Introduction
In simple magnetospheric current models the low-latitude current on the
day-side magnetopause flows from dawn to dusk. At higher latitudes it is
partially closed via dusk–dawn-directed currents lobe-ward of the cusp
(Fig. ). This picture was also confirmed by magnetohydrodynamic
(MHD) simulations for nominal solar wind conditions. If the solar wind
becomes a low Mach number flow, the current distributions derived from the
simulations are altered and the direction of the high-latitude portion of the
magnetopause current changes its direction into a dawn–dusk orientation
e.g..
Previous space missions allowed in situ investigations of several magnetopause
properties based on single or dual-spacecraft measurements. In such cases, it
is possible to estimate a current density calculating the ratio of the jump in the
magnetic field and a derived thickness of the current layer. Since 2000 the
multi-spacecraft mission Cluster has
enabled simultaneous magnetic field measurements
at the vertices of a tetrahedron formed by its four spacecraft. Applying the
so-called curlometer technique , the Cluster mission
enabled a new approach for the in situ 3-D current density determination.
The curlometer has been used in several studies, but when applied to the
day-side magnetopause often only a few selected events have been investigated as
case studies e.g.. performed a
statistical study of different properties of 154 magnetopause crossings
including the current density magnitude calculated via the curlometer
technique, but they did not analyse the calculated current directions. Using
magnetic field data from about 4000 Cluster magnetopause crossing events,
were able to perform a larger statistical study
based on single-spacecraft measurements without making use of the curlometer
technique. In their work they focused on the spatial distribution of energy
conversion processes across the magnetopause, where the sign of E⋅J allows the distinction between load and dynamo processes.
Three-dimensional geometry of day-side magnetopause currents.
Figure courtesy of Wolfgang Baumjohann.
The aim of our study is to add another piece to the picture of the global
current distribution at Earth's magnetopause, concentrating especially on the
orientation of current flows at different regions of the day-side
magnetopause in order to compare it with the existing models. Because of
Cluster's polar orbit we are able to intensively study the current structures
at high latitudes in the vicinity of the cusp regions.
Using the 3-D information obtained by the four Cluster spacecraft and
applying the curlometer technique allows us to directly investigate the local
3-D current densities. Hereby it is not necessary to know the actual
magnetopause orientation as in cases when the current density is derived from
data retrieved by fewer than four spacecraft
e.g..
To achieve an appropriate spatial resolution in terms of investigating global
magnetopause current structures, we confine our event selection by Cluster
configurations with inter-spacecraft distances no larger than about
300 km. In addition, we perform an error analysis of the curlometer
technique focussing on the special conditions in our study.
The curlometer technique
Definition
The curlometer analysis technique was first applied to magnetic field
measurements obtained by the Cluster spacecraft by .
Combining 3-D magnetic field data simultaneously measured by each spacecraft,
it estimates ∇×B and thus the local current density by
calculating the difference approximation
μ0J⋅(Δrij×Δrik)=ΔBij⋅Δrik-ΔBik⋅Δrij
of Ampère's law, where
Δrij=rj-riandΔBij=Bj-Bi,i,j,k=1,2,3
for each face (i,j,k) formed by the spacecraft tetrahedron. The variable
ri denotes the location of spacecraft i and Bi its
magnetic field vector measurement. Calculating the current densities for
three differently orientated faces allows the re-projection of the local
current density into a Cartesian coordinate system.
Error sources
The approximation made in Eq. () implies the assumption of
linear variations in the magnetic field across the spacecraft tetrahedron. To
check to what extent this assumption is violated
suggested to calculate ∇⋅B via
∇⋅BΔrij⋅Δrik×Δril=∑j,k,lΔBij⋅Δrik×Δril,
which becomes non-zero as a consequence of the influence of non-constant
spatial gradients in the magnetic field. Nevertheless,
and used model fields
to show that ∇⋅B does not reflect the error of the current
calculation very well when the spacecraft tetrahedron or the geometry of the
magnetic field is highly distorted.
