Author's Accepted Manuscript

Radial distribution of magnetic field in earthmagnetotail current sheet

Z.J. Rong, W.X. Wan, C. Shen, A.A. Petrukovich,W. Baumjohann, M.W. Dunlop, Y.C. Zhang

PII: S0032-0633(14)00220-7DOI: http://dx.doi.org/10.1016/j.pss.2014.07.014Reference: PSS3790

To appear in: Planetary and Space Science

Received date: 12 April 2014Revised date: 11 July 2014Accepted date: 31 July 2014

Cite this article as: Z.J. Rong, W.X. Wan, C. Shen, A.A. Petrukovich, W.Baumjohann, M.W. Dunlop, Y.C. Zhang, Radial distribution of magnetic field inearth magnetotail current sheet, Planetary and Space Science, http://dx.doi.org/10.1016/j.pss.2014.07.014

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Radial distribution of magnetic field in Earth

magnetotail current sheet

Z. J. Rong1, 2, W. X. Wan1, 2, C. Shen3, A. A. Petrukovich4, W. Baumjohann5,

M.W. Dunlop6, Y.C. Zhang3

1Key Laboratory of Earth and Planetary Physics, Institute of Geology and Geophysics,

Chinese Academy of Sciences, Beijing, 100029, China

2Beijing National Observatory of Space Environment, Institute of Geology and

Geophysics, Chinese Academy of Sciences, Beijing, 100029, China

3State Key Laboratory of Space Weather, Center for Space Science and Applied

Research, Chinese Academy of Sciences, Beijing 100190, China

4Space Research Institute, 84/32 Profsoyuznaya st., Moscow, 117997, Russia

5Space Research Institute, Austrian Academy of Sciences, 8042 Graz, Austria

6Rutherford Appleton Laboratory, Chilton, DIDCOT, Oxfordshire OX11 0QX, UK

Correspondence to: rongzhaojin@mail.iggcas.ac.cn

KEYWORDS: Magnetotail, Magnetic Structure, Current sheet

Running Title: RONG ET AL.: TAIL MAGNETIC FIELD

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Abstract

Knowing the magnetic field distribution in the magnetotail current sheet (CS) is

essential for exploring magnetotail dynamics. In this study, using a joint dataset of

Cluster/TC-1, the radial profile of the magnetic field in the magnetotail CS with radial

distances covering 8<r<20 RE under different geomagnetic activity states (i.e., AE ≤

100 nT for quiet intervals while AE > 100 nT for active times) and solar wind

parameters are statistically surveyed. Our new findings demonstrate that, independent

of the activity state, the field strength and Bz component (GSM coordinates) start the

monotonic increase prominently as r decreases down to ~11.5RE, which means the

dipole field starts to make a significant contribution from there. At least in the

surveyed radial range, the Bz component is found to be weaker in the midnight and

dusk sectors than that in the dawn sector, displaying a dawn-dusk asymmetry. The

occurrence rate of negative Bz in active times also exhibits a similar asymmetric

distribution, which implies active dynamics may occur more frequently at midnight

and dusk flank. In comparison with that in quiet intervals, several features can be seen

in active times: (1) a local Bz minimum between 10.5<r<12.5 RE is found in the dusk

region, (2) the Bz component around the midnight region is generally stronger and

experiences larger fluctuations, and (3) a sharp positive/negative-excursion of the By

component occurs at the dawn/dusk flank regions inside r<10 RE. The response to

solar wind parameters revealed that the Bz component is generally stronger under

higher dynamic pressure (Pdy>5 nPa), which may support the dawn-dusk squeezing

effect as presented by Miyashita et al. (2010). The CS By is generally correlated with

the interplanetary magnetic field (IMF) By component, and the correlation quality is

found to be better with higher penetration coefficient (the ratio of CS By to IMF By)

when IMF Bz is positive. The implications of the present results are discussed.

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1. Introduction

The Earth magnetotail current sheet (CS), which is located in the equatorial

region and called neutral sheet sometimes, is a transition layer separating the

anti-parallel lobe magnetic field lines (e.g. Ness, 1965, 1969; Behannon, 1970;

Speiser, 1973). As a basic physical quantity, the magnetic field in the CS (together

with the electric field) can control the dynamics of charged particles, affect the

space plasma distribution and evolution, so that the unambiguous knowledge of

magnetic field distribution and its dynamic variation is essential for exploring the

magnetotail dynamics.

Many studies on the magnetic field distribution in magnetotail, as well as in the

tail CS have been conducted with earlier satellite missions (e.g. Fairfield, 1979,

1986, 1992; Fairfield et al., 1987; Slavin et al., 1987; Tsurutani et al., 1984; Kaymaz

et al., 1994a, 1994b; Huang and Frank, 1994; Wang et al., 2004; Nakai et al., 1997;

Petrukovich, 2009). These studies demonstrate that the tail CS with radial distance

r< 20 RE might be a key region where the magnetic reconnection likely happens in

the substorm processes (e.g. Fairfield, 1986; Baumjohann, 2002; Nagai et al., 2005).

Meanwhile, more evidence has been presented that the final source for auroral

substorm onset is probably located in the near-earth current sheet with radial

distance r<15 RE (Lui, 1996), where the fast earthwards plasma flow is found to

brake substantially (e.g. Shiokawa et al.,1997; Birn et al., 1999; Panov, et al. 2010)

and ballooning mode instability is favorably to be triggered due to the transition of

magnetic field from dipole-like to tail-like (Hameiri et al., 1991; Liu, 1997).

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It is well known that the magnetic field structure in near-earth magnetotail

(r<20 RE) can be simply seen as the superposition of the dipole geomagnetic field

and the field generated by the tail and magnetopause current systems. The magnetic

field strength is assumed to increase significantly as radial distance decreasing. The

true and detailed radial distribution of magnetic field in near-earth magnetotail,

however, is not known so clearly, though some empirical or semi-empirical

magnetosphere models (e.g. Tsyganenko, 2002; Tsyganenko and Sitnov, 2007) are

available.

The radial distribution of magnetic field in CS containing the region r<20 RE

has been surveyed extensively by numerous spacecraft, e.g. ISEE 1 from 1978-1979

at X=-10~-22 RE (GSM coordinates, Huang and Frank, 1994), ISEE 1

from1978-1987 at r=3~23 RE (Nakai et al., 1999), Geotail at X=-9~-30 RE (Wang et

al., 2004；Petrukovich et al.,2009), AMPTE/CCE at r< 8.8 RE (Fairfield et al.,1987),

and the merged data of ISEE1, AMPTE/CCE, IMP 8 at X=-5~-60 RE (Rostoker and

Skone, 1993). However, either the field magnitude or the By, Bz component was

addressed solely in these studies, and no one had given the full view of magnetic

field radial profile under different geomagnetic activities and external solar wind

conditions. For instance, only the Bz component is addressed by Huang and Frank

(1994). The magnetic field strength and Bz component are studied by Nakai et al.

(1999), but it is concentrated in |Y|<5 RE, while the response to the storm/substorm

activities, as well as to the dynamic pressure of solar wind are only exhibited in the

form of regression analysis. The By component and the correlation with the

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interplanetary magnetic field (IMF) By component are investigated by Petrukovich

(2009). The Bx and Bz component are referred by Wang et al. (2004) (see their

Figure 9a and 9b) in the region |Y|<5 RE for the selected events of quiet periods (333

events) and growth-phase periods (130 events). Meanwhile, theoretical analysis and

event model demonstrate that a Bz minimum should be located in the inner current

sheet (e.g. Hau et al., 1989; Hau, 1991; Erickson, 1992; Sergeev et al., 1994;

Sergeev, 1996) due to the earthward plasma convection, and it may play an

important role in triggering the balloon instabilities and plasmoid formation (e.g.

Zhu and , 2013). However, the true existence of the local minimum of

Bz is disputable. The characteristics of Bz minimum are inferred in some studies (e.g.

