Radial distribution of magnetic field in earth magnetotail current sheet

Z.J. Rong a,b,n, W.X. Wan a,b, C. Shen c, A.A. Petrukovich d, W. Baumjohann e, M.W. Dunlop f,Y.C. Zhang c

a Key Laboratory of Earth and Planetary Physics, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, Chinab Beijing National Observatory of Space Environment, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, Chinac State Key Laboratory of Space Weather, Center for Space Science and Applied Research, Chinese Academy of Sciences, Beijing 100190, Chinad Space Research Institute, 84/32 Profsoyuznaya St., Moscow 117997, Russiae Space Research Institute, Austrian Academy of Sciences, 8042 Graz, Austriaf Rutherford Appleton Laboratory, Chilton, DIDCOT, Oxfordshire OX11 0QX, UK

a r t i c l e i n f o

Article history:Received 12 April 2014Received in revised form11 July 2014Accepted 31 July 2014Available online 11 August 2014

Keywords:MagnetotailMagnetic structureCurrent sheet

a b s t r a c t

Knowing the magnetic field distribution in the magnetotail current sheet (CS) is essential for exploringmagnetotail dynamics. In this study, using a joint dataset of Cluster/TC-1, the radial profile of themagnetic field in the magnetotail CS with radial distances covering 8oro20RE under differentgeomagnetic activity states (i.e., AEr100 nT for quiet intervals while AE4100 nT for active times)and solar wind parameters are statistically surveyed. Our new findings demonstrate that, independent ofthe activity state, the field strength and Bz component (GSM coordinates) start the monotonic increaseprominently as r decreases down to �11.5RE, which means the dipole field starts to make a significantcontribution from there. At least in the surveyed radial range, the Bz component is found to be weaker inthe midnight and dusk sectors than that in the dawn sector, displaying a dawn–dusk asymmetry. Theoccurrence rate of negative Bz in active times also exhibits a similar asymmetric distribution, whichimplies active dynamics may occur more frequently at midnight and dusk flank. In comparison with thatin quiet intervals, several features can be seen in active times: (1) a local Bz minimum between10.5oro12.5RE is found in the dusk region, (2) the Bz component around the midnight region isgenerally stronger and experiences larger fluctuations, and (3) a sharp positive/negative-excursion of theBy component occurs at the dawn/dusk flank regions inside ro10RE. The response to solar windparameters revealed that the Bz component is generally stronger under higher dynamic pressure(Pdy45 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, andthe correlation quality is found to be better with higher penetration coefficient (the ratio of CS By to IMFBy) when IMF Bz is positive. The implications of the present results are discussed.

& 2014 Elsevier Ltd. All rights reserved.

1. Introduction

The Earth magnetotail current sheet (CS), which is located in theequatorial region and called neutral sheet sometimes, is a transitionlayer separating the anti-parallel lobe magnetic field lines (e.g., Ness,1965, 1969; Behannon, 1970; Speiser, 1973). As a basic physicalquantity, the magnetic field in the CS (together with the electricfield) can control the dynamics of charged particles, affect the spaceplasma distribution and evolution, so that the unambiguous

knowledge of magnetic field distribution and its dynamic variationis 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 satellitemissions (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 tailCS with radial distance ro20RE might be a key region where themagnetic 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 finalsource for auroral substorm onset is probably located in thenear-earth current sheet with radial distance ro15RE (Lui, 1996),where the fast earthwards plasma flow is found to brake

Contents lists available at ScienceDirect

journal homepage: www.elsevier.com/locate/pss

Planetary and Space Science

http://dx.doi.org/10.1016/j.pss.2014.07.0140032-0633/& 2014 Elsevier Ltd. All rights reserved.

n Corresponding author at: Key Laboratory of Earth and Planetary Physics,Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing100029, China.

E-mail address: rongzhaojin@mail.iggcas.ac.cn (Z.J. Rong).

Planetary and Space Science 103 (2014) 273–285

substantially (e.g., Shiokawa et al.,1997; Birn et al., 1999; Panov,et al. 2010) and ballooning mode instability is favorably to betriggered due to the transition of magnetic field from dipole-like totail-like (Hameiri et al., 1991; Liu, 1997).

It is well known that the magnetic field structure in near-earthmagnetotail (ro20RE) can be simply seen as the superposition ofthe dipole geomagnetic field and the field generated by the tailand magnetopause current systems. The magnetic field strength isassumed to increase significantly as radial distance decreasing. Thetrue and detailed radial distribution of magnetic field in near-earthmagnetotail, however, is not known so clearly, though someempirical or semi-empirical magnetosphere models (e.g.,Tsyganenko, 2002; Tsyganenko and Sitnov, 2007) are available.