Both ∇×B and ∇⋅B are sensitive to the
shape of the spacecraft tetrahedron and its orientation with respect to the
ambient magnetic field. As demonstrated by the
curlometer results based on tetrahedron configurations near a regular
tetrahedron statistically lead to a higher accuracy of the current
determination for magnetic field structures of different degrees of
distortion than those based on irregular tetrahedron configurations. For this
work we therefore apply the curlometer only to magnetic field data which were
obtained by Cluster during configurations near a regular tetrahedron. To
quantify the shape of the tetrahedron we use the one-dimensional quality
factor QG, which is defined by
QG=True VolumeIdeal Volume+True SurfaceIdeal Surface+1
. The ideal volume and the ideal surface denote the
volume and the surface of a tetrahedron with a side length equal to the
average value of the six side lengths of the true tetrahedron. QG equals
its maximum value of 3 when the true tetrahedron is of perfect regular shape.
If all four spacecraft lie in a line, QG takes the minimum value of
1. This quality factor should not be confused with the one used in
, which gives the value of Eq. () and
does not contain any information about the Cluster geometry.
Of course the accuracy of the current determination by the curlometer also
depends on the accuracy of the determination of r and B and
on the correct timing of the measurements at all four spacecraft themselves.
give the measurement uncertainties of the FGM experiment
as 0.1 to 0.2 nT for low fields (|B|<200 nT) and below
0.4 nT for higher fields (|B|>200 nT). The accuracy of the
position determination was initially announced to meet 5 km. During
the mission and depending on the spacecraft constellation much better
accuracies of some tens to hundreds of metres were achieved. Further
discussions concerning the influences of timing and measurement errors can be
found, for example, in .
In order to use the quality factor, QG, as a selection criterion for our
study we conduct a brief analysis of the correlation between the error of the
current density determination and the quality factor. We therefore use a
model current tube which is occupied by a set of 10 000 model tetrahedron
configurations sensing the current's magnetic field at each tetrahedron's
vertices. The current determined by the curlometer technique for every model
tetrahedron is then compared to the initial current model.
We choose a cylindrical current tube with a homogeneous current density. The
size of the current tube is chosen in such a way that the complete set of
model tetrahedrons lies within the current tube. The tetrahedrons exhibit a
random orientation with respect to the current tube and their quality factors
cover values from about 1 to 3. Measurement errors, δB, are simulated by
adding random noise to the magnetic field values.
Relative error of the current density determination by the
curlometer
as a function of the tetrahedron's quality factor.
Figures and display the relative
error of the current density magnitude ΔJ=(|JCurlometer|-|Jmodel|)⋅|Jmodel|-1 and the deviation Δϕ of the
calculated current direction for a case with a model current density
Jmodel=30 nAm-2, an average inter-spacecraft
distance <d>=200 km, and a noise magnitude of δB=0.2 nT. Both the error in magnitude and the error in direction show
an approximately linear behaviour in the regime of 2.3<QG<2.9, while
at quality factors less then 2.2 the errors increase dramatically. For
smaller sizes of the tetrahedron or the current density the errors rise as
the noise value δB has more influence on the calculations. Our
investigation showed that halving <d> or Jmodel
approximately doubles ΔJ and Δϕ in the regime
QG>2.3. Simulating the effect of an error in position
determination of a worst-case value as big as δr=5 km
has only minor effects on the results and can be neglected. Based on our
results for typical conditions of the magnetopause crossing events we
investigate in our study, we decided to choose QG≥2.5 as a data
selection criterion. It allows us to expect accuracies of at least 2 to
10∘ in direction and 3 to 15 % for the relative error in
magnitude.
Deviation of the current density direction by the curlometer as a
function of the tetrahedron's quality factor.
Data selection and preparation
Data used
For our investigation we use Cluster magnetic field data from the fluxgate
magnetometer (FGM) at spin resolution
(0.25 Hz). Additionally, data from the Cluster Ion Spectrometry (CIS)
instrument are used to support the identification of
magnetopause crossings. The data are retrieved from the Cluster Active
Archive . To sufficiently match the spatial dimensions of
the magnetopause and its current flows we use data obtained while the average
distance between the Cluster spacecraft was about 300 km or less.
With this criterion we are limited to looking for day-side magnetopause
transitions within the time range from February to May 2002 and from
December 2003 to May 2004 where magnetic field data are available for 171
inbound and outbound orbit segments crossing the magnetopause. Because of the
evolution of the Cluster tetrahedron during each orbit, several segments,
mainly inbound ones, possess quality factors much lower than 2.5, where
reliable curlometer results can not be expected. This leaves us 106 orbit
segments suitable for our study. Figure illustrates the data
selection process.
