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Two different types of plasmoids in the plasma sheet: Cluster multisatellite analysis application

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The fine magnetic field structure of two successive plasmoids previously reported is investigated by magnetic rotation analysis using four Cluster satellite data. Between these two plasmoids, opposite trends of curvature radius (Rc) variations of the magnetic field lines from the boundary to the inner part are found. The different variations of Rc reflect that the two plasmoids have different magnetic configurations. The electric current density distributions for both plasmoids are found distinct. The By increase and abundant field‐aligned currents in the narrow core region of the first plasmoid indicate that a possible magnetic flux rope (MFR) core exists inside. The results indicate that the first observed plasmoid is of a magnetic loop (ML) type (with possible MFR core) and the second plasmoid is of a magnetic flux rope (MFR) type. The coexistence of ML and MFR in the near‐Earth plasma sheet may imply that multiple X line reconnection can occur by either an antiparallel or a component‐parallel way.
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Two different types of plasmoids in the plasma sheet: Cluster
multisatellite analysis application
Y. C. Zhang,
1
C. Shen,
1
Z. X. Liu,
1
Z. J. Rong,
2,3
T. L. Zhang,
4,5
A. Marchaudon,
6,7
H. Zhang,
2,3
S. P. Duan,
1
Y. H. Ma,
1,8
M. W. Dunlop,
9
Y. Y. Yang,
1,10
C. M. Carr,
11
and I. Dandouras
7
Received 27 February 2013; revised 19 August 2013; accepted 29 August 2013; published 17 September 2013.
[1]The ne magnetic eld structure of two successive plasmoids previously reported is
investigated by magnetic rotation analysis using four Cluster satellite data. Between these two
plasmoids, opposite trends of curvature radius (R
c
) variations of the magnetic eld lines from
the boundary to the inner part are found. The different variations of R
c
reect that the two
plasmoids have different magnetic congurations. The electric current density distributions
for both plasmoids are found distinct. The B
y
increase and abundant eld-aligned currents in
the narrow core region of the rst plasmoid indicate that a possible magnetic ux rope (MFR)
core exists inside. The results indicate that the rst observed plasmoid is of a magnetic loop
(ML) type (with possible MFR core) and the second plasmoid is of a magnetic ux rope
(MFR) type. The coexistence of ML and MFR in the near-Earth plasma sheet may imply that
multiple X line reconnection can occur by either an antiparallel or a component-parallel way.
Citation: Zhang, Y. C., et al. (2013), Two different types of plasmoids in the plasma sheet: Cluster multisatellite analysis
application, J. Geophys. Res. Space Physics,118, 5437–5444, doi:10.1002/jgra.50542.
1. Introduction
[2] Since the concept of magnetotail plasmoid was put
forward by Hones in his substorm study [Hones, 1977],
plasmoids in the different regions of the plasma sheet have
been widely investigated [e.g., Slavin et al., 1989, 1995,
2003a, 2003b; Moldwin and Hughes, 1991, 1992; Zong
et al., 2004, 2007; Kiehas et al., 2012]. Hones [1977] pointed
out that the magnetic eld lines in plasmoids have a two-
dimensional closed structure (magnetic loop, ML) [Richardson
et al., 1987, Richardson and Cowley,1985],whileHughes
and Sibeck [1987] argued that plasmoids appear as magnetic
ux rope (MFR) and have helical magnetic elds. During
the past few years, plasmoids at near-tail distances with
X>30R
E
resulting from multiple X line reconnection
(MXR) [Lee et al., 1985] have drawn more attention [e.g.,
Slavin et al., 2003a, 2003b; Zong et al., 2004, 2007;
Eastwood et al., 2005; Henderson et al., 2006; Zhang
et al., 2007; Walsh et al., 2007; Borg et al., 2012]. In most
of in situ observations, a common feature of plasmoids
(either ML or MFR) in the tail plasma sheet is the bipolar
B
z
component signature in the GSM coordinates (the GSM
frame will be used throughout this paper unless otherwise
stated). The plasmoid is denitely identied as a MFR when
the bipolar B
z
is accompanied by prominent |B
y
| enhance-
ment, because commonly, the core eld along the MFR axis
has its main component along the Ydirection [Slavin et al.,
2003a; Zong et al., 2004]. The situation becomes ambiguous,
however, when the |B
y
| enhancement is not so prominent; that
is, bipolar B
z
without |B
y
| enhancement can be produced either
by ML crossing where there is no core eld along the axis
direction, or by MFR edge crossing because the core elds
only concentrate at the MFR center (see Figure 1 in Zong et al.,
2004). In view of this, we refer to the bipolar B
z
signature as
plasmoid in general but cannot denitely state whether the
non-|B
y
|-enhancement plasmoid is due to a ML or to a MFR.
For the large-scale MFR at the distant tail, Hughes and
Sibeck [1987] pointed out that only one X line in the near-
Earth plasma sheet is needed and that B
y
component in the
plasma sheet is necessary. However, according to the MXR
theory [Lee et al., 1985], in the near-Earth plasma sheet, ML
is the product of antiparallel MXR, while MFR is the result
of component MXR. Discrimination between ML and MFR
and studying the ne magnetic eld structure of plasmoids
1
State Key Laboratory of Space Weather, Center for Space Science and
Applied Research, Chinese Academy of Sciences, Beijing, China.
2
Key Laboratory of Ionospheric Environment, Institute of Geology and
Geophysics, Chinese Academy of Sciences, Beijing, China.
3
Beijing National Observatory of Space Environment, Institute of
Geology and Geophysics, Chinese Academy of Sciences, Beijing, China.
4
Key Laboratory of Basic Plasma Physics, Department of Geophysics and
Planetary Sciences, University of Science and Technology of China, Hefei, China.
5
Space Research Institute, Austrian Academy of Sciences, Graz, Austria.
6
Laboratoire de Physique et Chimie de lEnvironnement et de lEspace,
Université dOrléans et CNRS, Orléans, France.
7
Now at Institut de Recherche en Astrophysique et Planétologie,
Université Paul Sabatier (UPS-OMP) et CNRS, Toulouse, France.
8
Space Science Institute, Macau University of Science and Technology,
Macao, China.
9
Rutherford Appleton Laboratory, Oxfordshire, UK.
10
College of Earth Science, University of Chinese Academy of Sciences,
Beijing, China.
11
Imperial College of Science, Technology and Medicine, London, UK.