The radial distribution of magnetic field in CS containing theregion ro20RE has been surveyed extensively by numerousspacecraft, e.g., ISEE 1 from 1978 to 1979 at X¼�10��22RE(GSM coordinates, Huang and Frank, 1994), ISEE 1 from 1978–1987at r¼3�23RE (Nakai et al., 1999), Geotail at X¼�9��30RE(Wang et al., 2004; Petrukovich, 2009), AMPTE/CCE at ro8.8RE(Fairfield et al.,1987), and the merged data of ISEE1, AMPTE/CCE,IMP 8 at X¼�5��60RE (Rostoker and Skone, 1993). However,either the field magnitude or the By, Bz component was addressedsolely in these studies, and no one had given the full view ofmagnetic field radial profile under different geomagnetic activitiesand external solar wind conditions. For instance, only the Bzcomponent is addressed by Huang and Frank (1994). The magneticfield strength and Bz component are studied by Nakai et al. (1999),but it is concentrated in |Y|o5RE, while the response to the storm/substorm activities, as well as to the dynamic pressure of solarwind are only exhibited in the form of regression analysis. The Bycomponent and the correlation with the interplanetary magneticfield (IMF) By component are investigated by Petrukovich (2009).The Bx and Bz component are referred by Wang et al. (2004) (seetheir Fig. 9a and b) in the region |Y|o5RE for the selected events ofquiet periods (333 events) and growth-phase periods (130 events).Meanwhile, theoretical analysis and event model demonstrate thata Bz minimum should be located in the inner current sheet (e.g.,Hau et al., 1989; Hau, 1991; Erickson, 1992; Sergeev et al., 1994,1996) due to the earthward plasma convection, and it may play animportant role in triggering the balloon instabilities and plasmoidformation (e.g. Zhu and Raeder, 2014). However, the true existenceof the local minimum of Bz is disputable. The characteristics of Bzminimum are inferred in some studies (e.g., Saito et al., 2010), butnot in the other studies (Yang et al., 2010; Artemyev et al., 2013;Petrukovich et al., 2013). The more detailed study about the radialprofile of Bz is needed to clarify this issue. Therefore, combiningwith geomagnetic index and solar wind parameters, this studyaims to fully re-examine the radial profile of the magnetic field inthe tail current sheet spanning the entire tail width, as well as theresponses to geomagnetic activity states and solar wind para-meters. To achieve this task, the magnetic field data of Cluster andTC-1 are used.

The Cluster mission (Escoubet et al., 2001) was launched in thesummer of 2000 into a 4�19.6RE polar, inertial orbit. One maingoal of the four-satellite mission is to investigate the dynamics ofthe near-Earth magnetotail. As shown in Fig. 1, in the earlier stageof Cluster orbit, e.g., 2001–2005, from the end of June to the earlyNovember annually, the Cluster tetrahedron traverses magnetotailaround apogee 15�19RE from the north-hemisphere to the south-hemisphere in the night side of magnetosphere, so that themagnetotail 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 magneticfield have been surveyed (e.g., Petrukovich et al., 2005; Rong et al.,2010; Rong et al., 2011). For the later orbit phase (since 2006), dueto the evolution of orbit precession, the orbit inclination decreases

gradually with apogee shifted southward, so that the near-earth CS(with ro15RE) can be also surveyed.

To coordinate with the measurements of Cluster, the TC-1, as onespacecraft (S/C) of Double Star mission, was launched into an equator-ial orbit of 1.1�13.4RE in December 2003 (Liu et al., 2005; Shen andLiu, 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 than13.4RE from the end of June to the early November annually.

The extension of Cluster measurements to the later stage withthe coordinated measurements of TC-1 provide a good opportu-nity to survey the radial magnetic field distribution in tail CSwithin ro20RE. Since four satellites of Cluster mission are closelyspaced, the four satellites mostly record the similar magnetic fieldmeasurements, hence, only the magnetic field data of singlesatellite, Cluster-3 (C3, Samba) is used here. We should remindreaders that there are two reasons for us to use the joint dataset ofTC-1/C3 though satellites such as Geotail (Nishida, 1994) orTHEMIS (Angelopoulos, 2009) with smaller orbit inclination canprovide more dataset for the survey. Firstly, the joint dataset ofTC-1/C3, with the same FGM on both satellites, is the continuum ofour previous studies (e.g., Rong et al., 2010, 2011). Secondly, TC-1has a similar orbit as THEMIS-D and E. As a result, to study theradial magnetic field distribution and its response to geomagneticactivity states and solar wind parameters within ro20RE, thespin-resolution (4-s) FGM data of C3 during 2001–2009 and TC-1during 2004 are used in this research, combining with the 1-minOMNI data set (it contains the shifted solar wind conditions at thenose of bow shock and the AE index, see http://omniweb.gsfc.nasa.gov/ (King and Papitashvili, 2005)).