This illustration of the data selection process shows the shrinking
number of suitable data sets. From over 2500 Cluster orbits only a few orbit
segments match the spatial requirements and the quality criterion for our
day-side magnetopause current investigation.
Data preparation
calculated typical values of the magnetopause
thickness of 500 to 3000 km at Cluster's high-latitude orbits used in
our study. Therefore, the chosen inter-spacecraft distances prove to be
suitable for our investigation of current features with spatial dimensions of
a few hundreds of kilometres and effectively damps the influence of currents
at scales up to a few tens of kilometres.
To reduce the influence of high-frequency fluctuations which are likely to
lead to uncertain curlometer results we apply a
100 s moving average to the 0.25 Hz Cluster data before
calculating the current densities and identifying current events. This value
is comparable to resolution limitations used in previous studies; for
example, used data resolutions of 1 to 5 min for
different events.
With a typical velocity of Cluster of about 2.5 kms-1 during
magnetopause crossings investigated in this study, our chosen averaging window
corresponds to a spatial averaging window of about 250 km along the
Cluster trajectory, which is consistent with the spatial limitations due to
the inter-spacecraft distances. The first two panels of Fig.
show the influence of the averaging window on the derived current density for
an example event.
Outbound magnetopause crossing through the
entry layer region on 18 March 2004. The upper and middle panels show the
magnetic field and the curlometer result in GSE coordinates with spin
resolution data and after application of a 100 s averaging window, respectively.
The lower panel shows CIS hot ion particle
density n, velocity v, and temperature T. A complete
magnetopause transition between 05:16 and 05:27 UT and a second contact
with the transition layer between 05:29 and 05:36 UT are visible. Both are
accompanied by accelerated plasma bursts and a distortion of the magnetic
field. The curlometer results shows a series of encounters with
similarly
orientated current layers across the transition layer.
The averaging window applied to the magnetic field data smooths the four
magnetic field measurement time series of each spacecraft. The curlometer
tool utilizes the six differences between those four individual measurements.
The averaging windows works as a low-pass filter and causes these differences
to lose only high-frequency information while all other information included
in the magnetic field measurements is maintained. As a result, the peak
values of the calculated current density become smaller, while the average
magnitude of the current components at scales of about 100 s and more
are not influenced significantly. The direction of the resulting current is
less fluctuating and shows a more stable behaviour in the time series. The
average direction along an identified current structure itself is influenced
by the 100 s window only to a minor extent. Comparing the curlometer
results of all current events investigated in this study with and without the
application of the averaging window leads to average deviations
of 6.1 % in magnitude and of 2.8∘ in angle.
For highly dynamic cases when Cluster crosses the magnetopause several times
along one segment of its trajectory, multiple current signatures are merged
by the 100 s averaging window. If the corresponding magnetic field
conditions are stable for about at least 100 s the resulting current
signature is treated as one magnetopause crossing event. Unstable conditions
during highly dynamic cases are filtered out due to this preprocessing and are
not included in this study.
Magnetopause crossing identification and classification
To identify an inner and an outer edge of the magnetopause currents for each
crossing, we perform a visual inspection of every selected magnetopause
transition event. First, the curlometer results are used to find the most
significant current structures. In a second step we check whether those
currents can be associated with the corresponding expected changes in the
plasma properties monitored in the ion particle data obtained by CIS. Because
of the relative movement of the magnetopause with respect to the Cluster
spacecraft we can regularly identify several magnetopause crossings within
one orbit segment. This enables us to enlarge our data basis for the
statistical survey. A total of 274 single current events are identified, and because of a
high value in ∇⋅B in one case 273 current events are used
in our study (see Fig. ).
Figure shows an example of a magnetopause crossing during the
outbound orbit branch on 18 March 2004. Cluster encounters the magnetopause
twice; the first encounter between 05:16 and 05:27 UT is a complete
transition through the magnetopause and the second one between 05:29 and
05:36 UT enters the transition layer partially. The relative motion of the
magnetopause leads to several contacts with the current layer, as visible in
the current density derived by the curlometer in the second panel of the
figure.