Corresponding author: Y. C. Zhang, State Key Laboratory of Space
Weather, Center for Space Science and Applied Research, Chinese
Academy of Sciences, Beijing 100190, China. (zyc@nssc.ac.cn)
©2013. American Geophysical Union. All Rights Reserved.
2169-9380/13/10.1002/jgra.50542
5437
JOURNAL OF GEOPHYSICAL RESEARCH: SPACE PHYSICS, VOL. 118, 54375444, doi:10.1002/jgra.50542, 2013
are important to study the properties of MXR occurrence in
space plasma. To separate ML from MFR and to study
the plasmoids structure, methods such as MFR model data
tting [Lepping et al., 1990; Moldwin and Hughes, 1991;
Kivelson and Khurana, 1995; Zhang et al., 2008], Grad-
Shafranov reconstruction [Hu and Sonnerup, 2002],
curlometer electric current measurement [Dunlop et al.,
2002], the single-point method [Rong et al., 2013], and
the multipoint analysis methods [Shen et al., 2003, 2007]
can provide useful analysis tools. For example, given
some restriction on the plasmoid conguration, MFR
models usually will result into a series of parameters tting
the plasmoid observations with least errors. If the tting
results do not include obvious axial eld,maybewecan
classify this plasmoid as a ML. Among these methods, the
multipoint magnetic rotation analysis (MRA) developed
by Shen et al. [2007] and based on four-spacecraft
tetrahedron measurements allows to directly investigate
the 3-D geometric structure of magnetic eld lines
independently of any default restriction.
[3] With the MRA method [Shen et al., 2007], we analyze
two successive plasmoids previously investigated by
Eastwood et al. [2005] and Henderson et al. [2006] but from
the different aspects of the curvature radius R
c
variations and
the current density distributions in them. The emphasis lies
on the different magnetic conguration determined in these
two plasmoids, which can help to differentiate the plasmoid
structures between the ML type and the MFR type.
2. Observations
[4] At the beginning of 2 October 2003, Cluster observed
two successive B
z
bipolar signatures in the tail plasma sheet
at 00:47:00 UT at GSM (16.8771, 7.763, 3.1343) R
E
and at 00:51:30 UT at (16.8786, 7.7671, 3.2046) R
E
.
Figure 1 shows an overview of the Cluster (C1) ion data
[Rème et al., 2001] and the magnetic eld data [Balogh
et al., 2001] for the interesting time slot containing the B
z
bipolar signatures. The plasma is found to have the following
properties: ion density of ~0.3/cm
3
, ion temperature of
~2 keV, positive B
x
component, and, except for the regions
with bipolar B
z
signatures, magnetic eld intensity ranges
between 5 and 15 nT. During the intervals with the two bipo-
lar B
z
signatures, the plasma beta is less than 1 (the typical
beta value in the near-Earth plasma sheet is usually much
greater than 1), which is a typical indicator of the existence
of plasmoids due to the strong elds inside these plasmoids
[Slavin et al., 2003a; 2012; Henderson et al., 2006; Zhang
et al., 2007]. These observations indicate that Cluster was
located in the northern part of the plasma sheet and that
possible plasmoids exist. After the time of 00:51:46 UT (blue
vertical line in Figure 1), the earthward velocity of the ion
ow displays an obvious increase after the passage of the
bipolar B
z
signature. Determined from the ion velocity and
the duration of the bipolar B
z
signature, these two bipolar
B
z
signals have a space transverse scale of about 1 R
E
. The
separation between the Cluster spacecraft is about 300 km.
[5]Therst south-then-north B
z
signature is accompanied
by a tailward-then-earthward ow. These observations are
usually explained as the satellite passing through a tailward-
moving X line [Ueno et al., 1999]. However, Eastwood
et al. [2005] identied that this south-then-north B
z
signature
instead was moving earthward. They interpreted the observa-
tions as an active earthward-moving plasmoid resulting from
MXR [Lee et al., 1985], which is the rstinsituevidenceof
the occurrence of MXR in the plasma sheet. The tailward-
then-earthward ows come from two X lines separately
located at the earthside and the tailside of this plasmoid.
Two X lines are reconnecting the plasma sheet elds and are
producing an active plasmoids between them. Moreover,
except the region near the B
z
inection point, the total
pressure (fourth panel from the top in Figure 1) is balanced,
which implies that this B
z
bipolar is not a transient magnetic
disturbance such as waves [Lee et al., 1988]. In our calcula-
tion of the total pressure, the dynamic pressure (~0.04 nPa)
is taken into account, because the reversed ow will induce
the antidirected pressure on this plasmoid and contribute to
the pressure balance. One point that should be emphasized
in this case is that the |B
y
| enhancement located at the B
z
inection point is not so prominent. This impedes us from
determining whether this plasmoid is a ML or a MFR. To
answer this question, a detailed investigation of the observed
magnetic eld is required.
[6] Compared with the rst signal, the second B
z
bipolar
signature has the clear characteristics of a MFR [Moldwin
and Hughes, 1991; Slavin et al., 2003a; Shen et al., 2007;
Walsh et al., 2007; Zong et al., 2004; Borg et al., 2012;
Kiehas et al., 2012]: B
z
south-to-north turning is associated
with sharp increases in |B
x
| and |B
y
|, both of which correspond
to components of the strong core eld in MFR. The enhance-
ment in |B
x
| overrides the enhancement in |B
y
|, implying that
Figure 1. Cluster (C1) observations between 00:45 and
00:55 UT on 2 October 2003. From top to bottom: ion
density, ion temperature, ion velocity (GSM coordinates), total
pressure (ion pressure plus magnetic pressure plus dynamic
pressure), ion plasma β
i
, and magnetic eld (GSM coordinates).
Blue vertical line indicates the time of 00:51:46 UT when faster
ow appears.
ZHANG ET AL.: TWO DIFFERENT TYPES OF PLASMOIDS
5438
the axis of the MFR largely deviates from the traditional
dawn-dusk direction. The existence of faster ow following
this MFR and the lack of faster ow at the earthside indicate
that this MFR is a fossilone (released from the tailward
MXR region). According to the analysis of Henderson
et al. [2006], this MFR has the following main features: the
principal axis direction at (X,+Y,Z), nearly eld-aligned
current inside the MFR, and the radial expansion due to the
imbalance total pressure.