Geocentric solar magnetospheric (GSM) coordinates are usedthroughout the study without special statement. In addition, thespherical coordinates (r, θ, φ) for the Earth-centered positionvector are defined in the frame of GSM. r is the radial distance. Thepolar angle θ (01rθr1801) is the angle between the þZ-axis andthe vector. The azimuth angle φ (01rφr3601) of vector isdefined as the angle anticlockwise deviated from the þX-axis inthe XY-plane when seen towards �Z-axis. For example, the dawndirection or �Y-direction is (θ¼901, φ¼2701), while the duskdirection or þY-direction is (θ¼901, φ¼901).

2. Statistical study

2.1. Selection and preparation of data

To determine the tail CS crossing unambiguously, the criteria asadopted in our previous studies (Rong et al., 2010, 2011), i.e.,Bx(ti) �Bx(tiþ1)o0 (where, ti, tiþ1 are the two successive measure-ments), combined with the lower strength of the magnetic field(o100 nT) and the nightside location of S/C (901rφr2701,ro20 RE), are used in the first instance. Second, visual inspectionof the low plasma temperature (o10�106 K), high density(41 cm3), and the tail-ward plasma velocity (Vxo�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 (Fujmoto et al., 1998). Then,applying the linear interpolation to the data set, the interpolatedparameters when Bx¼0, i.e., CS center can be grouped correspond-ingly as the basis data set for this study.

One should note that closer to earth, typically within ro8RE (thetypical hinging distance of tail CS is about 8�10RE (e.g., Tsyganenkoet al., 1998; Tsyganenko and Fairfield, 2004)), the magnetosphere ismainly ordered by dipole tilt angle, thus the Bx¼0 in GSM may notrepresent the true CS center, and the Bx component might be betterpresented in the Solar Magnetic coordinates according to dipole tilt

Z.J. Rong et al. / Planetary and Space Science 103 (2014) 273–285274

angle (e.g., Fairfield et al., 1987). Therefore only the region8oro20RE is concerned here in GSM coordinates.

Based on the above criteria, in total 26483 data points (18962data points for C3 and 7521 data points for TC-1) for the CS centerare obtained. Fig. 2 shows the detected CS location in the XY plane(Fig. 2a) and YZ plane (Fig. 2b). Obviously, the joint magnetic fielddataset can well cover the radial distances between 8RE and 20RE.To simplify the surveyed region, as shown in Fig. 2a, the tail CS aredivided roughly into three regions based on the azimuthal loca-tion, that is, dawn flank: 2101rφo2701, midnight region:1501oφo2101, and the Dusk flank: 901rφr1501. The nominalmagnetopause is marked as a dashed line with empirical standoffdistance r0¼11RE and tail flaring level α¼0.58; from the model ofShue et al. (1997). Note that, due to a significant data gap andfewer CS crossings around midnight, CS samples are significantlymissed at midnight (Y�0).

The dynamic variation of the magnetic field in the tail CS isstrongly associated with geomagnetic activity. The CS is found tobe thinning (indicated by minor Bz component) in growth phase ofa substorm, and thickens (enhanced Bz component) in the explo-sive and recovery phase (e.g., Baumjohann et al., 1992; Sanny et al.,1994; Petrukovich et al., 2007). However, it is not so easy todiagnose the substorm phases exactly for each crossing event inthe whole dataset. Thus, for simplification, the states of geomag-netic activity are roughly divided into quite times and active timesmerely based on the AE index, though the diagnosis of ‘geomag-netic substorm/storm phases’ might be more physically appro-priate than the AE index. Similarly to that defined by Slavin et al.(1987), we defined the quiet times as the moments whenAEr100 nT, while the active times corresponds to AE4100 nT.

