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

Abstract

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.

Full text

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 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 (R
c
) variations of the magnetic field lines from
the boundary to the inner part are found. The different variations of R
c
reflect that the two
plasmoids have different magnetic configurations. The electric current density distributions
for both plasmoids are found distinct. The B
y
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.
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 field 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
flux rope (MFR) and have helical magnetic fields. 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 definitely identified as a MFR when
the bipolar B
z
is accompanied by prominent |B
y
| enhance-
ment, because commonly, the core field 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 field along the axis
direction, or by MFR edge crossing because the core fields
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 definitely 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 fine magnetic field 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 l’Environnement et de l’Espace,
Université d’Orléans 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, 5437–5444, 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
fitting [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 configuration, MFR
models usually will result into a series of parameters fitting
the plasmoid observations with least errors. If the fitting
results do not include obvious axial field,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 field 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 configuration 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 field 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 field 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 fields 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
flow 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]Thefirst south-then-north B
z
signature is accompanied
by a tailward-then-earthward flow. These observations are
usually explained as the satellite passing through a tailward-
moving X line [Ueno et al., 1999]. However, Eastwood
et al. [2005] identified 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 firstinsituevidenceof
the occurrence of MXR in the plasma sheet. The tailward-
then-earthward flows come from two X lines separately
located at the earthside and the tailside of this plasmoid.
Two X lines are reconnecting the plasma sheet fields and are
producing an active plasmoids between them. Moreover,
except the region near the B
z
inflection 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 flow 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
inflection 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 field is required.
[6] Compared with the first 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 field 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 field (GSM coordinates).
Blue vertical line indicates the time of 00:51:46 UT when faster
flow 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 flow following
this MFR and the lack of faster flow at the earthside indicate
that this MFR is a “fossil”one (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 field-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 field geometric
structure and to find the possible differences between these
two observed plasmoids, we will compute the time series of
the R
c
of the magnetic field 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)isconfined to follow the magnetic
field direction (b=B/|B|) , the resulted rotation rate, i.e., b(∇b),
is the curvature of the magnetic field line (ρ
c
), and further-
more, the curvature radius (R
c
=ρ
c1
) can be evaluated.
Combining the measured band the calculated R
c
,howmag-
netic field lines geometrically configure can be revealed.
Both ρ
c
and R
c
are significant indicators reflecting how
magnetic field lines configure. 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 first-order coefficient
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 fields produced
by Z-directed axis current Ior the projection of MFR magnetic fields 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 field line are shown; the circled line indicates the magnetic fields of ML. (c) Comparison of
the measured and analytic R
c
at these two crossing paths for the ML configuration; (d) comparison of the
measured and analytic R
c
at the two crossing paths for the MFR configuration. 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/D≤0.1, 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 field in small-scale magnetic struc-
tures such as near-tail plasmoids, we first 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 first modeled structure is the circled mag-
netic fields produced by a straight current I, because they have
a similar circled magnetic configuration 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 fields 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
flux 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 field 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) first ML-type plasmoid and of the (b) second MFR-type
plasmoid. The two figures have the same format. From top to bottom: the GSM-B
z
components from
the four Cluster satellites, the curvature radius (R
c
)ofthefield 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
field, 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 flow as already
shown with the vertical blue line in Figure 1: before the blue line, the R
c
of the magnetic field lines
obeys the trend in Figure 2d and the MFR is force-free; after the blue line, the previous situation is
broken by faster flow.
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 field 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 field and current density directions. In
BRN orthogonal coordinates linked to the magnetic field
line, B lies along the magnetic field 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 figure) to the inner part of the first 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
inflection point (red vertical line).
In contrast, as shown in Figure 3b, the R
c
of the magnetic
field 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
inflection 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 firstmeettheredmagneticinflection
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 first plasmoid except the region near the B
z
inflection 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
field 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 field-
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 first observa-
tional evidence of MXR in the tail plasma sheet by identi-
fying the first 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 fine structure of
flux 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 fields as shown in
Figure 2d. These clearly demonstrate that the first
plasmoid can be represented by a ML structure. As shown
in Figure 2b, the magnetic fieldinanidealMLforms
closed concentric circles and is not helical. In this config-
uration, the radius to the axis center ( ρ) approximates the
R
c
of the magnetic field. Thus, the inner magnetic field in
theMLhasasmallerR
c
than the outer magnetic field. As
a result, the first plasmoid is preliminary identified 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 field 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
find that the flow after this region has higher earthward
speed than the flow before the blue line. This faster flow
would push the magnetic field earthward and introduce a
magnetic pileup region at the trailing edge of this MFR. In this
region, the curled MFR magnetic field lines will be pushed by
the after-neighboring faster flow to extend along the Z
direction and then to become straighter. Thus, the straighter
magnetic fields have a higher R
c
. Through the comparison of
the different R
c
variations in two plasmoids by MRA, we
can definitely identify if the plasmoids absent of prominent
core field is a ML or MFR configuration.
[14] The different magnetic configurations 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 first 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 field-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
J¼∇B¼1
ρ
∂Bz
∂ϕ∂Bϕ
∂z

^
ρþ∂Bρ
∂z∂Bz
∂ρ

^
ϕ
þ1
ρ
∂ρBϕ

∂ρ1
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 JB¼∂Bρ
∂z∂Bz
∂ρ

^
ϕ,JR¼ 1
ρ
∂Bz
∂ϕ∂Bϕ
∂z

^
ρ, and JN¼1
ρ
∂ρBϕ
ðÞ
∂ρ1
ρ
∂Bρ
∂ϕ

^
Z. For
an ideal circled ML, owing to the circular magnetic configu-
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 configuration
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 field-aligned currents, and there are two B
x
dips at
both sides of the B
z
inflection 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 flux 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 region”as 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 finally identified as a ML with a
possible MFR core. The difference is that the outer fields
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
inflection 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 fields.
[16] In the second MFR-type plasmoid, the angles
between intense current density and magnetic field 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 field lines, so this MFR can be described as
nearly force-free. Interestingly, the direction of the current
is found to change from field-aligned in the leading part to
antifield-aligned in the trailing part of the MFR, and the
parallel/antiparallel currents display an asymmetry: anti-
parallel currents cross the B
z
inflection point and reach the
negative B
z
region. This phenomenon has been so far rarely
observed. Considering that MFR is the “fossil”signature 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 fields
in the magnetic reconnection occupy about 30% of the
total magnetic field magnitude, the Hall currents strictly
perpendicular to the quadrupole magnetic fields can be
nearly aligned to the total magnetic field [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 configuration is destroyed by the
pushing of the neighboring plasma, which resembles the
destruction of the force-free configuration 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 fields 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 field
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 fields
there 4 min later, with the less shear angle favoring MFR for-
mation by component MXR. The flux rope core within the
ML also supports this explanation: the inner and less-sheared
plasma sheet fields are first reconnected at two separated X
lines to form flux rope core; with the outward development
of MXR, the outer and large sheared plasma sheet fields are
reconnected to form ML. However, this explanation needs
further investigation of the vertical distribution of the shear
angles between the pair of magnetic fields 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 field lines from the edge to the
inner part of these two plasmoids are exhibited: the decreas-
ing R
c
in the first 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 configuration of concentric
circles in the first 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 field variation and strong field-aligned current in
the core region indicates the possibility that a flux 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 fields, we
identified it as a ML with possible MFR core. For the MFR-
type plasmoid, its force-free configuration 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 field 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 fields
in the northern and southern plasma sheet have significantly
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 configuration
but less satellite separation compared to Cluster, could pro-
vide more opportunity to perform the same analysis and
deeply investigate the fine 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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