[7] According to IMAGE (International Monitor for
Auroral Geomagnetic Effects) magnetometer array data and
the AE index (AE >900 nT, not shown here), an intense
substorm occurred between 20:00 UT and 24:00 UT on 1
October 2003. These plasmoids observations followed the
recovery phase of this substorm.
3. Benchmark and Analysis
[8] To clearly investigate the magnetic eld geometric
structure and to nd the possible differences between these
two observed plasmoids, we will compute the time series of
the R
c
of the magnetic eld lines and the electric current
density by MRA, point-by-point along the path of Cluster.
[9] The main idea of the MRA method is to investigate
the 3-D magnetic topology by calculating the rotation rate
(l(b)=
l
b) of the magnetic unit vector b(b=B/|B|) along
an arbitrary direction (l)[Shen et al., 2007; Rong et al.,
2011]. The characteristic directions of bcan indicate the
characteristic directions of the magnetic structure. For
example, for the typical current sheet crossing, the direction
with the largest magnetic rotation corresponds to the normal
of the current sheet, while for the MFR crossing, the direc-
tion with the least magnetic rotation rate corresponds to
the principle axis of the MFR [Shen et al., 2007]. Further,
if the rotation direction (l)isconned to follow the magnetic
eld direction (b=B/|B|) , the resulted rotation rate, i.e., b(b),
is the curvature of the magnetic eld line (ρ
c
), and further-
more, the curvature radius (R
c
=ρ
c1
) can be evaluated.
Combining the measured band the calculated R
c
,howmag-
netic eld lines geometrically congure can be revealed.
Both ρ
c
and R
c
are signicant indicators reecting how
magnetic eld lines congure. A key step in MRA is the
calculation of the tensor gradient of the magnetic unit vector
(b,i.e.,
j
b
i
,whereiand jdenote the three components).
From four-point measurements of the Cluster mission,
j
b
i
can be evaluated by calculating the rst-order coefcient
of Taylor expansion of measured magnetic vectors (see
Figure 2. (a) The blue lines show the paths of the mesocenter of the test tetrahedron (Y1 = 0.41 R
E
and
Y2 = 0.81 R
E
) crossing the modeled structures; the circled lines indicate the ML magnetic elds produced
by Z-directed axis current Ior the projection of MFR magnetic elds on the cross section perpendicular
to the principle axis Z. (b) The cylindrical coordinates (^
ρ,
^
ϕ,
^
Z) and the local coordinates (
^
B,
^
R,
^
N)at
the magnetic eld line are shown; the circled line indicates the magnetic elds of ML. (c) Comparison of
the measured and analytic R
c
at these two crossing paths for the ML conguration; (d) comparison of the
measured and analytic R
c
at the two crossing paths for the MFR conguration. The green curves in
Figures 2c and 2d indicate the variations of the normalized magnetic magnitude B
T
(to the maximum at
the central points of path Y1) for path Y1 = 0.41.
ZHANG ET AL.: TWO DIFFERENT TYPES OF PLASMOIDS
5439
Appendix C in Shen et al. [2007]) with a relative error
ordered L/D,whereLis the size of the Cluster tetrahedron
and Dis the typical spatial transverse scale of the magnetic
structure. Empirically, when L/D0.1, the calculated result
is reliable. The detailed description and application of MRA
are given in the study of Shen et al. [2007].
[10] To check the ability of MRA to recover the rotational
characteristics of magnetic eld in small-scale magnetic struc-
tures such as near-tail plasmoids, we rst use MRA to calculate
the R
c
for two modeled magnetic structures with a characteristic
scale of 1 R
E
and at two different distances from the structure
center (Y1 =0.41R
E
,Y2 =0.81R
E
)(Figure2a;thecrosssection
of both models): the rst modeled structure is the circled mag-
netic elds produced by a straight current I, because they have
a similar circled magnetic conguration compared to the ideal
2-D ML (Figure 2a); the other one is a kind of MFR model
(Elphic-Russell (ER) model) [Elphic and Russell, 1983]. The
separation of the test tetrahedron is set to 600 km to guarantee
that in the benchmark L/D (600 km/1 R
E
)hasthesamevalue
as in above in situ observations (L/D ~ 300km/0.5 R
E
~0.1).
In cylindrical coordinates(Figure 2b), for magnetic elds pro-
duced by a straight current, the magnetic unit vector has only
one component b
ϕ
= 1, and the curvature radius is naturally
R
c
=r; in addition, the three components of the magnetic unit
vector in the ER model is expressed as b
r
=0,b
ϕ
=cos[β(r)],
b
z
=sin[β(r)], where βrðÞ¼
π
2exp r2=a2
ðÞ,ris the distance
from the principal axis, and ais the characteristic scale of the
ux rope. For this model, the curvature radius can be
deduced as R
c
=r/cos
2
[β(r)] analytically. Figures 2c and 2d
display the comparison of the measured R
c
from the test tetra-
hedron (blue lines) and the variation of analytic R
c
(red lines)
for the models of ML and MFR separately. It is obvious that
R
c
in ML and MFR have totally different variations: for ML
(Figure 2c), R
c
becomes smaller toward the center, and for
MFR (Figure 2d), the trend is reversed since the eld lines
inside an MFR tend to straighten along the axis when
approaching the center. We can see that the measured R
c
devi-
ates very little from the analytical results for the inner path
(Y1 =0.41R
E
)aswellasfortheedgepath(Y2 =0.81R
E
). So
we have shown that for L/D ~0.1casessuchaswhatwewill
show later in this paper, MRA can recover R
c
variations
reliably with little error. The variations of the normalized
magnetic magnitude B
T
(to the maximum at the central points
of the path) for path Y1 =0.41R
E
are also shown in
Figures 2c and 2d as a comparison to the variations of R
c
.