Based on this definition, there are 8558 crossing points duringquiet times and 17,925 crossing points for the active times

−20−15−10−50510−15

−10

−5

0

5

10

15

Xgse(RE)

Z gse(R

E)

−15−10−5051015−15

−10

−5

0

5

10

15

Ygse(RE)

Z gse(R

E)

200120022003200420052006200720082009TC−1

Fig. 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 (337 orbit), 2003 (490 orbit), 2004 (644orbit), 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 magnetotailinvestigation. The nominal magnetopause is marked as the dashed line.

−20−15−10−505101520−20

−15

−10

−5

0

5

10

15

20

Ygsm(RE)

X gsm(R

E)

Dusk

Midnight

Dawn

−20 −15 −10 −5 0 5 10 15 20−20

−15

−10

−5

0

5

10

15

20

Ygsm(RE)

Z gsm(R

E)

TC−1C3

Fig. 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. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Z.J. Rong et al. / Planetary and Space Science 103 (2014) 273–285 275

obtained. Fig. 3 shows the radial profile of crossing numbers andthe normalized occurrence rate for both activity states (it is theratio of the number in the bin to the amount in that state). Thevalue is averaged in a bin of 1RE (the width of bin is assumed to be1RE in the following radial plots). In these panels, the green lines,red lines and blue lines are plotted for the dusk flank region,midnight region and the dawn region respectively. From Fig. 3, thecrossing number during active times is basically larger than thatduring quiet times, which, being consistent with the results ofDavey et al. (2012), may imply the CS would flap more severely inactive times than that during quiet times. It is interesting to notethat, the crossing number is enhanced greatly at r�14RE and�19RE. The double-peaks probably arise from the apogee locationfor Cluster(r�19RE) and TC-1(r�13.5RE). The spacecraft moveslowly near apogee and would have more chance to cross the CS.Thus, one cannot simply infer the CS flaps locally as a doubleradial-peak.

Since the coupling of solar wind/magnetosphere is stronglycontrolled by IMF and the dynamic pressure of solar wind, Pdy (e.g.,Vasyliunas et al., 1982), only the parameters IMF By, IMF Bz and Pdyfrom OMNI dataset are used to study the possible dependence onthe solar wind parameters. Fig. 4 shows the averaged IMF By, Bzcomponent and Pdy against the radial distance for the active andquiet time period. The corresponding error bars are plottedaccordingly. The length of error bar in each panel, estimated asthe 2� 1:96ðσ= ffiffiffi

np Þ(ðσ= ffiffiffi

np Þ is the standard error of mean), repre-

sents the confidence interval with level 95%. The same meaning isassumed in the following error bar plots.

In quiet times, the averaged IMF Bz is basically positive(þ1�2 nT), and the dynamic pressure is lower (Pdyo2 nPa).In contrast, in the active times, the averaged IMF Bz is basicallynegative (�1��2 nT) and the dynamic pressure is higher(Pdy42 nPa). Thus, it seems the active times tend to appear inthe period of negative IMF Bz as well as the higher dynamicpressure. The averaged IMF By is randomly within 75 nT in thewhole radial range regardless of the activity states. The depen-dence of CS magnetic field on the solar wind parameters will beaddressed more in Section 3.

With the prepared dataset above, the radial distributions ofmagnetic field at magnetotail CS center with radial distance8REoro20RE will be studied exclusively in the followingsubsections.

2.2. Profile of magnetic field strength and the Bz component

In this subsection, the radial profile of magnetic field and itscomponents under different activity states are studied. As shown inFig. 5, the averaged radial profile of the magnetic field strength(indicated by Bmin, Bmin¼(By2þBz

2)1/2), the Bz component, and the Bycomponent are shown respectively from top to bottom in the leftcolumn for the quiet times and in the right column for the activetimes. Particularly, to show our results against the dipole field, thegeomagnetic dipole field in the magnetic equatorial plane, i.e.Bmin¼Bz (dipole axis is assumed towards þZ axis), is plotted as blackdashed lines for both activity states, wherein the adopted dipolemoment is ME�7.8�1022 A m2 (for the year 2000).

0

750

1500

2250

3000

Num

ber

Total

0

750

1500

2250

3000

Num

ber

Quiet TimeDuskMidnight

Dawn

0

0.025

0.05

0.075

0.1

Occ

urre

nce

rate

0

750

1500

2250

3000

Num

ber

Radial distance (RE)

Active Time

8 9 10 11 12 13 14 15 16 17 18 19 200

0.025

0.05

0.075

0.1

Occ

urre

nce

rate

Fig. 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. (For interpretation of the references to color in this figure, the reader is referred to the web version of thisarticle.)