The high-latitude Cluster orbits intersect the magnetopause roughly in the
vicinity of the polar cusps. The varying formation and movement of the
magnetopause, depending on the solar wind conditions, as well as the
evolution of the Cluster orbits over time cause the Cluster magnetopause
crossings to happen at different locations on the magnetopause. Based on the
plasma properties along the Cluster trajectory it is possible to classify the
crossing events with respect to different regions at the magnetopause.
In our study we divide all crossing events into the following classes:
low-latitude-like boundary (LL), entry layer (EL), cusp (C), and plasma
mantle (PM) transition. Figure shows the location of
these regions at the magnetopause. Transitions showing signatures that made
it difficult to distinguish between an entry layer and a cusp transition are
ascribed to a fifth group: EL + C.
The low-latitude-like boundary transitions are located on the magnetopause
sunward of the cusp region . Characteristic for
the low-latitude-like boundary transition is a significant drop in the ion
density and the ion velocity accompanied by an increase in temperature
e.g.. It separates the cold
magnetosheath plasma from the hot and thin magnetospheric plasma. In most
cases the low-latitude-like boundary also shows a clear change in the
orientation of the magnetic field. Adjacent to the low-latitude-like boundary
layer and the cusp the entry layer represents a region where magnetosheath
plasma is injected into the magnetosphere e.g.. The changes in plasma
density and temperature are similar to those of low-latitude-like
transitions. In addition, the entry layer can be characterized by bursts
of accelerated sheath plasma that exceeds the flow velocity of the
magnetosheath . During these plasma bursts, the
magnetic field often undergoes rapid fluctuations as well as drops in
magnitude. Figure displays a typical signature of a
transition through the entry layer.
Illustration of the location of the different regions used to classify the
magnetopause crossing events. Red denotes the low-latitude-like boundary
(LL), blue the entry layer (EL), yellow the cusp (C), and magenta the plasma
mantle (PM) transitions. The current flow along nested loops around the cusp
is pictured with blue lines.
At the cusp region, the plasma flow is intermittent, sometimes stagnant, and
the temperature is raised compared to the sheath and lobe plasma
e.g.. Particle energy spectrograms show isotropic
and broadened energy distributions during cusp transitions
e.g.. The magnetic field is
fluctuating and often drops to very low magnitudes during a cusp transition
e.g.. Plasma mantle transitions are located at
the high-latitude magnetopause tail-ward of the cusp region. They can be
identified by magnetosheath-like plasma within the transition region and in
the adjacent plasma of the magnetospheric lobes. The plasma shows a
relatively steady tail-ward plasma flow and a significant temperature
anisotropy e.g.. The
density lies in between those found in the magnetospheric lobe plasma and
sheath plasma.
Reference magnetopause
Because magnetosphere's scaling depends on the varying solar wind conditions
the intersection of the Cluster orbits with the magnetopause scatter
significantly when displayed in a geocentric solar ecliptic (GSE) coordinate
system. To use a common frame of reference for all events investigated in our
study we introduce a reference magnetopause. For simplification, we use a
second-order approximation, i.e. a paraboloidal magnetopause shape, which is
valid as we are not considering the far tail regions in our study. Following
we use the parametrization
x=ΔMP-∑t=y,zcMP,tt2.
ΔMP depicts the sub-solar magnetopause stand-off distance
with respect to the centre of the Earth (see Fig. ). The
geometric parameters cMP,t represent the magnetopause curvature
in t=y and t=z direction. deduce values of
cMP,y=0.41ΔMP,cMP,z=0.51ΔMP
from an analytical zeroth-order approach solving the MHD equations in the
magnetosheath.
For each identified current the mean value of the tetrahedron barycentre's
position vector is calculated. By radial projection along the
Earth–spacecraft line the intersection of this vector with the reference
magnetopause is calculated (compare Fig. ).
Results
Directions of magnetopause currents
The 273 magnetopause currents investigated in our study
allocate into our five classes as follows: 75
low-latitude-like transitions, 66 entry layer transitions,
48 events showing characteristics of both entry layer and cusp transitions,
53 cusp transitions and 31 plasma mantle transitions.
Illustration of the model magnetopause used as a reference magnetopause
for data presentation. The dotted lines show example projections of two
different currents from their true location to the location at the reference
magnetopause.