They increase inward for both the ML and MFR models and
have the evenly prominent variations as R
c
have, while the
trends of the B
T
and R
c
variations are reversed for ML. One
point is that the ML model here is only a simple magnetic struc-
ture that resulted from a straight current I, which is used to test
the MRA method, but true MLs may have different magnetic
structures and different trends of magnetic magnitude
Figure 3. The MRA results of the (a) rst ML-type plasmoid and of the (b) second MFR-type
plasmoid. The two gures have the same format. From top to bottom: the GSM-B
z
components from
the four Cluster satellites, the curvature radius (R
c
)oftheeld lines in plasmoids, the current density
components in the BRN coordinates, and the ratio of the main current density component (main cur-
rent density component is J
N
in Figure 3a except during the interval indicated by the blue vertical
lines and J
B
in Figure 3b) to the sum of the other two components, the angle between the magnetic
eld, and the current density directions (θ
°
). The two red vertical lines in Figures 3a and Figure 3b
indicate the minimum R
c
and the maximum R
c
at the central region of the ML and the MFR sepa-
rately. In the regions outside the two vertical blue lines in Figure 3a, J
N
dominates the current inten-
sity. In Figure 3b, the vertical blue line indicates the time of appearance of faster ow as already
shown with the vertical blue line in Figure 1: before the blue line, the R
c
of the magnetic eld lines
obeys the trend in Figure 2d and the MFR is force-free; after the blue line, the previous situation is
broken by faster ow.
ZHANG ET AL.: TWO DIFFERENT TYPES OF PLASMOIDS
5440
variation. For example, Slavin et al. [1989] pointed that
contrary to the MFR and ML here, traditional MLs at dis-
tant tail have the decreased magnetic magnitude toward the
center, which is the kind of MLs that may degenerate
quickly due to the strong inward force from magnetic
pressure and magnetic tension. However, they must have a
similar trend of curvature radius variation as the ML model
shown here.
[11] From top to bottom, Figures 3a and 3b show the
observations of the two magnetic B
z
bipolar signatures
by the four Cluster satellites, the R
c
of the eld lines in
plasmoids, the current density components, the ratio of
the main current density component (main current density
component is J
N
in Figure 3a except during the interval
indicated by the blue vertical lines and J
B
in Figure 3b)
to the sum of the other two components, and the angle
between magnetic eld and current density directions. In
BRN orthogonal coordinates linked to the magnetic eld
line, B lies along the magnetic eld direction, R lies along
the direction of magnetic curvature, and N completes the
right-hand orthogonal set, as displayed in Figure 2b. As
we can see in Figure 3a, it is interesting to note that R
c
decreases from the boundary (the beginning and ending
of the gure) to the inner part of the rst plasmoid. R
c
has a value of about 2 R
E
at the boundary and a minimum
value of 0.4 R
E
at the B
z
inection point (red vertical line).
In contrast, as shown in Figure 3b, the R
c
of the magnetic
eld shows an opposite variation trend; that is, it increases
from the outer toward the center (red vertical line) in the re-
gion of the MFR before 00:51:46 UT (blue vertical line). R
c
reaches a maximum of ~0.9 R
E
at the center. It should be
noted that the point of maximum R
c
does not coincide with
the B
z
inection point but has an offset toward the trailing
part. A satellite can have variable ways crossing MFR due
to the different directions of the motion of MFR relative to
the satellite [Borg et al., 2012]. In this case, the asym-
metric B
z
signal (less and shorter negative B
z
but larger
and longer positive B
z
) implies that Cluster has the
chance to cross MFR at path Y3 as shown in Figure 2a.
Thus, Cluster will rstmeettheredmagneticinection
point and then meet the green innermost point (which
has the maximum R
c
). After the blue line, R
c
does not
display the same decreasing trend toward the boundary
as shown for the leading part of this plasmoid but re-
mains at a higher value of ~0.6 R
E
.
[12] Another difference in these two plasmoids is the current
density distribution, shown in Figures 3a and 3b. In most re-
gions (the regions outside of the two blue vertical lines in
Figure 3a) of the rst plasmoid except the region near the B
z
inection point (the regions between the two blue vertical lines
in Figure 3a), the total current intensity is less than 10 nA. This
value is comparable with the current density in the plasma
sheet but is far smaller than that generally encountered in
MFR [Slavin et al., 2003b]. In these regions, the dominant
component of current intensity is J
N
(|J
N
|/(|J
B
|+|J
R
|) 1). In
the region between the two blue lines, J
B
dominates the current
density. The current density in the second plasmoid
(Figure 3b) is more intense and mainly lies along the magnetic
eld direction (|J
B
|/(|J
R
|+|J
N
|) >1) before 00:51:46 UT
(blue vertical line); however, after the blue line, the current
density becomes suddenly weaker and is no longer eld-
aligned. The MRA calculation of current density in the second
plasmoid obtains the similar results as the curlometer calcula-
tion showed in Henderson et al.[2006].
4. Discussions and Summary
[13]Eastwood et al. [2005] showed the rst observa-
tional evidence of MXR in the tail plasma sheet by identi-
fying the rst bipolar B
z
as an active plasmoid with
possible MFR structure. However, MRA here shows that
R
c
decreases gradually from its edge to its inner part.
The time series of R
c
is more in agreement with the R
c
characteristics of a two-dimensional ML (as seen in
Figure 2c). Recently, Yang et al. (The ne structure of
ux ropes in geomagnetotail: Cluster observations,
Journal of Geophysical Research, under review, 2013)
statistically found that the inward increasing R
c
is a
certainly general feature of the MFR elds as shown in
Figure 2d. These clearly demonstrate that the rst
plasmoid can be represented by a ML structure. As shown
in Figure 2b, the magnetic eldinanidealMLforms
closed concentric circles and is not helical. In this cong-
uration, the radius to the axis center ( ρ) approximates the
R
c
of the magnetic eld. Thus, the inner magnetic eld in
theMLhasasmallerR
c
than the outer magnetic eld. As
a result, the rst plasmoid is preliminary identied as a
ML type. In the ideal ML case, the R
c
is zero at the central
axis and has maximum value at the edge, and the ratio of
the R
c
to the maximum R
c
will gradually decrease from 1
at the edge to 0 at the central axis. In this case, the R
c
has
a maximum value of about 2 R
E
at the edge (the beginning
and ending of Figure 3a) and a minimum value of 0.4 R
E
at the center (red vertical line). The ratio of the minimum
R
c
to the maximum R
c
is 0.2 which is small. This means
that the trajectory of Cluster crosses near the center of this
ML. On the contrary, the R
c
variation before the vertical
blue line in the second plasmoid (Figure 3b) is similar to
the MFR scenario shown in Figure 2d: R
c
decreases
gradually from the inner part to the edge. This trend indi-
cates that the magnetic eld in this plasmoid becomes
more curled with increasing distance from the center.