Z.J. Rong et al. / Planetary and Space Science 103 (2014) 273–285276

2.2.1. OverviewOne prominent feature can be found from Fig. 5, that is, the

magnetic field strength Bmin or the Bz component increasesprominently as radial distance decreasing down to r�11.5REirrespective 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 �20RE to �11RE, but sharplyincreases up to 40 nT as r decreases down to �8RE. It also has thesimilar trend for the active times. By comparison, such kind

distribution features cannot be seen from the By distribution asshown in Fig. 5c and f. The detailed By distribution will beaddressed in Section 2.4.

Another prominent feature is that the radial profile of Bmin or Bzshows an evident dawn–dusk asymmetry. For the range of14oro20RE in the quiet times, the Bz at both flank regions arelarger than that in the midnight region, and the strength of Bz atthe dawn flank region is larger than that at the dusk flank region.While for the same range in the active times, Bz around the

−10

−5

0

5

10

IMF

Bz(n

T)

Quiet time

−10

−5

0

5

10

IMF

By(n

T)

Dusk flankMidnight regionDawn flank

8 10 12 14 16 18 200

2

4

6

8

Pdy

(nP

a)

Radial distance (RE)

−10

−5

0

5

10

IMF

Bz(n

T)

Acitve time

−10

−5

0

5

IMF

By(n

T)

8 10 12 14 16 18 200

2

4

6

8

Pdy

(nP

a)Radial distance (RE)

Fig. 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.

0

20

40

60

80

Bm

in(n

T)

Quiet time

0

20

40

60

80

Bz(n

T)

8 9 10 11 12 13 14 15 16 17 18 19 20−40

−20

0

20

40

By(n

T)

Radial distance (RE)

20

40

60

80

Bm

in(n

T)

Active time

20

40

60

80

Bz(n

T)

Dusk flankMidnight regionDawn flankDipole field

8 9 10 11 12 13 14 15 16 17 18 19 20−40

−20

0

20

40

By(

nT)

Radial distance (RE)

Fig. 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 activitystates.

Z.J. Rong et al. / Planetary and Space Science 103 (2014) 273–285 277

midnight region is comparable to that at the dusk flank region butstill evidently weaker than that at the dawn flank region. As itdecreases down to the range 9oro14RE, in the quiet times, Bz atthe midnight region becomes comparable to that at the dusk flankregion but still evidently weaker than that at the dawn flankregion. But for the same range in the active times, the Bz becomescomparable in the whole dawn–dusk regions, particularly forro12RE. Hence, the radial profile of Bmin or Bz displays a dawn–dusk asymmetry which is more evident in the quiet times with alengthwise scale 11RE at least.

2.2.2. Comparison with dipole fieldFrom Fig. 5, for the midnight region during quiet times, the Bmin

and Bz are generally weaker than that of the dipole field within theregion 8oro20RE, whereas the “weaker region” reduces to8oro16RE during active times. At both flank regions and parti-cularly for the dawn flank, regardless of the states, Bz is weakerthan the dipole field within 8oro14RE, and it is a bit strongerthan the nominal dipole field outside r414RE. These results areconsistent with that of the T07 model (Tsyganenko and Sitnov,2007) where the existence of a “weaker region” is physicallyrelated to the diamagnetic effect as induced by the tail currentsystems. Because the duskward partial ring current and cross-tailcurrent would induce a southward field in the inner current sheet,leading to the depressed geomagnetic field there.

The comparison with dipole field demonstrates that the actualprofile 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 versus active timesTo exhibit the difference in both states, the upper panels of

Fig. 6 show the radial distribution of Bz component at differentregions in the quiet times (black lines) against that in the activetimes (red lines). The lower panels show the standard deviation ofBz, σz, at the corresponding location, which can indicate thefluctuation amplitude of Bz.

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

component in the midnight region and dawn flank region

(r412RE) is generally stronger during active times than that inquiet times, while it is not so obvious at the dusk flank region(Fig. 6a). Since the magnetotail CS beyond the hinging distance canbe on average seen as a plane parallel to the GSM XY plane, exceptvery close to the flanks (e.g., Tsyganenko and Fairfield, 2004; Ronget al., 2011), Bz basically acts as the normal component to the CSplane, and the magnitude of Bz can approximately indicate thecurvature radius of magnetic field lines or the thickness of CS if CScan be seen as 1-D structure (Büchner and Zelenyi, 1989; Shenet al., 2003; Shen et al., 2007). Consequently, the enhanced Bzcomponent in active times may imply that the CS is generallythicker than that in quiet times.