Saito et al., 2010), but not in the other studies (Yang et al., 2010; Artemyev et al.,

2013; Petrukovich et al, 2013). The more detailed study about the radial profile of

Bz is needed to clarify this issue. Therefore, combining with geomagnetic index and

solar wind parameters, this study aims to fully re-examine the radial profile of the

magnetic field in the tail current sheet spanning the entire tail width, as well as the

responses to geomagnetic activity states and solar wind parameters. To achieve this

task, the magnetic field data of Cluster and TC-1 are used.

The Cluster mission (Escoubet et al., 2001) was launched in the summer of

2000 into a 4 × 19.6 RE polar, inertial orbit. One main goal of the four-satellite

mission is to investigate the dynamics of the near-Earth magnetotail. As shown in

Figure 1, in the earlier stage of Cluster orbit, e.g. 2001-2005, from the end of June

to the early November annually, the Cluster tetrahedron traverses magnetotail

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around apogee 15~19 RE from the north-hemisphere to the south-hemisphere in the

night side of magnetosphere, so that the magnetotail can be investigated fully in the

dawn-dusk direction. With the FGM data of Cluster (Balogh, et al., 1997; Balogh, et

al., 2001) in the earlier stage, the distribution properties of magnetic field have been

surveyed (e.g. Petrukovich et al., 2005; Rong et al., 2010; Rong et al, 2011). For the

later orbit phase (since 2006), due to the evolution of orbit precession, the orbit

inclination decreases gradually with apogee shifted southward, so that the near-earth

CS (with r< 15 RE) can be also surveyed.

To coordinate with the measurements of Cluster, the TC-1, as one spacecraft

(S/C) of Double Star mission, was launched into an equatorial orbit of 1.1×13.4 RE

in Dec. 2003 (Liu et al., 2005; Shen et al., 2005). The FGM on board TC-1 is

identical to that on board Cluster, and provides the magnetic field measurements

(Carr et al., 2005, 2006), covering the near-earth magnetotail at radial distance less

than 13.4 RE from the end of June to the early November annually.

The extension of Cluster measurements to the later stage with the coordinated

measurements of TC-1 provide a good opportunity to survey the radial magnetic

field distribution in tail CS within r <20 RE. Since four satellites of Cluster mission

are closely spaced, the four satellites mostly record the similar magnetic field

measurements; hence, only the magnetic field data of single satellite, Cluster-3 (C3,

Samba) is used here. We should remind readers that there are two reasons for us to

use the joint dataset of TC-1/C3 though satellites such as Geotail (Nishida, 1994) or

THEMIS (Angelopoulos, 2009) with smaller orbit inclination can provide more

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dataset for the survey. Firstly, the joint dataset of TC-1/C3, with the same FGM on

both satellites, is the continuum of our previous studies (e.g. Rong et al., 2010; Rong

et al., 2011). Secondly, TC-1 has a similar orbit as THEMIS-D and E. As a result, to

study the radial magnetic field distribution and its response to geomagnetic activity

states and solar wind parameters within r<20 RE, the spin-resolution (4-s) FGM data

of C3 during 2001–2009 and TC-1 during 2004 are used in this research, combining

with the 1-min OMNI data set (it contains the shifted solar wind conditions at the

nose of bow shock and the AE index, see http://omniweb.gsfc.nasa.gov/ (King and

Papitashvili, 2005)).

Geocentric solar magnetospheric (GSM) coordinates are used throughout the study

without special statement. In addition, the spherical coordinates (r, θ, φ) for the

Earth-centered position vector are defined in the frame of GSM. r is the radial

distance. The polar angle θ (0°≤θ≤180°) is the angle between the +Z-axis and the

vector. The azimuth angle φ (0°≤φ≤360°) of vector is defined as the angle

anticlockwise deviated from the +X-axis in the XY-plane when seen towards −Z-axis.

For example, the dawn direction or −Y-direction is (θ=90°, φ=270°), while the dusk

direction or +Y- direction is (θ=90°, φ=90°).

2. Statistical Study

2.1 Selection and Preparation of Data

To determine the tail CS crossing unambiguously, the criteria as adopted in our

previous studies (Rong et al., 2010, 2011), i.e., Bx(ti)·Bx(ti+1) < 0 (where, ti, ti+1 are

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the two successive measurements), combined with the lower strength of the

magnetic field (<100 nT) and the nightside location of S/C (90°≤φ≤270°, r<20 RE),

are used in the first instance. Second, visual inspection of the low plasma

temperature (<10×106 K), high density (>1 cm3), and the tail-ward plasma velocity

(Vx < −100 km/s) near both flanks (June to earlier July and later October‐November,

etc.) excludes crossings of the magnetosheath (Lucek et al., 2005) and low-latitude

boundary layer (Fujimoto et al., 1998). Then, applying the linear interpolation to the

data set, the interpolated parameters when Bx=0, i.e., CS center can be grouped

correspondingly as the basis data set for this study.

One should note that closer to earth, typically within r<8 RE (the typical hinging

distance of tail CS is about 8~10 RE (e.g. Tsyganenko et al., 1998; Tsyganenko and

Fairfield, 2004)), the magnetosphere is mainly ordered by dipole tilt angle, thus the

Bx=0 in GSM may not represent the true CS center, and the Bx component might be

better presented in the Solar Magnetic coordinates according to dipole tilt angle (e.g.

Fairfield et al., 1987). Therefore only the region 8<r<20 RE is concerned here in

GSM coordinates.

Based on the above criteria, in total 26483 data points (18962 data points for C3

and 7521 data points for TC-1) for the CS center are obtained. Figure 2 shows the

detected CS location in the XY plane (Figure 2a) and YZ plane (Figure 2b).

Obviously, the joint magnetic field dataset can well cover the radial distances

between 8 RE and 20 RE. To simplify the surveyed region, as shown in Figure 2a,

the tail CS are divided roughly into three regions based on the azimuthal location,

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that is, Dawn flank: 210°≤φ<270°, Midnight region: 150°<φ<210°, and the Dusk

flank: 90°≤φ≤150°. The nominal magnetopause is marked as a dashed line with

empirical standoff distance r0 =11 RE and tail flaring level α=0.58; from the model

of Shue et al. (1997). Note that, due to a significant data gap and fewer CS crossings

around midnight, CS samples are significantly missed at midnight (Y~0).

The dynamic variation of the magnetic field in the tail CS is strongly associated

with geomagnetic activity. The CS is found to be thinning (indicated by minor Bz

component) in growth phase of a substorm, and thickens (enhanced Bz component)

in the explosive and recovery phase (e.g. Baumjohann et al., 1992; Sanny et al.,

1994; Petrukovich et al., 2007). However, it is not so easy to diagnose the substorm

phases exactly for each crossing event in the whole dataset. Thus, for simplification,

the states of geomagnetic activity are roughly divided into quite times and active

times merely based on the AE index, though the diagnosis of ‘geomagnetic

substorm/storm phases’ might be more physically appropriate than the AE index.

Similarly to that defined by Slavin et al. (1987), we defined the quiet times as the

moments when AE ≤100 nT, while the active times corresponds to AE >100 nT.

Based on this definition, there are 8558 crossing points during quiet times and

17925 crossing points for the active times obtained. Figure 3 shows the radial

profile of crossing numbers and the normalized occurrence rate for both activity

states (it is the ratio of the number in the bin to the amount in that state). The value

is averaged in a bin of 1 RE (the width of bin is assumed to be 1 RE in the following

radial plots). In these panels, the green lines, red lines and blue lines are plotted for

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the dusk flank region, midnight region and the dawn region respectively. From

Figure 3, the crossing number during active times is basically larger than that

during quiet times, which, being consistent with the results of Davey et al., (2012),

may imply the CS would flap more severely in active times than that during quiet

times. It is interesting to note that, the crossing number is enhanced greatly at r~14

RE and ~19 RE. The double-peaks probably arise from the apogee location for

Cluster(r~19 RE) and TC-1(r~13.5 RE). The spacecraft move slowly near apogee and

would have more chance to cross the CS. Thus, one cannot simply infer the CS flaps

locally as a double radial-peak.