However, the R
c
in the region after the blue line remains
at high value and does not obey the trend shown in
Figure 2d. By checking the ion velocity (Figure 1), we
nd that the ow after this region has higher earthward
speed than the ow before the blue line. This faster ow
would push the magnetic eld earthward and introduce a
magnetic pileup region at the trailing edge of this MFR. In this
region, the curled MFR magnetic eld lines will be pushed by
the after-neighboring faster ow to extend along the Z
direction and then to become straighter. Thus, the straighter
magnetic elds have a higher R
c
. Through the comparison of
the different R
c
variations in two plasmoids by MRA, we
can denitely identify if the plasmoids absent of prominent
core eld is a ML or MFR conguration.
[14] The different magnetic congurations in ML and MFR
are induced by the different distributions of current density in
them. As shown in Figure 3a, most regions (the regions out-
side the two vertical blue lines) of the rst ML-type plasmoid
is current-scarce with two components of J
R
and J
B
less than
J
N
except the region near the center, while in Figure 3b, the
second MFR-type plasmoid is current-abundant with in-
tense eld-aligned current. To simplify the discussion, we
ZHANG ET AL.: TWO DIFFERENT TYPES OF PLASMOIDS
5441
place an ideal circular two-dimensional ML in a cylindrical
coordinate system (Figure 2b), with the ML axis in the Z
direction. It is known that in a cylindrical coordinate
system, the current density is expressed as
J¼B¼1
ρ
Bz
ϕBϕ
z

^
ρþBρ
zBz
ρ

^
ϕ
þ1
ρ
ρBϕ

ρ1
ρ
Bρ
ϕ

^
Z:
[15] The three axis directions in local BRN coordinates
correspond to
^
ϕ,^
ρ, and
^
Z directions in the cylindrical
coordinate system (Figure 2b); thus, we get JB¼Bρ
zBz
ρ

^
ϕ,JR¼ 1
ρ
Bz
ϕBϕ
z

^
ρ, and JN¼1
ρ
ρBϕ
ðÞ
ρ1
ρ
Bρ
ϕ

^
Z. For
an ideal circled ML, owing to the circular magnetic congu-
ration of B= [0, B
ϕ
(ρ), 0], J
R
and J
B
would disappear, and the
residual current J
N
would come from JN¼1
ρ
ρBϕ
ðÞ
ρ

^
Z,
which theoretically represents the distribution model of the
current in ML. For the outer regions (outside the two vertical
blue lines) of the actual ML here, J
B
and J
R
do not disappear
completely, because ML cannot be a perfect circle in nature,
while the lower J
R
and J
B
values with respect to the main
component J
N
indicate that the current in these regions coin-
cides with the above-mentioned theoretical result. Due to the
weak total current J
T
, most of these ML outer regions could
be seen as current-free. Obviously, this ML conguration
needs a strong current along the central axis to support it just
as is observed for J
N
near the ML center in Figure 3a.
However, it is unexpected that J
B
overwhelms J
N
near the
center, which indicates that this ML cannot be represented
by a simple magnetic structure produced by a strong axis cur-
rent and that it has a more complicated current-abundant
structure in the central region. We can see that the central
region of this ML is characterized by the B
y
increase and
abundant eld-aligned currents, and there are two B
x
dips at
both sides of the B
z
inection point (Figure 1), which is very
different from the depression of the magnetic intensity in the
distant tail ML [Richardson et al.,1987,Richardson and
Cowley, 1985]. Slavin et al. [1995] and Zong et al.[1997]
interpreted similar observations as plasmoids with a force-
free magnetic ux rope (MFR) core, and based on these ob-
servations, Zong et al.[2004] gave the possible signals of
the plasmoid with a MFR core in their Figure 1b. So we
prefer to interpret the above-mentioned more complicated
current-abundant structure in the central regionas a possi-
ble MFR core. Because the majority of this plasmoid shows
the feature of ML and the inside MFR core only occupies a
narrow central region, it is nally identied as a ML with a
possible MFR core. The difference is that the outer elds
enveloping the MFR core are helical in the case of Slavin
et al. [1995] and are looped in this plasmoid. The little
enhancement of |B
y
| corresponding to B
z
inection implies
that Cluster only sweeps the edge of the MFR core, and then
the R
c
during two blue lines does not display an obvious
increase. The intense current aligned to the principal axis
at the core of this MFR core will contribute to support the
outside loop elds.
[16] In the second MFR-type plasmoid, the angles
between intense current density and magnetic eld direc-
tions are in the range of 0
ο
45°at the leading part of the
MFR and 135
ο
180°at its trailing part before the blue line
(Figure 3b). The direction of the current is nearly aligned to
the magnetic eld lines, so this MFR can be described as
nearly force-free. Interestingly, the direction of the current
is found to change from eld-aligned in the leading part to
antield-aligned in the trailing part of the MFR, and the
parallel/antiparallel currents display an asymmetry: anti-
parallel currents cross the B
z
inection point and reach the
negative B
z
region. This phenomenon has been so far rarely
observed. Considering that MFR is the fossilsignature of
MXR, these antidirected currents may be related to the Hall
currents generated from multiple X lines if this MFR has
just been released from the reconnection region [Deng
et al., 2004]. Because the quadrupole magnetic elds
in the magnetic reconnection occupy about 30% of the
total magnetic eld magnitude, the Hall currents strictly
perpendicular to the quadrupole magnetic elds can be
nearly aligned to the total magnetic eld [Pritchett, 2001].
If the reconnection at the tailside of MFR is more intense
than that at the earthside, the Hall currents from the tailside
reconnection will have the chance to overwhelm the Hall cur-
rents from the earthside reconnection and to reach the negative
B
z
region. With regard to the magnetic pileup region behind
the blue line, the force-free conguration is destroyed by the
pushing of the neighboring plasma, which resembles the
destruction of the force-free conguration at the leading edge
of the MFR reported by Slavin et al. [2003b].