Current directions for
LL (left) and EL (right) transitions in GSE coordinates at the reference
magnetopause projected into the x–y plane (top panel) and
y–z plane (middle panel). The grey paraboloid and ellipsoids represent the
magnetopause position at z=0 and x=0.2,0.5,0.8ΔMP, respectively.
The colour code represents the Jx direction. The polar histograms show the
occurrence rate of the current angle within the y–z plane with
respect to the positive y axis.
Figures to show the normalized
x–y component and y–z component of all currents calculated by the
curlometer for each class. The circles depict the position of each
magnetopause crossing on the reference magnetopause projected into the
x–y plane and the y–z plane of a GSE coordinate system. The arrows of
normalized length represent the direction of the current flow within these
planes. The colour gives information about the x component of each current:
green and red indicate that the currents point towards the Sun and towards
the Earth, respectively. The angle between the current and the x axis is
depicted in the legend. Currents that are shown in black are flowing nearly
parallel to the y–z plane. The lighter the colours the more perpendicular
the current flows with respect to the y–z plane. The bottom panel of the
figures additionally show the occurrence rate of the current angle within the
y–z plane with respect to the positive y axis.
As visible in the figures a distinction of low-latitude-like, entry layer,
cusp and plasma mantle transitions based purely on the crossing's location on
the chosen reference magnetopause would not be possible as the circles cover
roughly the same areas for all pictured classes.
Of the 75 currents in the LL case (Fig. ), 63 exhibit a
positive y component. This corresponds well to the classical model of the
day-side Chapman–Ferraro current flowing from dawn to dusk at low latitudes
as illustrated in Fig. . The colour code shows that on the dawn
side (y<0) of the magnetopause the currents dominantly point towards the
Sun, whereas the dusk side (y>0) is dominated by currents pointing
earthward. This also conforms to the magnetopause's elliptical shape, leading to
sunward current flows at dawn and earthward current flows at dusk along the
magnetopause.
In the EL case, 13 of the investigated currents are pointing dawn-ward and 53
are pointed dusk-ward. All the currents on the dawn side point towards the
Sun or flow nearly parallel to the y–z plane. On the dusk side again the
opposite is the case. The curlometer results of LL and EL cases show
qualitatively the same behaviour regarding the Jy and Jz components.
In contrast to the LL case the Jz component is more significant for EL
transitions. Interestingly, only one magnetopause crossings on the southern
hemisphere has been assigned to the EL class due to the plasma properties. Twelve currents associated with the entry layer transitions exhibit negative
z components. In the picture of nested current rings around the cusp region
as illustrated in Figs. and for currents just
below the cusp on the day-side magnetopause one would expect negative z-
and positive x components at the dawn side and just the opposite, positive
z and negative x component, at the dusk side. The current directions
from the curlometer determined for the EL class are not in agreement with
this model. However, as the origin of the day-side entry layer is thought to
be the process of day-side reconnection it is
quite probable that the magnetopause's shape does not equal the smooth
geometry of a quiet and simplified magnetopause at this region.
Same as Fig. but for EL + C transitions.
We assigned 48 currents to the EL + C class (Fig. )
for cases showing entry layer as well as cusp transition characteristics. The
events are concentrated within a range of ±1ΔMP from
the x–y plane. Compared to the LL and EL case we find a turn of the current
flow with respect to the Jy and the Jz component, clearly visible in
the histogram of Fig. . Twenty-six of the EL + C currents
possess a dusk–dawn orientation and 22 a dawn–dusk orientation. The numbers
are the same for northward and southward directions. The distribution of
the Jx component is also almost even, with 25 currents pointing towards the
Sun and 23 towards the Earth. As visible by the number of black
arrows in Fig. the Jx component exhibits a decreased
magnitude compared to LL and EL transitions.
Same as Fig. but for C (left) and PM (right)
transitions.
The C case (Fig. , left) with 53 currents used in this
study shows a growing ratio of 36 / 17 of dusk–dawn to dawn–dusk
orientations clearly marking the change in the current direction between
low-latitude and high-latitude regions on the day-side magnetopause. Like in
the EL + C case several currents are more parallel to the y–z plane compared
to the LL and EL currents.