Since the coupling of solar wind/magnetosphere is strongly controlled by IMF

and the dynamic pressure of solar wind, Pdy (e.g. Vasyliunas et al., 1982), only the

parameters IMF By, IMF Bz and Pdy from OMNI dataset are used to study the

possible dependence on the solar wind parameters. Figure 4 shows the averaged

IMF By, Bz component and Pdy against the radial distance for the active and quiet

time period. The corresponding error bars are plotted accordingly. The length of

error bar in each panel, estimated as the 2 1.96nσ

× (nσ is the standard error of

mean), represents the confidence interval with level 95%.. The same meaning is

assumed in the following error bar plots.

In quiet times, the averaged IMF Bz is basically positive (+1~2 nT), and the

dynamic pressure is lower (Pdy<2 nPa). In contrast, in the active times, the averaged

IMF Bz is basically negative (-1~-2 nT) and the dynamic pressure is higher (Pdy >2

nPa). Thus, it seems the active times tend to appear in the period of negative IMF Bz

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as well as the higher dynamic pressure. The averaged IMF By is randomly within ±5

nT in the whole radial range regardless of the activity states. The dependence of CS

magnetic field on the solar wind parameters will be addressed more in Section 3.

With the prepared dataset above, the radial distributions of magnetic field at

magnetotail CS center with radial distance 8 RE<r<20 RE will be studied exclusively

in the following subsections.

2.2 Profile of magnetic field strength and the Bz component

In this subsection, the radial profile of magnetic field and its components under

different activity states are studied. As shown in Figure 5, the averaged radial

profile of the magnetic field strength (indicated by Bmin, Bmin =(By2+Bz

2)1/2), the Bz

component, and the By component are shown respectively from top to bottom in the

left column for the quiet times and in the right column for the active times.

Particularly, to show our results against the dipole field, the geomagnetic dipole

field in the magnetic equatorial plane, i.e. Bmin=Bz (dipole axis is assumed towards

+Z axis), is plotted as black dashed lines for both activity states, wherein the

adopted dipole moment is ME~7.8×1022A·m2 (for the year 2000).

2.2.1 Overview

One prominent feature can be found from Figure 5, that is, the magnetic field

strength Bmin or the Bz component increases prominently as radial distance

decreasing down to r~11.5 RE irrespective of activity states (see the black vertical

dashed lines). Taking Bz in quiet times for example, Bz increases slowly from ~3 nT

to ~10 nT as r decreases from ~20 RE to ~11 RE, but sharply increases up to 40 nT as

r decreases down to ~8 RE. It also has the similar trend for the active times. By

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comparison, such kind distribution features cannot be seen from the By distribution

as shown in Figure 5c and Figure 5f. The detailed By distribution will be addressed

in subsection 2.4.

Another prominent feature is that the radial profile of Bmin or Bz shows an evident

dawn-dusk asymmetry. For the range of 14 <r<20 RE in the quiet times, the Bz at

both flank regions are larger than that in the midnight region, and the strength of Bz

at the dawn flank region is larger than that at the dusk flank region. While for the

same range in the active times, Bz around the midnight region is comparable to that

at the dusk flank region but still evidently weaker than that at the dawn flank region.

As it decreases down to the range 9<r<14 RE, in the quiet times, Bz at the midnight

region becomes comparable to that at the dusk flank region but still evidently

weaker than that at the dawn flank region. But for the same range in the active times,

the Bz becomes comparable in the whole dawn-dusk regions, particularly for r<12

RE. Hence, the radial profile of Bmin or Bz displays a dawn-dusk asymmetry which is

more evident in the quiet times with a lengthwise scale 11 RE at least.

2.2.2 Comparison with Dipole field

From Figure 5, for the midnight region during quiet times, the Bmin and Bz are

generally weaker than that of the dipole field within the region 8<r<20 RE, whereas

the “weaker region” reduces to 8<r<16 RE during active times. At both flank regions

and particularly for the dawn flank, regardless of the states, Bz is weaker than the

dipole field within 8<r<14 RE, and it is a bit stronger than the nominal dipole field

outside r >14 RE. These results are consistent with that of the T07 model (Tsyganenko

and Sitnov, 2007) where the existence of a “weaker region” is physically related to the

diamagnetic effect as induced by the tail current systems. Because the duskward

partial ring current and cross-tail current would induce a southward field in the inner

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current sheet, leading to the depressed geomagnetic field there.

The comparison with dipole field demonstrates that the actual profile cannot be

simply described by the dipole field model. In Section 4, a further similar comparison

with the T01 model (Tsyganenko, 2002) will be detailed.

2.2.3 Quiet times vs. Active times

To exhibit the difference in both states, the upper panels of Figure 6 show the

radial distribution of Bz component at different regions in the quiet times (black lines)

against that in the active times (red lines). The lower panels show the standard

deviation of Bz, zσ , at the corresponding location, which can indicate the fluctuation

amplitude of Bz.

It is interesting to note from Figure 6b and Figure 6c that the averaged Bz

component in the midnight region and dawn flank region (r>12 RE) is generally

stronger during active times than that in quiet times, while it is not so obvious at the

dusk flank region (Figure 6a). Since the magnetotail CS beyond the hinging distance

can be on average seen as a plane parallel to the GSM XY plane, except very close

to the flanks (e.g. Tsyganenko and Fairfield, 2004; Rong et al., 2011), Bz basically

acts as the normal component to the CS plane, and the magnitude of Bz can

approximately indicate the curvature radius of magnetic field lines or the thickness

of CS if CS can be seen as 2-D structure (Büchner and Zelenyi, 1989; Shen et al.,

2003; Shen et al., 2007). Consequently, the enhanced Bz component in active times

may imply that the CS is generally thicker than that in quiet times.

It is interesting to note in Figure 5e and Figure 6a that in active times there is an

evident depression of Bz in 10.5<r<12.5 RE in the dusk region. The local Bz

minimum observed here seemed consistently with the earlier theoretic prediction

(e.g. Hau et al., 1989; Hau 1991; Erickson, 1992). Meanwhile, the fluctuation

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represented by zσ , shown in the lower panels of Figure 6, clearly indicate that the Bz

component in the active times fluctuates more sevrely than that in quiet times

2.3. Negative Bz component

The Bz component in tail CS is normally positive. However, due to some

dynamic processes occurred in the tail CS, e.g. magnetic reconnection, current

disruption, magnetic turbulence, flux ropes, transient field-aligned current etc.,

sometimes, the negative Bz (Bz<0) can appear (Sharma et al. 2008). Therefore, the

appearance of negative Bz can be seen as an indicator of activities though the

occurrence probability is very low, and the survey of negative Bz distribution could

reveal the distribution of dynamic activities to some extent. Totally, the crossing

number with negative Bz in our dataset is 1130, accordingly, the total occurrence

probability of negative Bz is ~0.043 and ignorable. Though the total occurrence

probability is ignorable, the probability distribution, as shown in Figure 7, displays

some interesting properties.

From Figure 7a for the quiet times, the appearance of negative Bz is basically

concentrated in the midnight region, and the appearance probability is decreased as

radial distance decreased. By comparision, as shown in Figure 7b, the frequency of

negative Bz is higher in active time than that in quiet time, particularly for the

midnight and dusk regions. Moreover, the negative Bz during active time can occur

closer to the Earth. These results may imply that, the magnetic activities, such as

magnetic reconnection, are inclined to occur around the midnight and dusk flank

region, manifesting an dawn-dusk asymmetry. In contrast to the quiet time intervals,

during active times, the activity appears to occur more frequently closer to earth.

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2.4. Profile of By component

It is clear from Figure 5c and Figure 5f that, regardless of activity state, the By

component around the midnight region is generally ignorable, but becomes negative

as approaching both flanks. Such features have been noticed previously (Petrukovich,

2011; Rong et al., 2011), and it can be explained by the seasonal modulation of the

dipole tilt angle on the warping of current sheet (Petrukovich, 2011). The typical CS

model (Tsyganenko and Fairfield, 2004) show that when the dipole tilt angle is

positive (dipole axis is sunward), the CS at both flanks would warp down toward the

-Z direction,vice versa. Accordingly the magnetic field in the CS would be bent along

the warped CS normal, so that a net By component is notably induced at both flanks.