[17] In the near-Earth plasma sheet, ML is the product of
antiparallel MXR, while MFR is the result of component
MXR. Cluster observed the ML at 00:47 UT and the MFR
at 00:51 UT. During these 4 min, Cluster moved 300 km
toward the central of the plasma sheet. It is interesting how
two different types of plasmoids can be observed in such a
short time interval with not so large space separation. Our
proposed explanation is that the shear angles between
the pair of magnetic elds in the north sheet and in the
south sheet may become larger with the distance from the
innermost region of the plasma sheet. At the time around
00:47 UT, Cluster meets the outer north plasma sheet eld
which has the large shear angle (~180°) with its counterpart
in the south plasma sheet. A large shear angle will favor the
formation of ML by the occurrence of the antiparallel
MXR. Cluster entered the inner plasma sheet and the elds
there 4 min later, with the less shear angle favoring MFR for-
mation by component MXR. The ux rope core within the
ML also supports this explanation: the inner and less-sheared
plasma sheet elds are rst reconnected at two separated X
lines to form ux rope core; with the outward development
of MXR, the outer and large sheared plasma sheet elds are
reconnected to form ML. However, this explanation needs
further investigation of the vertical distribution of the shear
angles between the pair of magnetic elds in the asymmetric
plasma sheet [Cowley, 1981].
[18] In summary, this study has presented the analysis of
two successive tail plasmoids observed by Cluster, following
an intense substorm recovery phase. Based on the MRA, the
different R
c
variations of the eld lines from the edge to the
inner part of these two plasmoids are exhibited: the decreas-
ing R
c
in the rst plasmoid is found to be consistent with the
ZHANG ET AL.: TWO DIFFERENT TYPES OF PLASMOIDS
5442
features of ML, while the increasing R
c
toward axis center in
the second plasmoid is noted to be consistent with the
features of MFR. The magnetic conguration of concentric
circles in the rst ML-type plasmoid is found to introduce
the main current along its axis direction. In the outer region
of this case, as this axis current is weak, the outer part of this
ML can be depicted as current-free, but an intense current at
the center is indispensable to maintain the whole ML. The
magnetic eld variation and strong eld-aligned current in
the core region indicates the possibility that a ux rope core
exists inside this nontraditional ML. Because the MFR core
only concentrates at the narrow central region and the majority
of this plasmoid is occupied by the outer looped elds, we
identied it as a ML with possible MFR core. For the MFR-
type plasmoid, its force-free conguration can be sharply
changed by the velocity difference between the MFR and the
neighboring plasma. Our results can be used to judge whether
an observed plasmoid without prominent core eld is either of
the ML type (even with a MFR core) or of the MFR type. The
discrimination between ML and MFR in the near-Earth
plasma sheet has an implication in understanding how the
MXR occurs (antiparallel versus component reconnection).
Two different types of the successive plasmoids with time in-
terval of 4min also invoke some open questions, e.g., Is there
any relation between these two different types of plasmoids?
Can they evolve into each other? Do the pair of magnetic elds
in the northern and southern plasma sheet have signicantly
variable shear angles within the distance of 300 km in GSM
Zdirection? The future Magnetospheric MultiScale mission
(four satellites) to be launched in 2014 (http://mms.gsfc.nasa.
gov/index.html), which has the same tetrahedral conguration
but less satellite separation compared to Cluster, could pro-
vide more opportunity to perform the same analysis and
deeply investigate the ne magnetic and current structure
in plasmoids, the evolution of plasmoid, and the plasmoid-
related dynamic progress in the plasma sheet, as it should
encounter more plasmoids in the tail and at the magneto-
pause due to its equatorial orbit.
[19]Acknowledgments. We are deeply grateful to the late Edward W.
Hones Jr. for his great contribution to the study of substorm and plasmoid.
This work was supported by the National Natural Science Foundation of
China grants 41231066, 40804033, and 41211120182; National Basic
Research Program of China (973 Program) (2011CB811404); and the
Specialized Research Fund for State Key Laboratories. We specially acknow-
ledge the use of IMAGE data and AE data.
[20]Masaki Fujimoto thanks Akimasa Ieda and an anonymous reviewer
for their assistance in evaluating this paper.
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Four-spacecraft missions are probing the Earth's magnetospheric environment with high potential for revealing spatial and temporal scales of a variety of in-situ phenomena. The techniques allowed by these four spacecraft include the calculation of vorticity and the magnetic curvature analysis (MCA), both of which have been used in the study of various plasma structures. Motivated by curved magnetic field and vortical structures induced by Kelvin- Helmholtz (KH) waves, we investigate the robustness of the MCA and vorticity techniques when increasing (regular) tetrahedron sizes, to interpret real data. Here, for the first time, we test both techniques on a 2.5D MHD simulation of KH waves at the magnetopause. We investigate in particular the curvature and flow vorticity across KH vortices and produce time series for static spacecraft in the boundary layers. The combined results of magnetic curvature and vorticity further help us to understand the development of KH waves. In particular, first, in the trailing edge, the magnetic curvature across the magnetopause points in opposite directions, in the wave propagation direction on the magnetosheath side and against it on the magnetospheric side. Second, the existence of a ‘turnover layer’ in the magnetospheric side, defined by negative vorticity for the duskside magnetopause, which persists in the saturation phase, is reminiscent of roll-up history. We found significant variations in the MCA measures depending on the size of the tetrahedron. This study lends support for cross-scale observations to better understand the nature of curvature and its role in plasma phenomena.
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We review and summarize the applications of the Grad-Shafranov (GS) reconstruction technique to space plasma structures in the Earth’s magnetosphere and in the interplanetary space. We organize our presentations following the branches of the “academic family tree” rooted on Prof. Bengt U. Ö. Sonnerup, the inventor of the GS method. Special attentions are paid to validations of the GS reconstruction results via (1) the direct validation by co-spatial in-situ measurements among multiple spacecraft, and (2) indirect validation by implications and interpretations of the physical connection between the structures reconstructed and other related processes. For the latter, the inter-comparison and interconnection between the large-scale magnetic flux ropes (i.e., Magnetic Clouds) in the solar wind and their solar source properties are presented. In addition, we also summarize various GS-type (or -like) reconstruction and an extension of the GS technique to toroidal geometry. In particular, we point to a possible advancement with added complexity of “helical symmetry” and mixed helicity, in the hope of stimulating interest in future development. We close by offering some thoughts on appreciating the scientific merit of GS reconstruction in general.