With 31 currents in the PM class (Fig. , right) the
minority of the investigated current structures are located at the
high-latitude magnetopause on the night side of the cusp. From models a current flow
from dusk to dawn is expected in this region. The results of our study agree
with this quite well, as visible in the histogram of Fig. .
In addition the current's Jz components fit well to the magnetopause's
draped shape around the Earth. On the dawn side most of the currents of the
southern hemisphere are pointing towards north and those at the northern
hemisphere are pointing towards south. The PM transitions also shows the
narrowest Jx-distribution of all five classes. In total, 22 of 31 currents exhibit
angles with respect to the x axis of less than 20∘.
Dependence on solar wind conditions
We use 5 min averaged OMNI data which are already time-shifted to the
bow shock nose prior to each current event in order to investigate
dependencies on the solar wind conditions. OMNI data are available for 270 of
the current events. The average magnitude of the interplanetary magnetic
field (IMF) is 5.98 nT. The IMF is directed southward in 160 cases
and northward in 110 cases. Figure shows the polar
histograms of the Jyz directions for IMF Bz<0 and Bz>0
separately. Independently from the magnetopause region the currents observed
during northward IMF possess a wider distribution in direction than during
southward IMF. In both cases LL and EL currents are dominantly orientated in
the dawn–dusk direction and C and PM currents in the dusk–dawn direction. Only the
currents ascribed to the EL + C case show a clearly different orientation
depending on the solar wind Bz component. For southward IMF the dawn–dusk
orientation is maintained by 13 out of 22 currents. For northward IMF 15 out
of 26 currents possess a dusk–dawn orientation. This indicates that the
overall observed change in direction of the magnetopause currents at the
vicinity of entry layer and cusp contains a dependency from the IMF
Bz component.
Occurrence rate of the current angle within the y–z plane with
respect to the positive y axis during southward (left) and northward
(right) IMF for LL, EL, EL + C, C, and PM transitions (from top to
bottom).
In MHD simulations showed that a dawn–dusk
orientated current tail-ward of the cusp arises in the case of a strong
southward IMF with Bz=-20 nT. In our study we only find four
events at the PM region with Bz<-6 nT and the smallest value of
Bz is -8.8 nT. Those four events correspond to nominal solar
wind conditions and they possess currents with negative Jy components.
Hence, we are not able to observe any high-latitude magnetopause currents
during IMF conditions that would allow us a comparison of the curlometer
results with the simulation results by .
Location of currents with respect to the plasma regimes
Regarding the particle density, velocity, and temperature data in the example
presented in Fig. one can identify three different plasma
regimes: the day-side magnetosphere plasma on the left-hand side until
05:16 UT and between 05:27 and 05:29 UT, the magnetosheath plasma on the
right-hand side from 05:36 UT, and the transition region during 05:16 to
05:27 UT, when Cluster traverses the magnetopause, and 05:29 to 05:36 UT,
when the magnetopause movement causes a contact with the magnetopause. The
curlometer results in the second panel of Fig. show that the
current structures are observed while Cluster is situated within the
transition regime in this example.
In our survey we find that the location of magnetopause current structures
varies with respect to the location of the outer edge of changing plasma
properties for different magnetopause encounters. We distinguish the
following four categories as shown in Fig. .
(A) The current onset lies within the magnetosheath plasma and ends within
100 km radial distance from the outer edge of plasma changes. (B) The
current structure spans across the location of the outermost plasma property
changes, beginning in the magnetosheath end ending within the transition
regime. (C) The current onset lies entirely within the transition regime and
within 100 km from the location of the outermost plasma changes.
(D) The current structure lies within the transition regime but is detached
from the outer edge of the plasma changes. A case where the current lies
beyond the transition regime within the magnetosphere plasma does not appear
in our study.
Schematic representation of the categorization of the current
locations with respect to the ambient plasma regimes. The outermost edge,
where changes in the plasma can be observed, is represented by the changing
background colour. The four cases show currents that lie in front of (A),
across (B), shortly behind (C) and clearly detached from (D) this
edge.
Occurrence rate of the current locations for the different
transition regions as described in the text and by
Fig. .
Counting the occurrence rates of the location categories shows that the
distributions are similar for the LL and the EL case as well as for the
EL + C and the C case. Therefore those cases are summarized in
Fig. , depicting the rates for all investigated
magnetopause crossings.