Petrukovich (2009, 2011) argued that the By in CS is positively correlated with dipole

tilt angle at dusk and midnight region, a weaker negative correlation exists with tilt

angle in the dawn region within r<15 RE, and the tilted related-By is found to be

stronger closer to the earth.

Here, to confirm the effect of dipole tilt angle on CS By component, Figure 8 plots

the averaged By component and the dipole tilt angle distribution in the dawn-dusk or

azimuthal direction within different radial scopes. The azimuthal variations of dipole

tilt angle in all panels of Figure 8 are similar. Obviously, the positive/negative

correlation with the dipole tilt angle at dusk/dawn region can be clearly found in all

panels except Figure 8d (it will be discussed later). This means that, within 8<r<20

RE, the appearance of By component at both flank regions is easily to be modulated by

the dipole tilt angle in terms of the argument of Petrukovich (2011). It is interesting to

note from Figure 8 except Figure 8d (see also Figure 5c and Figure 5f) that negative

By besomes stronger at both flanks closer to earth, which may imply the By

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component at both flanks is more apt to be modulated by the dipole tilt angle as being

closer to earth, as also noticed by Petrukovich (2011).

It is noteworthy that in Figure 8d or in Figure 5f for the active times, in the

inner-earth region, i.e. 8<r<10RE, a sudden positive-excursion/negative-excursion of

By component at the dawn/dusk flank regions occurrs and, hence, it cannot be the

result of dipole tilt effect. Since the averaged IMF By is less than 5nT (Figure 4b and

Figure 4e), such kind of enhancement of By component also cannot be attributed to

the IMF By penetration. The enhanced field-aligned currents (FACs) system seems a

plausible reason to explain it. The FACs generally consists of region-1 (R1) and

region-2 (R2) FACs (Mcpherron,1995). The R1 FACs is closed with the low latitude

boundary layers while R2 FACs is closed with the partial ring current. The FACs at

both hemispheres would converge into or diverge from the equatorial plane. If the

subsystems of FACs at both hemispheres are identical, the induced By component in

CS should be cancelled and vanished. However, if the FACs is dominant at one

hemisphere, a net By component will be induced in the CS. Therefore, as being

sketched in Figure 9, the oberved By-excursion at both flanks in active times may

favor the FACs enhancement which are northern-hemisphere dominant. It is

interesting to note that, Shi et al. (2010) statistically found the field-aligned currents

in magnetotail has the similar hemispheric-asymmetry, that is, the intensity of FACs

in northern hemisphere is more intense than that in the southern hemisphere.

Actually, we had checked the events of By-excursion at both flanks. It is found,

though the amount of events is limited (68 data points), all these events are only

appeared in active times, and are related to the geomagnetic storm/substorm processes.

17

Previous observations also show the enhancement of FACs in low altitude during the

period of storm/substorm (e.g., Wang et al., 2006; Wang et al., 2013). Certainly, to

confirm our interpretation, more cases of By-excursion are needed in the future.

3. Responses to solar wind parameters

In this section, we will study the response of magnetic field to solar wind

parameters, especially the solar wind dynamic pressure and the IMF By component.

We should remind readers that since the IMF Bz component can modulate the

geomagnetic activity (e.g.Nishida,1975), that is, when IMF Bz is positive the

geomagnetic activities is usually in quiet time, vice versa (see Figure 4a and Figure

4d), the response to IMF Bz have been discussed actually to some extent in the

subsection 2.2.3.

3.1 Effect of solar wind dynamic pressure

Many studies demonstrated that the enhanced dynamic pressure of solar wind,

denoted by Pdy, can compresses the magnetosphere, resulting in various global and

dynamic changes in the magnetosphere. The response of the magnetotail to the

sudden variation of solar wind pressure has been studied extensively, and most of

them focused on the lobe magnetic field (e.g., Kawano et al., 1992; Collier et al., 1998;

Huttunen et al., 2005, and references therein). There are few studies concentrating on

the response of magnetic field in tail CS, particularly for the long-term averaged

period. Since the polarity of IMF Bz, as a key factor, controls the solar wind energy

coupling with the magnetosphere, here, we would check the discrepant response of

magnetic field in tail CS to the Pdy under the positive/negative IMF Bz. For simplicity,

the Pdy >5 nPa is defined as higher pressure, while it is lower pressure when Pdy<5

nPa.

18

The upper panels of Figure 10 show the response of the Bz component in different

regions to the lower Pdy and higher Pdy under the negative IMF Bz. Similarly, the

response under positive IMF Bz are shown in the lower panels of Figure 10. As seen

in Figure 10, regardless of the sign of IMF Bz, the Bz component in tail CS is

generally enhanced during the higher Pdy period than that during the lower Pdy period,

which is more evident at the dawn flank region. The result of an enhanced Bz in tail

CS during the higher period is consistent with the previous case studies of the sudden

Pdy jump (e.g. Keika et al., 2008; Miyashita et al., 2010).

Miyashita et al. (2010) proposed possible reasons to explain the response of plasma

sheet Bz component to the sudden enhancement of solar wind dynamic pressure. The

enhancement of dynamic pressure may cause the compression of magnetotail in all

directions. If the compression in dawn-dusk direction dominant, it would lead to the

increase of Bz by squeezing the magnetic field lines. In contrast, if the north-south

direction dominant, a decrease of Bz would appear due to the more tail-like magnetic

field line configuration. However, the explanation is only built on several cases, it still

lacks the support of statistical study. Although the long-term averaged variation of Pdy

addressed here is temporally different from the sudden jump of Pdy, the response of

tail Bz to the transition from the long-term averages for low Pdy to the high Pdy periods,

we believe, is just like a sudden jump of Pdy following the same physical logic.

Therefore, here, in terms of the explanations of Miyashita et al., our statistical results

may favor the compression of higher Pdy is dominant in the dawn-dusk direction.

In contrast to the Bz enhancement, no evident response of By to the higher dynamic

pressure is found (not shown here).

19

3.2 Correlationship between CS By and IMF By

Numerous statistical surveys have demonstrated that the upstream IMF By

component is the primary driver of the By component in magnetotail CS (Petrukovich,

2011, and the references therein), though sometimes the sign of CS By oppositing to

that of IMF By is noticed (Petrukovich, 2009; Rong et al., 2012). It is found the IMF

By penetration coefficient in the CS increases towards Earth from ~0.2 in the distant

tail to ~0.6 in the ISEE-1, 2 dataset (Sergeev, 1987) and to ~0.8 at the GOES orbit

(Wing et al., 1995). Petrukovich (2009) also confirmed the earthward enhancement of

the penetration coefficient within -30<X<-10 RE with the Geotail dataset. However,

the higher penetration coefficient does not necessarily imply the correlation

coefficient is better, and it is still unclear whether there is any discrepancy about the

penetration and correlation coefficient under different IMF Bz sign. With the joint

dataset, we would like to re-examine the radial dependance of the correlation between

CS By and IMF By.

Since the By component is apt to be controlled by the dipole tilt angle at both flank

regions (Petrukovich, 2011) and sensitive to the enhanced current system (including

the FAC-2) in the inner magnetotail, the correlation analysis is focused around the

midnight region (150°<φ<210°) within the radial scale 10≤r<20 RE, according to the

sign of IMF Bz.

In Figure 11, for the outer region (15≤r<20 RE, upper panels) and inner region

(10≤r<15 RE, lower panels), the scattering plots of IMF By and CS By for the whole

dataset (left column), the negative IMF Bz (middle column), and the positive IMF Bz

(right column) are shown respectively. In each panel, the derived correlation

coefficient (c.c.) and the penetration coefficient of IMF By (the ratio of CS By to IMF

20

By) are given. It is clear for the whole dataset from Figure 11, in the outer region, the

penetration coefficient is relatively low, ~0.5, whereas the penetration coefficient

becomes higher, ~0.67, in the inner region. These values of the earthward enhanced

penetration coefficient are comparable to that reported by Petrukovich (2009).