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Energetic (>35 keV) ion bursts in the deep geomagnetic tail associated with the passage of 37 plasmoids are examined using data from the energetic particle anisotropy spectrometer (EPAS) instrument on ISEE 3. These bursts can usually be divided into four distinct phases: (1) strongly tailward streaming ions observed in the lobe for a few minutes prior to plasmoid entry, commencing ∼25 min after geomagnetic substorm onset; (2) the plasmoid interval, when the energetic ions have a broader tailward angular distribution arising from convection with the plasmoid; (3) the “post-plasmoid” plasma sheet, where more strongly tailward streaming ions are observed in the plasma sheet on field lines disconnected from the earth at the substorm neutral line; and (4) a strongly tailward streaming ion population extending into the lobe for a few minutes after exit from the plasma sheet. We concentrate here on the streaming ion “boundary layers” observed in the lobe at the leading and trailing edges of these bursts. In a majority of these layers, a clear dawn-dusk gradient anisotropy and energy dispersion are evident at the leading edge, and a similar gradient anisotropy with “reverse” dispersion is evident at the trailing edge. It is shown however that the dispersion at onset is not consistent with simple time of flight from a near-earth neutral line or from a neutral line retreating tailward during substorm recovery. Instead, observations of 90° pitch angle ions with a time resolution of 16 s are used to infer that the ion onset is due to a layer of energetic ions expanding outward from the tail center plane and engulfing the spacecraft. At the trailing edge of the burst, this layer contracts back across the spacecraft toward the center plane. Mean expansion and contraction speeds are 94±74 km s−1 and 99±100 km s−1 respectively, with boundary layer thicknesses of ∼3 RE. From these observations, it is concluded that the expansion of the ion layer is caused predominantly by the ion layer being swept across the spacecraft by the arrival of the plasmoid in the deep tail, contributing ∼60 km s−1 to the expansion speed, rather than by a thickening of the region of lobe field lines disconnected at the substorm neutral line which expands at ∼35 km s−1. The energy dispersion at the leading edge can be reconciled with a near-earth neutral line in this case. Using this dispersion and the measured expansion speed of the layer, the electric field along the near-earth substorm neutral line is deduced. Values derived from layer expansions and contractions are both ∼0.4 mV m−1, equivalent to ∼110 kV across a ∼40-RE tail width.
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[1] Examination of Geotail measurements in the near-tail (X > −30 RE) has revealed the presence of small flux ropes in the plasma sheet. A total of 73 flux rope events were identified in the Geotail magnetic field measurements between November 1998 and April 1999. This corresponds to an estimated occurrence frequency of ∼1 flux rope per 5 hours of central plasma sheet observing time. All of the flux ropes were embedded within high-speed plasma sheet flows with 35 directed Earthward, 〈Vx〉 = 431 km/s, and 38 moving tailward, 〈Vx〉 = −451 km/s. We refer to these two populations as “BBF-type” and “plasmoid-type” flux ropes. The flux ropes were usually several tens of seconds in duration, and the two types were readily distinguished by the sense of their quasisinusoidal ΔBz perturbations, i.e., ∓ for the “BBF” events and ± for the “plasmoid” events. Most typically, a flux rope was observed to closely follow the onset of a high-speed flow within ∼1–2 min. Application of the Lepping-Burlaga constant-α flux rope model (i.e., J = αB) to these events showed that approximately 60% of each class could be acceptably described as cylindrical, force-free flux ropes. The modeling results yielded mean flux rope diameters and core field intensities of 1.4 RE and 20 nT and 4.4 RE and 14 nT for the BBF and plasmoid-type events, respectively. The inclinations of the flux ropes were small relative to the GSM X–Y plane, but a wide range of azimuthal orientations were determined within that plane. The frequent presence of these flux ropes in the plasma sheet is interpreted as strong evidence for multiple reconnection X-lines (MRX) in the near-tail. Hence, our results suggest that reconnection in the near-tail may closely resemble that at the dayside magnetopause where MRX reconnection has been hypothesized to be responsible for the generation of flux transfer events.
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The first (M1), second (M2), and third (M3) MESSENGER flybys of Mercury traversed the planet's magnetotail from 1.25 to 3.25 RM downstream of the planet, where RM is Mercury's radius (2440 km). The encounters took place under northward, southward, and variable-polarity interplanetary magnetic field (IMF), respectively. The magnetic field strength B in Mercury's magnetotail follows a power law decrease with increasing antisunward distance ∣X∣, B ˜ ∣X∣G, with G varying from -5.4 for northward to -1.6 for southward IMF. Low-latitude boundary layers (LLBLs) containing strong northward magnetic field were detected at the tail flanks during two of the flybys. The observed thickness of the LLBL was ˜33% and 16% of the radius of the tail during M1 and M3, respectively, but the boundary layer was completely absent during M2. Clear signatures of tail reconnection are evident in the M2 and M3 magnetic field measurements. Plasmoids and traveling compression regions were observed during M2 and M3 with typical durations of ˜1-3 s, suggesting diameters of ˜500-1500 km. Overall, the response of Mercury's magnetotail to the steady southward IMF during M2 appeared very similar to steady magnetospheric convection events at Earth, which are believed to be driven by quasi-continuous reconnection. In contrast, the M3 measurements are dominated by tail loading and unloading events that resemble the large-scale magnetic field reconfigurations observed during magnetospheric substorms at Earth.
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We present an investigation of magnetic flux ropes observed by the four Cluster spacecraft during periods of magnetic reconnection in the Earth's magnetotail. Using a list of 21 Cluster encounters with the reconnection process in the period 2001-2006 identified in Borg et al. (2012), we present the distribution and characteristics of the flux ropes. We find 27 flux ropes embedded in the reconnection outflows of only 11 of the 21 reconnection encounters. Reconnection processes associated with no flux rope observations were not distinguishable from those where flux ropes were observed. Only 7 of the 27 flux ropes show evidence of enhanced energetic electron flux above 50 keV, and there was no clear signature of the flux rope in the thermal particle measurements. We found no clear correlation between the flux rope core field and the prevailing IMF By direction.
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On August 22, 2001 all 4 Cluster spacecraft nearly simultaneously penetrated a magnetic flux rope in the tail. The flux rope encounter took place in the central plasma sheet, βi ∼ 1–2, near the leading edge of a bursty bulk flow. The “time-of-flight” of the flux rope across the 4 spacecraft yielded Vx ∼ 700 km/s and a diameter of ∼1 Re. The speed at which the flux rope moved over the spacecraft is in close agreement with the Cluster plasma measurements. The magnetic field profiles measured at each spacecraft were first modeled separately using the Lepping-Burlaga force-free flux rope model. The results indicated that the center of the flux rope passed northward (above) s/c 3, but southward (below) of s/c 1, 2 and 4. The peak electric currents along the central axis of the flux rope predicted by these single-s/c models were ∼15–19 nA/m2. The 4-spacecraft Cluster magnetic field measurements provide a second means to determine the electric current density without any assumption regarding flux rope structure. The current profile determined using the curlometer technique was qualitatively similar to those determined by modeling the individual spacecraft magnetic field observations and yielded a peak current density of 17 nA/m2 near the central axis of the rope. However, the curlometer results also showed that the flux rope was not force-free with the component of the current density perpendicular to the magnetic field exceeding the parallel component over the forward half of the rope, perhaps due to the pressure gradients generated by the collision of the BBF with the inner magnetosphere. Hence, while the single-spacecraft models are very successful in fitting flux rope magnetic field and current variations, they do not provide a stringent test of the force-free condition.
