of spacecraft wakes? Removing narrow wakes, such as those sometimes encountered
in the solar wind (Fig. 12a), can be done on a routine basis,
but the wide enhanced wakes we have discussed in Sect. 3.3
are more difficult to correct, since their signature is quite similar to that of a large-scale electric field and is often dominant
288
in the data. A technique based on establishing relations between the spin harmonics in the high-resolution data is attempted by Engwall and Eriksson (2005), but it is not clear
if this method can be made practical for routine analysis.
However, by using the information from CIS and EDI for determining offsets and wake effects at low frequencies, EFW
data can clearly achieve high accuracy over a wide frequency
range, even in cases where wake effects would otherwise
cause problems. Frequencies above the spin frequency are
not greatly affected by wide wakes, so it is possible to combine spin-resolution data from EDI with higher frequency
measurements, to obtain accurate high-resolution data, even
if no other data are available for comparison. Comparisons to
EDI and CIS/FGM data are thus included in the preparation
of EFW data for the Cluster Active Archive (Lindqvist et al.,
2005), which also includes a data product containing electric
fields filtered above the first spin harmonics.
A well understood wake effect is not only a problem: it is
also a means to measure properties of the plasma causing the
wake. Recently, Engwall et al. (2005)2 have demonstrated
that it is indeed possible to derive polar wind flow speed from
the wake information obtained by combining EFW and EDI
data.
Acknowledgements. Many thanks to E. Engwall for very useful discussion and cooperation. Data from the Cluster FGM and CIS instruments have been used with kind permission from the respective principal investigators, A. Balogh (succeeded by E. Lucek) and
H. Rème.
Topical Editor T. Pulkkinen thanks K. Tsuruda and
N. Cornilleau-Wehrlin for their help in evaluating this paper.
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