However, from Figure 11a and Figure 11b, the sampled IMF By range are quite

different between the inner CS and outer CS events. For Figure 11a, the range of IMF

By is ~ -20 - ~40 nT, whereas most samples of IMF By are dropped into |IMF By|<10

nT. The difference of statistical correlation (correlation coefficient and the penetration

coefficient) might be induced follow a logical train of thought due to the different

sample range of IMF By. To further check the discrepancy of “IMF By penetration”

under different polarity of IMF Bz for the same IMF By range, the samples of IMF By

at both regions are confined to |IMF By|<10 nT. The correlation analysis under the

interval of positive and negative IMF Bz, are plotted in the middle and right column of

Figure 11 respective.

It is clear from Figure 11, at the both regions for |IMF By|<10 nT, the CS By is

worse correlated with IMF By (c.c. ~0.4), and the penetration coefficient is lower (it is

~0.4/~0.63 for the outer/inner region) when IMF Bz is negative. Whereas, it has better

correlation (c.c. ~0.5-0.6) and higher penetration coefficient (it is ~0.53/~0.85 for the

outer/inner region) when IMF Bz is positive. It implies the polarity of IMF Bz may has

the ability to affect the penetration coefficient of IMF By.

It is believed that, in contrast to the +IMF Bz, during the interval of -IMF Bz, the

magnetotail plasma convection is enhanced, the magnetotail flux ropes and magnetic

reconnection are appeared more frequently. The strength of By component in

magnetotail would increase significantly due to the compression by the enhanced

earthward convection (Hau and Erickson, 1995). The core field of magnetotail flux

21

rope (By is the proxy) is usually much stronger than the IMF By, though its polarity is

basically consistent with IMF By (e.g. Zhang et al., 2008). Near the Hall region of

magnetic reconnection, the By component with quadruple polarity is induced (e.g.,

Runvo et al., 2003; Borg et al., 2005), while some plasma instabilities, e.g. Weibel

instability (e.g., Baumjohann et al., 2010), may occur simultaneously to generate the

By component. Therefore, a scenario could be depicted: during the interval of -IMF Bz,

some internal processes, i.e. enhanced convection, flux ropes, magnetic reconnection,

and plasma instabilities etc. which could enhance or even generate the By with sign

opposite to IMF By, would occur more frequently, so that it may lower the correlation

coefficient and penetration of IMF By. However, our analysis presented here is

preliminary, and it requires further investigation.

4. Discussion

There are several points which deserve to be discussed more thoroughly.

1) Our results revealed that the magnetic field strength Bmin and the Bz component

at the magnetotail current sheet center of entire tail width enhance prominently

as radial distance decreasing down to r~11.5 RE independent of the activity state.

It implies that the earthward plasma flow embedding in CS would start

significantly diversion by the enhanced magnetic field strength around

r~10-12RE which is often believed to be mapped to the equatorial part of the

auroral zone (e.g. Baumjohann, 2002; Zhang et al., 2009).

As to the radial profile of Bz, one should note that, after merging the

observation of Bz component by many earlier satellites, e.g. ISEE1,

AMPTE/CCE, IMP 8, Rostoker and Skone (1993) have derived an empirical

formula for the radial dependence of the Bz component, which is expressed as

22

0.4 47.8 125302xzB e x− −= + . By test (not shown here), we find this formula is more

suitable to describe the quiet time Bz profile for the midnight region.

We find that, around the midnight region, the Bz in active times is evidently

larger than that in quiet times beyond r~8 RE. In contrast, within r<8.8 RE,

Fairfield et al. (1987) found the magnetic field strength in CS decreased in active

times (indicated by the increased Kp index). Therefore, combining with the

results of Fairfield et al., one can reaches a conclusion that Bz in active times is

larger than that in quiet times beyond r>8 RE, but smaller within r< 8 RE.

Accordingly, one can reasonably infer that an enhanced duskward current is

developed around r~8-9 RE in active times.

2) Our results demonstrate that the radial profile of Bmin or Bz displays a clear

dawn-dusk asymmetry, i.e. the magnitude of Bmin or Bz at the dawn flank region is

larger than that in the dusk flank and midnight region, which is more evident

during quiet times within 9<r<20 RE.. This may imply the CS thickness in the

dawn flank region is usually larger than that in the midnight and dusk flank region.

In addition, in Section 2.3, the distribution of negative Bz during active times

consistently shows a similar asymmetry. Actually, the asymmetry has been also

noticed in previous studies (Fairfield et al., 1986; Rong et al., 2010, 2011). With

the ISEE1’s measurement within - 20≤X≤-6 RE, |Y|≤ 7 RE, the derived current

density in CS are found stronger within -3<Y<6 RE displaying evident dawn-dusk

asymmetry. It is also noticed that the fast flow in the near-earth magnetotail based

on THEMIS-D observation are strongly localized in the local time sector

21:00-01:00 (McPherron et al., 2011). The tail dawn-dusk asymmetry might be

causally associated with the dawn-dusk asymmetric distribution of auroral

substorm onset (Frey et al., 2004; see the discussion of Rong et al., 2011). The

23

reasons for the asymmetry are unclear, a summary of the possible reasons is given

by Vlasova et al. (2002). Recent simulation demonstrate that the asymmetry is

probably regulated by the spatial variation in ionospheric conductance (Zhang et

al., 2012).

3) As we mentioned above, in the dusk region, a local minimum in Bz is presented

within 10.5<r<12.5 RE in active time (see Figure 5e and Figure 6a). Previous

theoretical studies (e.g. Hau et al., 1989; Erickson, 1992) predicted that the 2-D

force-balanced magnetic field models with constant entropy would exhibit a local

Bz minimum in the inner plasma sheet by the steady adiabatic earthward

convection (Hau et al., 1989; Hau, 1991; Erickson, 1992). The local Bz minimum

is noticed at r~12 RE in a SMC event model (Sergeev et al., 1994; Sergeev, 1996),

and it is supported by indirect observational evidence from the pre-midnight

sector of the near-Earth plasma sheet (Saito et al., 2010). Considering all these

facts, it seems the spatial features of local Bz minimum exhibited in our survey

satisfy that one as being predicted in the convection theory. We had checked the

plasma data, IMF conditions, the geomagnetic field data at ground stations and the

quick look of AE plots associated with the local Bz minimum in dusk region. It is

found most of the data points are actually related with the southern IMF and

higher long duration (larger than 4 hours) AE index but no substorm signatures,

which satisfies the typical characteristics of SMC. Hence, our observation results

support that the local minimum Bz in the inner plasma sheet is brought by the

earthward convection. We should remember that the Bz minimum does not

contradict the enhanced Bz as we found in subsection 2.2.3. The Bz minimum is

located within 10.5<r<12.5 RE in the dusk region, while the enhanced Bz during

active times appears mainly around the midnight region.

24

4) The radial profile revealed here cannot be simply reproduced by the empirical

models. Besides of the comparison with dipole field in Figure 5, the radial profile

of Bz from T01 model (Tsyganenko, 2002) is shown in Figure 12 for the further

comparison. The dusk flank, midnight region, and the dawn flank are simply

corresponded to the meridians with azimuthal angle φ=120°, φ=180°, and φ=240°

respectively. For the quiet time, Dst, IMF By, and IMF Bz are set to zero; while

for the active time, Dst=-30nT, IMF By=0 nT, IMF Bz =-6 nT. The dynamic

pressure for both states are set to Pdy=2 nPa. Moreover, the solar wind speed ~400

km/s, dipole tilt angle ~0° are input for both activity states. Several inconsistent

aspects can be noticed from T01 model: 1. T01 doesn’t show the evident

dawn-dusk asymmetry (the minor Bz difference between dawn and dusk in the

inner magnetosphere as shown in Figure 12 results from the dawn-dusk

asymmetric partial ring current); 2. The Bz in the midnight region is larger than

that at both flanks for r>14.5 RE in quiet times and r>12 RE in active times

(actually, T01 model only used data sunward of X = –15 RE); while, our survey

indicate Bz in the midnight is usually weaker than that at both flanks; 3. In active

time, there is a wider depression of Bz within 10<r<18 RE in the midnight region,

while, our survey indicates that the depression of Bz is only presented within

10.5<r<12.5 RE for the dusk flank region. Hence, one should be careful when

applying this model.