For magnetopause currents observed at LL and EL most of the currents, 111 out
of 141 are located across or adjacent to the outermost edge of plasma
changes. This result also holds for the PM case, where 23 of 31 currents
are found in direct vicinity of the location where plasma changes are first
observed. In contrast to this the distribution for EL + C and C cases
shows a significant number, 79 of 101, of completely detached current
structures. Once again this fits with the idea of a turbulent cusp region,
where the formation of a clear and steady magnetopause current is unlikely.
Overall we count 48 current structures that are located in front of the
transition regime identified by the changes in plasma properties (category A)
and 127 currents clearly detached (category D). As indicated by the colours
in Fig. our survey shows no clear evidence for an
influence of the IMF orientation on the location of the currents. Checking
for a dependence on the IMF magnitude leads to the same result.
Current magnitudes
For better visibility the current directions in Figs. ,
and are displayed with normalized
magnitudes. A statistic of the true averaged magnitudes for all observed
current events is presented in Fig. . As northward and
southward IMF does not influence the distribution in a significant way we
omit the indication of the IMF Bz component in this depiction. With 182
out of 273, the majority of the evaluated currents possess averaged magnitudes
of 5 to 20 nA m-2 independently of the magnetopause
region they are observed at. For larger magnitudes of the IMF (lower panel)
the current magnitudes are increased. This can be explained by the enhanced
magnetic pressure of magnetosheath plasma, which scales with pmag∼|B|2 and the increased compression of the magnetosphere. Average
current densities between 30 and 85 nA m-2 regularly
appear especially for C and PM cases during stronger IMF. A similar result was
reported by , who evaluated the peak current
density values for 52 magnetopause crossings, showing that PM current peak
magnitudes were about 2 times larger than those at the LL region.
Conclusions
Applying the presented selection criteria to the available Cluster data
allows us to investigate 273 current events with average inter-spacecraft
distances of about 300 km and less. The results of our survey, based
on the usage of the curlometer technique, show that the magnetopause current
flow directions of these current events match expectations based on existing
magnetopause current models and MHD simulations. We find dawn–dusk-orientated
currents on the day side of the cusp and dusk–dawn-orientated currents at high
latitudes on the night side of the cusp. Following the ellipsoid-like shape of the
magnetopause, the low-latitude currents point towards the Sun at dawn and towards
Earth at dusk, whereas the high-latitude currents flow towards lower latitudes
at the side of the magnetopause. The majority of the investigated currents
around the cusp region confirm the picture of closed current loops.
In cases of entry layer, entry layer plus cusp, and cusp transitions that lie
in between the low-latitude-like boundary and the plasma mantle transition region, we
find gradually changing current direction and a wider distribution in direction
that can be explained by the turbulent local boundary leading to an unstable
formation of the magnetopause with variable topology
e.g..
Occurrence rate of current density magnitudes averaged across each
current event for solar wind magnetic field magnitudes smaller (upper panel)
and greater (lower panel) than 6 nT.
The current directions observed in the entry layer plus cusp case show a
dependence on the IMF Bz component. In the other four cases, the current
direction of the majority of the currents is not influence by the IMF
orientation but the current directions are distributed significantly wider
during northward than during southward IMF.
The comparison of the location of the currents with the outermost edge of
changes in the plasma environment shows that the current structures lie in
front of, across, or behind the edge
of the transition regime. For the cusp and the entry layer plus cusp cases
most of the currents are completely detached from the outer edge of this
regime. At the other regions of the magnetopause the majority of the currents
lie in the close vicinity of this edge as one would expect for cases of a
clearly formed boundary. In several of theses cases the current features are
observed slightly but clearly in front of the change in the plasma
properties. The location of the current with respect to the plasma
environment is shown to be independent of IMF orientation and magnitude.
Calculating the averaged current density magnitudes for all current events
shows typical values of 5 to 20 nA m-2. Average current
magnitudes are slightly higher during higher IMF magnitudes. Some currents at
the entry layer plus cusp and the plasma mantle region possess larger current
densities up to 85 nA m-2, especially for IMF magnitudes
|B|>6 nT. This result is in accordance with earlier similar
investigations of the peak current magnitudes at magnetopause crossings on the
day and night side of the cusp by .