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On January 15, 1994, the ion spectrometer high energy particle - low energy particle detector (HEP-LD) on the Japanese spacecraft Geotail observed five quasi-periodic energetic ion bursts in the deep tail (X= -96 RE). These bursts were associated with plasmoid-like structures in the magnetic field components. In addition, three multiple TCR groups were identified in the interval. The observations in the distant tail occurred during a time interval of substorm activity which also produced multiple injections in the geosynchronous orbit region. The HBP-LD observations show that Bz bipolar plasmoid-like structures are associated with tailward flowing particle bursts. However, earthward flowing particle bursts are predominantly associated with bipolar signatures in By. In addition, an oxygen burst was seen in the back of a plasmoid (postplasmoid) which showed both By and Bz bipolar magnetic field signatures. The oxygen burst lasted for 23 min, and the density ratio (O/H) reached 15% for the HEP-LD energy range (in the same plasmoid, this ratio was approximately 1% before the oxygen burst). The oxygen burst exhibited a strong beam-like structure which occupied only 6 ∼ 7% of the full solid angle (4π). We suggest that energized oxygen ions of ionospheric origin travel downtail in the narrow postplasmoid-plasma sheet which trails the plasmoid. Furthermore, we suggest that the magnetosphere dissipated larger quantities of energy during this very intense substorm event by ejecting multiple relatively small plasmoids rather than through the formation and ejection of a single large plasmoid.
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Observations of the Earth's magnetotail made by the four Cluster spacecraft on October 2 2003 are presented. Multi-spacecraft analysis is used to show that the variations in field and flow observed in the vicinity of the magnetotail current sheet are most consistent with a series of two active reconnection sites bounding an Earthward moving flux rope. We demonstrate that a single spacecraft analysis of the same data leads to the incorrect conclusion that a single X-line is moving tailward. The implications of this in relation to the interpretation of single spacecraft observations are outlined. These results show that reconnection can occur simultaneously at different points in the near-Earth magnetotail current sheet, providing (further) important experimental validation of multiple X - line reconnection theories on the mesoscale (tens of ion inertial length) level.
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For the first time, the Cluster spacecraft have collected 3-D information on magnetic field structures at small to medium scales in the Earth's dayside magnetosphere. We focus here on the first application of the Curlometer (direct estimation of the electric current density from curl(B), using measured spatial gradients of the magnetic field) analysis technique. The applicability of this multipoint technique is tested, for selected events within the data set, in the context of various mission constraints (such as position, timing, and experimental accuracy). For the Curlometer, nonconstant spatial gradients over the spacecraft volume, time dependence, and measurement errors can degrade the quality of the estimate. The estimated divergence of the magnetic field can be used to monitor (indirectly) the effect of nonconstant gradients in the case of many magnetic field structures. For others, and at highly distorted spacecraft configurations, this test may not reflect the quality of the Curlometer well. The relative scales and relative geometry between the spacecraft array and the structures present, as well as measurement errors, all are critical to the quality of the calculation. We demonstrate that even when instrumental and other errors are known to contribute to the uncertainty in the estimate of the current, a number of current signatures within the magnetosphere can be plausibly determined in direction, if not absolute size. A number of examples show consistent currents at the magnetopause, both separate from, and nearby or in the cusp region. Field-aligned currents near the polar cap boundary are also estimated reliably. We also demonstrate one example of an anomalous current arising from the effect of a highly distorted spacecraft configuration.
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On 21 October 2010, ARTEMIS spacecraft P2, located at about -57 REGSM in the Earth's magnetotail, observed a series of flux ropes during the course of a moderate substorm. Subsequently, ARTEMIS spacecraft P1, located about 20 RE farther downtail and farther into the lobe than P2, observed a series of TCRs, consistent with the flux ropes observed by P2. The dual-spacecraft configuration allows simultaneous examination of these phenomena, which are interpreted as an O-line, followed by a series of flux ropes/TCRs. An inter-spacecraft time of flight analysis, assuming tailward propagation of cross-tail aligned ropes, suggests propagation speeds of up to ˜2000 km/s. A principal axis investigation, however, indicates that the flux ropes were tilted between 41° and 45° in the GSM x-y-plane with respect to the noon-midnight meridional plane. Taking this into account, the tailward propagation speed of the different flux ropes is determined to be between 900 and 1400 km/s. The same timing analysis also reveals that the flux rope velocity increased progressively from one flux rope to the next. A clear correlation between the magnetic field and plasma flow components inside the flux ropes was observed. As possible mechanisms leading to the formation of tilted flux ropes we suggest (a) a progressive spreading of the reconnection line along the east-west direction, leading to a boomerang-like shape and (b) a tilting of flux ropes during their formation by non-uniform reconnection with open field lines at the ends of the flux ropes. The progressive increase in the propagation velocity from the first to the last flux rope may be evidence of impulsive reconnection: initially deep inside the plasma sheet the reconnection rate is slow but as reconnection proceeds at the plasma sheet boundary and possibly lobes, the reconnection rate increases.
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On the basis of a two-dimensional incompressible MHD code, the plasma dynamics of a long magnetotail is simulated under a constant and time-varying driving force delivered from the solar wind. It is found that under a constant driving force the magnetic fields in the magnetail tend to reconnect impulsively and the formation of X line and plasmoids occurs intermittently and repeatedly every 2-4 hours. Under a time-varying driving force the post-driven phase of a plasmoid formation and the spontaneous reconnection process are also studied. The results show that magnetic reconnection in the magnetotail during magnetospheric substorms and storms is basically a driven process. A complete sequence of the event, going from the gradual pile-up of magnetic flux to the formation and the antiearthward convection of the new X line and to the ejection of plasmoids from the antiearthward end of the magnetotail, requires the presence of the driving force.