5. Summary

This study has statistically surveyed the radial profile of magnetic field in the

magnetotail current sheet within the region 8<r<20 RE of the entire tail width and

based on the joint magnetic field dataset of Cluster and TC-1. Many related issues are

25

addressed and compared with previous studies. The new contributions from our study

can be summarized as follows:

1. For the radial profile: it is found, basically independent of geomagnetic activity,

the magnetic field strength Bmin and Bz component are enhanced prominently as

radial distance decreasing down to r~11.5 RE. This feature cannot seen simply

from the models and no one had presented it explicitly as far as we know. The

strength of Bmin or Bz are weaker in the midnight and dusk flank than that in dawn

flank displaying a dawn-dusk asymmetry. Although the asymmetry has been

noticed in previous studies, the radial scale of asymmetry is only presented in our

study, that is, the asymmetry is evident at least within 9 <r<20 RE in the quiet

times, but 14 <r<20 RE in the active times. The occurrence probability of negative

Bz in active times also shows the similar asymmetric distribution.

2. Features in active times: previous studies noticed that the magnitude of magntic

field or the Bz component is stronger during substorms (Huang and Frank,1994;

Nakai et al.,1997,1999). However, from our study, this point is only valid in the

midnight and dawn flank, but not for the dusk flank. Additionally, a local Bz

minimum within 10.5<r<12.5 RE in the dusk region in active times is found

statistically for the first time, which provide evidence for previous theoretical

predictions. Our new findings also demonstrated that, the sharp

positive-excursion/negative-excursion of By component at the dawn/dusk flank

regions occurs inside r<10 RE in active times, which may imply that the

enhancement of FACs that are northern-hemisphere dominant are developed in

active times.

3. Responses to solar wind parameters: previous case studies (Keika et al., 2008;

Miyashita et al., 2010) of Pdy jump found the stronger Bz component in plasma

26

sheet may appear. Here, through a statistical survey for the first time, we explicitly

confirm that the Bz component is indeed generally stronger during the period of

higher solar wind dynamic pressure. Although the CS By generally correlated with

IMF By is well known, it has not been checked whether there is any difference for

different polarities of IMF Bz. Here, we find the CS By is better correlated with

IMF By, and the penetration coefficient (the ratio of CS By to IMF By) is higher

when IMF Bz is positive. In addition, we have confirmed the earthward

enhancement of IMF By penetration coefficient, which was reported previously by

Petrukovich (2009).

Acknowledgments

The authors are thankful to the ESA Cluster Active Archive, Double Star Chinese

Data Center, and the GSFC/SPDF OMNIWeb interface (http://omniweb.gsfc.nasa.gov)

for providing the Cluster FGM data, TC-1 FGM data, and OMNI data, respectively.

This work is supported by the Chinese Academy of Sciences (KZZD-EW-01-2),

National Basic Research Program of China (973 Program) grant 2011CB811404 and

2011CB811405, the National Natural Science Foundation of China grant 41104114,

41374180, 41321003, 40974101, 41131066, 41211120182, China Postdoctoral

Science Foundation Funded Project 2012T50132, and the Research Fund for the State

Key Laboratory of Lithospheric Evolution. The work by M. W. Dunlop is partly

supported by CAS visiting professorship for senior international scientists grant

2012T1G0018. The authors thank the helpful discussions with H. Zhang, J.-H. Shue,

P. Zhu, and H. V. Malova. Z. J. Rong would like to acknowledge the hospitality of

27

IRF, Kiruna, Sweden.

Reference

Angelopoulos, V., 2009. The THEMIS Mission, in: Burch, J. L., Angelopoulos V.

(Eds.), The THEMIS Mission, Springer, New York, pp.5–34, doi:

10.1007/978-0-387-89820-9_2.

Artemyev, A. V., et al., 2013. Profiles of electron temperature and Bz along Earth’s

magnetotail. Ann. Geophys. 31, 1109–1114.

Balogh, A., et al., 1997. The Cluster magnetic field investigation. Space Sci. Rev. 79,

65-91.

Balogh, A., et al., 2001. The Cluster magnetic field investigation: Overview of inflight

performance and initial results. Ann. Geophys. 19, 1207-1218.

Baumjohann, W., Paschmann, G., Nagai T., 1992. Thinning and expansion of the

substorm plasma sheet. J. Geophys. Res. 97, 17173–17175,

doi:10.1029/92JA01519.

Baumjohann, W., 2002. Modes of convection in the magnetotail. Phys. Plasmas. 9,

3665–3667, doi:10.1063/1.1499116.

Baumjohann, W., Nakamura, R. Treumann, R. A., 2010. Magnetic guide field

generation in collisionless current sheets. Ann. Geophys. 28, 789–793, doi:

10.5194/angeo-28-789-2010.

Behannon, K., 1970. Geometry of the Geomagnetic Tail. J. Geophys. Res. 75, 743-753.

Birn, J.,et al.1999, Flow braking and the substorm current wedge. J. Geophys. Res. 104,

28

19895–19903, doi: 10.1029/1999JA900173.

Borg, A. L. et al., 2005. Cluster encounter of a magnetic reconnection diffusion region

in the near- Earth magnetotail on September 19, 2003. Geophys. Res. Lett. 32,

L19105, doi: 10.1029/2005GL023794.

Büchner, J., Zelenyi, L. M.,1989. Regular and chaotic charged particle motion in

magnetotaillike field reversals: 1. Basic theory of trapped motion. J. Geophys. Res.

94(A9), 11821–11842, doi:10.1029/JA094iA09p11821.

Carr, C. et al., 2005. The Double Star magnetic field investigation: instrument design,

performance and highlights of the first year’s observations. Ann. Geophys. 23,

2713–2732.

Carr, C. et al., 2006. The Double Star magnetic field investigation: Overview of

instrument performance and initial results. Adv. Space Res. 38, 1828–1833.

Collier, M. R. et al., 1998. Multispacecraft observations of sudden impulses in the

magnetotail caused by solar wind pressure discontinuities: Wind and IMP 8. J.

Geophys. Res. 103(A8), 17293–17305.

Cowley, S. W. H., 1981. Asymmetry effects associated with the X-component of the

IMF in a magnetically open magnetosphere. Planet. Space Sci. 29, 809-818.

Davey, E. A. et al., 2012. Storm and substorm effects on magnetotail current sheet

motion. J. Geophys. Res.117, A02202, doi: 10.1029/2011JA017112.

Erickson, G. M., 1992. A quasi‐static magnetospheric convection model in two

dimensions. J. Geophys. Res. 97, 6505.

Fairfield, D., 1979. On the Average Configuraton of the Geomagnetic Tail. J. Geophys.

29

Res. 84(A5), 1950-1958.

Fairfield, D. H.,1986. The magnetic field of the equatorial magnetotail from 10 to 40

RE. J. Geophys. Res. 91(A4), 4238–4244, doi: 10.1029/JA091iA04p04238.

Fairfield, D. H. et al.,1987. The magnetic field of the equatorial magnetotail:

AMPTE/CCE observations at R < 8.8 RE. J. Geophys. Res. 92(A7), 7432–7442,

doi:10.1029/JA092iA07p07432.

Fairfield, D. H., 1992. On the structure of the distant magnetotail: ISEE 3. J. Geophys.

Res. 97(A2), 1403–1410, doi:10.1029/91JA02388.

Fujmoto, M., Terasawa, T., Mukai, T., 1998. The lower‐latitude boundary layer in the

tail‐flanks, in: Nishida, A., Baker, D. N., Cowley, S. W. H. (Eds.), New Perspectives

on the Earth’s Magnetotail. Geophys. Monogr. Ser. vol. 105, AGU, Washington, D.

C, pp. 33–44,

Gordeev, E., Amosova, M., Sergeev V., 2012. IMF Bx effect on the magnetotail neutral

sheet geometry and dynamics. Geophysical Research Abstracts. Vol. 14,

EGU2012-14437, EGU General Assembly 2012.

Hameiri, E., Laurence, P., Mond, M., 1991. The ballooning instability in space plasmas.

J. Geophys. Res. 96(A2), 1513–1526, doi:10.1029/90JA02100.

Hau, L.‐N. et al., 1989. Steady state magnetic field configurations for the Earth’s

magnetotail. J. Geophys. Res. 94(A2), 1303–1316, doi: 10.1029/JA094iA02p01303.

Hau, L.‐N., 1991. Effects of steady state adiabatic convection on the configuration of

the near ‐ Earth plasma sheet: 2. J. Geophys. Res. 96(A4), 5591–5596, doi:

10.1029/90JA02619.

30

Hau, L.-N., Erickson, G. M., 1995. Penetration of the interplanetary magnetic field By

into Earth’s plasma sheet. J. Geophys. Res. 100(A11), 21,745–21,751, doi:

10.1029/95JA01935.

Huang, C. Y., Frank L. A., 1994. Magnitude of BZ in the neutral sheet of the

magnetotail. J. Geophys. Res. 99(A1), 73–82, doi: 10.1029/93JA01752.

Huttunen, K. E. J. et al., 2005. Cluster observations of sudden impulses in the

magnetotail caused by interplanetary shocks and pressure increases. Ann. Geophys.

23(2), 609–624.

Kawano, H. et al., 1992. Rotational polarities of sudden impulses in the magnetotail

lobe. J. Geophys. Res. 97(A11), 17177–17182.

Kaymaz, Z. et al, 1994a. Magnetotail views at 33RE: IMP 8 magnetometer observations.

J. Geophys. Res. 99(A5), 8705–8730, doi: 10.1029/93JA03564.

Kaymaz, Z. et al., 1994b. Interplanetary magnetic field control of magnetotail magnetic

field geometry: IMP 8 observations. J. Geophys. Res. 99(A6), 11113–11126, doi:

10.1029/94JA00300.

Keika, K., et al., 2008. Response of the inner magnetosphere and the plasma sheet to a

sudden impulse. J. Geophys. Res. 113, A07S35, doi: 10.1029/2007JA012763.

King, J. H., Papitashvili, N. E., 2005. Solar wind spatial scales in and comparisons of

hourly Wind and ACE plasma and magnetic field data. J. Geophys. Res. 110,

A02104, doi:10.1029/2004JA010649.

Liu, W. W., 1997. Physics of the explosive growth phase: Ballooning instability

revisited. J. Geophys. Res. 102(A3), 4927–4931, doi:10.1029/96JA03561.

31

Liu, Z. X. et al., 2005. The Double Star mission. Ann. Geophys. 23, 2707–2712.

Lucek, E. A. et al., 2005. The magnetosheath. Space Sci. Rev. 118, 95–152, doi:

10.1007/s11214-005-3825-2.

Lui, A.,1996. Current disruption in the Earth's magnetosphere: Observations and

models. J. Geophys. Res. 101(A6), 13067-13088.

McPherron, R. L., 1995. Magnetospheric dynamics, in: Kivelson, M.G., Russell, C.T.

(Eds.), introduction to space physics. Cambridge University Press, Cambridge,

pp.400- 458.

McPherron, R. L., 2011. Characteristics of plasma flows at the inner edge of the

plasma sheet. J. Geophys. Res. 116, A00I33, doi: 10.1029/2010JA015923.

Miyashita, Y. et al., 2010. Plasma sheet changes caused by sudden enhancements of the

solar wind pressure. J. Geophys. Res. 115, A05214, doi: 10.1029/2009JA014617.

Nagai, T. et al., 2005. Solar wind control of the radial distance of the magnetic

reconnection site in the magnetotail. J. Geophys. Res. 110, A09208, doi:

10.1029/2005JA011207.

Nakai, H., Kamide, Y., Russell, C. T., 1997. Statistical nature of the magnetotail current

in the near-Earth region. J. Geophys. Res. 102(A5), 9573–9586, doi:

10.1029/97JA00136.

Nakai, H., Kamide, Y., Russell, C. T., 1999. Dependence of the near-Earth magnetotail

magnetic field on storm and substorm activities. J. Geophys. Res. 104(A10),

22701–22711, doi:10.1029/1999JA900273.

Ness, N. F.,1965. The Earth’s magnetotail. J. Geophys. Res. 70, 2989–3005, doi:

32

10.1029/JZ070i013p02989.

Ness, N. F., 1969. The geomagnetic tail. Rev. Geophys. 7(1, 2), 97-127.

Nishida, A., 1975. Interplanetary field effect on the magnetosphere. Space Sci. Rev. 17,

353–389.

Nishida, A., 1994. The Geotail Mission. Geophys. Res. Lett. 21, 2871–2873.

Ohtani, S. I., Shay, M. A., Mukai, T., 2004. Temporal structure of the fast convective

flow in the plasma sheet: Comparison between observations and two-fluid

simulations. J. Geophys. Res. 109, A03210, doi: 10.1029/2003JA010002.

Panov, E. V., et al., 2010. Multiple overshoot and rebound of a bursty bulk flow.

Geophys. Res. Lett. 37, L08103, doi: 10.1029/2009GL041971.

Petrukovich, A. A. et al., 2005. Cluster vision of the magnetotail current sheet on a

macroscale. J. Geophys. Res. 110, A06204, doi: 10.1029/2004JA010825.

Petrukovich, A. A.et al., 2007. Thinning and stretching of the plasma sheet. J. Geophys.

Res. 112, A10213, doi: 10.1029/2007JA012349.

Petrukovich, A. A., 2009. Dipole tilt effects in plasma sheet By: statistical model and

extreme values. Ann. Geophys. 24, 1343–1352.

Petrukovich, A. A., 2011. Origins of plasma sheet By. J. Geophys. Res. 116, A07217,

doi: 10.1029/2010JA016386.

Petrukovich, A. A. et al., 2013. Cluster observations of ∂Bz/∂Bx during growth phase

magnetotail stretching intervals. J. Geophys. Res. 118, 5720 – 5730,

doi:10.1002/jgra.50550.

Rong, Z.J. et al., 2010. Statistical survey on the magnetic field in magnetotail current

33

sheets: Cluster observations. Chinese Sci. Bull. 55, 2542–2547, doi:

10.1007/s11434-010-3096-5.

Rong, Z. J. et al., 2011. Statistical survey on the magnetic structure in magnetotail

current sheets. J. Geophys. Res. 116, A09218, doi: 10.1029/2011JA016489.

Rong, Z. J. et al., 2012. Profile of strong magnetic field By component in magnetotail

current sheets. J. Geophys. Res. 117, A06216, doi: 10.1029/2011JA017402.

Rostoker, G., Skone, S., 1993. Magnetic flux mapping considerations in the auroral

oval and the Earth's magnetotail. J. Geophys. Res. 98(A2), 1377–1384,

doi:10.1029/92JA01838.

Saito, M. H. et al., 2010. Spatial profile of magnetic field in the near‐Earth plasma

sheet prior to depolarization by THEMIS: Feature of minimum B. Geophys. Res.

Lett. 37, L08106, doi: 10.1029/2010GL042813.

Sanny, J., R. L. McPherron, C. T. Russell, D. N. Baker, T. I. Pulkkinen, and A. Nishida

(1994), Growth-phase thinning of the near-Earth current sheet during the CDAW 6

substorm. J. Geophys. Res. 99, 5805.

Sergeev, V. A., 1987. Penetration of the By component of the interplanetary magnetic

field (IMF) into the tail of the magnetosphere. Geomagn. Aeron. 27, 612–615.

Sergeev, V. et al., 1994. Hybrid state of the tail magnetic configuration during steady

convection events. J. Geophys. Res. 99(A12), 23571–23582, doi:

10.1029/94JA01980.

Sergeev, V. A., Pellinen, R. J., Pulkkinen T. I., 1996. Steady magnetospheric convection:

A review of recent results. Space Sci. Rev. 75, 551–604, doi: 10.1007/BF00833344.

34

Sharma, A. S. et al., 2008. Transient and localized processes in the magnetotail: a

review. Ann. Geophys. 26, 955–1006, 2008.

Shen, C., et al., 2003. Analyses on the geometrical structure of magnetic field in the

current sheet based on cluster measurements. J. Geophys. Res. 108(A5), 1168, doi:

10.1029/2002JA009612.

Shen, C., Liu, Z., 2005. Double Star project – master science operations plan. Ann.

Geophys. 23, 2851–2859.

Shen, C. et al., 2007. Magnetic field rotation analysis and the applications. J. Geophys.

Res. 112, A06211, doi: 10.1029/2005JA011584.

Shen, C. et al., 2012. Spatial gradients from irregular, multiple-point spacecraft

configurations. J. Geophys. Res. 117, A11207, doi: 10.1029/2012JA018075.

Shi, J. K. et al., 2010. South-north asymmetry of field-aligned currents in the

magnetotail observed by Cluster. J. Geophys. Res. 115, A07228, doi:

10.1029/2009JA014446.

Shiokawa, K., Baumjohann, W., Haerendel, G., 1997. Braking of high-speed flows in

the near-Earth tail. Geophys. Res. Lett. 24, 1179– 1182.

Shue, J.-H. et al., 1997. A new functional form to study the solar wind control of the

magnetopause size and shape, J. Geophys. Res., 102(A5), 9497–9511, doi:

10.1029/97JA00196.

Slavin, J. A. et al., 1987. Magnetic configuration of the distant plasma sheet: ISEE-3

observations, in: Lui, A. T. Y. (Eds.), Magnetotail Physics. JHU Press, Baltimore, pp.

59-64,

35

Speiser, T. W., 1973. Magnetospheric current sheets. Radio Sci. 8(11), 973–977.

Tsurutani, B. T. et al., 1984. Magnetic structure of the distant geotail from −60 to −220

Re: ISEE‐3. Geophys. Res. Lett. 11(1), 1–4.

Tsyganenko, N. A. et al., 1998. Global configuration of the magnetotail current sheet

as derived from Geotail, Wind, IMP 8 and ISEE 1/2 data. J. Geophys. Res. 103(A4),

6827–6841, doi:10.1029/97JA03621.

Tsyganenko, N. A., 2002. A model of the near magnetosphere with a dawn-dusk

asymmetry, 2, Parameterization and fitting to observations. J. Geophys. Res.

107(A8), doi:10.1029/2001JA000220.

Tsyganenko, N. A., Fairfield, D. H., 2004. Global shape of the magnetotail current

sheet as derived from Geotail and Polar data. J. Geophys. Res. 109, A03218, doi:

10.1029/2003JA010062.

Tsyganenko, N. A., Sitnov, M. I., 2007. Magnetospheric configurations from a

high-resolution data-based magnetic field model. J. Geophys. Res. 112, A06225, doi:

10.1029/2007JA012260.

Vasyliunas, V.M. et al., 1982. Scaling relations governing magnetospheric energy

transfer. Planet. Space Sci. 30(4), 359-365,

Vlasova, N. A., Sosnovets, E. N., Chuchkov E. A., 2002. A study of long-term strong

dawn-dusk asymmetry of the earth's magnetosphere in 1991. Adv. Space Res. 30(10),

2273-2278.

Wang, C.-P. et al., 2004. Midnight radial profiles of the quiet and growth-phase plasma

sheet: The Geotail observations. J. Geophys. Res. 109, A12201, doi:

36

10.1029/2004JA010590.

Wang, H., et al., 2006. Field-aligned currents observed by CHAMP during the intense

2003 geomagnetic storm events. Annales Geophysicae. 24, 311–324.

Wang, H., et al.,2010. Substorm Time Ionospheric Field-Aligned Currents as Observed

by CHAMP. Chinese Journal of Geophysics. 53, 339–346, doi: 10.1002/cjg2.1502.

Wing, S. et al., 1995. A large statistical study of the entry of interplanetary magnetic

field Y‐component into the magnetosphere. Geophys. Res. Lett. 22, 2083–2086.

Yang, J., Toffoletto, F. R., Song, Y., 2010. Role of depleted flux tubes in steady

magnetospheric convection: Results of RCM-E simulations. J. Geophys. Res. 115,

A00I11, doi:10.1029/2010JA015731.

Zhang, B., et al., 2012. Magnetotail origins of auroral Alfvénic power. J. Geophys. Res.

117, A09205, doi:10.1029/2012JA017680.

Zhang, L. Q., et al., 2009. Convective bursty flows in the near-Earth magnetotail inside

13 RE. J. Geophys. Res. 114, A02202, doi: 10.1029/2008JA013125.

Zhang, Y. C. et al., 2008. Relationship Between the Magnetic Flux Ropes in

Magnetotail and Interplanetary Magnetic Field. Chinese Journal of Space Science.

2008, 28(2), 97-101.

Zhu, P., Raeder, J., 2014. Ballooning Instability-Induced Plasmoid Formation in

Near-Earth Plasma Sheet. J. Geophys. Res. 119, 131–141,

doi:10.1002/2013JA019511.

37

Figure 1. The Cluster orbits (C3, Samba) shown in XZ plane (a) and YZ plane(b) in

GSE coordinates in the year 2001(on 183 orbit), 2002 (337orbit), 2003 (490 orbit),

2004 (644 orbit), 2005 (797 orbit), 2006(951 orbit), 2007(1104 orbit), 2008(1258

orbit), and 2009(1412 orbit), as well as the TC-1 orbit (227 orbit) in 2004 for the

magnetotail investigation. The nominal magnetopause is marked as the dashed line.

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Figure 2. The locations of CS center observed by C3 during 2000-2009 (black dots)

and TC-1 during 2004(red dots) as being projected onto the XY plane (a) and the

YZ plane (b) in GSM coordinates. The nominal magnetopause is marked as the

dashed line. The blue dashed lines divide the tail CS roughly into three regions, i.e.

dusk flank, midnight, and dawn flank region.

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Figure 3. The radial distribution of CS crossing number for the total dataset (a), the

quiet time (b), and for the active time (c). While, in panel b and c, the normalized

occurrence (dot-dashed lines) are shown correspondingly in the right-Y axis.

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Figure 4. The averaged IMF Bz (a,d), By component (b,e) and the dynamic pressure

of solar wind (c,f) at the radial location of S/C under different activity states.

Figure 5. The radial profile of magnetic field strength, Bmin (a, d), Bz component (b,

e), and the By component (c, f) in tail CS center in different regions and

geomagnetic activity states.

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Figure 6. The radial profile of Bz (upper panels) and its fluctuation (lower panels,

represented by the standard deviation σz) in quiet times (black lines) and active times

(red lines).

Figure 7. The radial distribution of negative Bz occurrence probability at different

regions in quiet times (a) and active times (b).

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Figure 8. The azimuthal distribution of By component( red lines)) and dipole tilt angle

(blue dotes) within different radial scopes.

Figure 9. The sketched diagram to illustrate the induced By component by the

enhanced FACs system at the nothern hemisophere during the active time.

43

Figure 10. The radial distribution of Bz at different regions under lower dynamic

pressure (black lines) and higher dynamic pressure of solar wind (red lines). The

upper panels are plotted for the conditions of negative IMF Bz while the lower panels

is for the positive IMF Bz.

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Figure 11. The scattering plots of IMF By versus CS By component around the

midnight region. The upper panels are for the outer CS region (15≤r<20 RE), while

lower panels are for the inner CS region (10≤r≤15 RE). The line in each panel

represents the least-square line.

Figure 12. The radial profile of Bz component in tail CS as derived from T01

model. The dusk flank, midnight region, and the dawn flank are simply corresponded

to the meridians with azimuthal angle φ=120°, φ=180°, and φ=240°.

45

Highlights

• Magnetic field strength increases inward prominently at 11.5 RE down tail.

• Magnetic field has a dawn-dusk asymmetry within 9~20 RE down tail.

• Direct evidence for Local Bz minimum within 10.5<r<12.5 RE are presented.

• Bz in current sheet is stronger under higher solar wind dynamic pressure

• By in current sheet is better correlated with IMF By when IMF is northward.