It is interesting to note in Figs. 5e and 6a that in active timesthere is an evident depression of Bz in 10.5oro12.5RE in the duskregion. The local Bz minimum observed here seemed consistentlywith the earlier theoretic prediction (e.g., Hau et al., 1989; Hau1991; Erickson, 1992). Meanwhile, the fluctuation represented byσz , shown in the lower panels of Fig. 6, clearly indicate that the Bzcomponent in the active times fluctuates more sevrely than that inquiet times

2.3. Negative Bz component

The Bz component in tail CS is normally positive. However, dueto some dynamic processes occurred in the tail CS, e.g. magneticreconnection, current disruption, magnetic turbulence, flux ropes,transient field-aligned current etc., sometimes, the negative Bz(Bzo0) can appear (Sharma et al. 2008). Therefore, the appear-ance of negative Bz can be seen as an indicator of activities thoughthe occurrence probability is very low, and the survey of negativeBz distribution could reveal the distribution of dynamic activitiesto some extent. Totally, the crossing number with negative Bz inour dataset is 1130, accordingly, the total occurrence probability ofnegative Bz is �0.043 and ignorable. Though the total occurrenceprobability is ignorable, the probability distribution, as shown inFig. 7, displays some interesting properties.

From Fig. 7a for the quiet times, the appearance of negativeBz is basically concentrated in the midnight region, and theappearance probability is decreased as radial distance decreased.

0

5

10

15

20

25

30

35

40

Bz(n

T)

Dusk flank

8 9 10 11 12 13 14 15 16 17 18 19 200

5

10

15

20

σ z(nT)

r (RE)

Midnight region

8 9 10 11 12 13 14 15 16 17 18 19 20

r (RE)

Dawn flank

8 9 10 11 12 13 14 15 16 17 18 19 20

r (RE)

Quite timeActive time

Fig. 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). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Z.J. Rong et al. / Planetary and Space Science 103 (2014) 273–285278

By comparison, as shown in Fig. 7b, the frequency of negative Bz ishigher in active time than that in quiet time, particularly for themidnight and dusk regions. Moreover, the negative Bz duringactive time can occur closer to the Earth. These results may implythat, the magnetic activities, such as magnetic reconnection, areinclined to occur around the midnight and dusk flank region,manifesting an dawn–dusk asymmetry. In contrast to the quiettime intervals, during active times, the activity appears to occurmore frequently and more closer to earth.

2.4. Profile of By component

It is clear from Fig. 5c and f that, regardless of activity state, theBy component around the midnight region is generally ignorable,but becomes negative as approaching both flanks. Such featureshave been noticed previously (Petrukovich, 2011; Rong et al.,2011), and it can be explained by the seasonal modulation of thedipole tilt angle on the warping of current sheet (Petrukovich,2011). The typical CS model (Tsyganenko and Fairfield, 2004)shows that when the dipole tilt angle is positive (dipole axis issunward), the CS at both flanks would warp down toward the-Z direction,vice versa. Accordingly the magnetic field in the CSwould be bent along the warped CS normal, so that a net Bycomponent is notably induced at both flanks. Petrukovich (2009,2011) argued that the By in CS is positively correlated with dipoletilt angle at dusk and midnight region, a weaker negative correla-tion exists with tilt angle in the dawn region within ro15RE, andthe 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, Fig. 8 plots the averaged By component and the dipoletilt angle distribution in the dawn–dusk or azimuthal directionwithin different radial scopes. The azimuthal variations of dipoletilt angle in all panels of Fig. 8 are similar. Obviously, the positive/negative correlation with the dipole tilt angle at dusk/dawn regioncan be clearly found in all panels except Fig. 8d (it will bediscussed later). This means that, within 8oro20RE, the appear-ance of By component at both flank regions is easily to bemodulated by the dipole tilt angle in terms of the argument ofPetrukovich (2011). It is interesting to note from Fig. 8 exceptFig. 8d (see also Fig. 5c and f) that negative By besomes stronger atboth flanks closer to earth, which may imply the By component atboth flanks is more apt to be modulated by the dipole tilt angle asbeing closer to earth, as also noticed by Petrukovich (2011).

It is noteworthy that in Fig. 8d or in Fig. 5f for the activetimes, in the inner-earth region, i.e. 8oro10RE, a sudden

positive-excursion/negative-excursion of By component at thedawn/dusk flank regions occurs and, hence, it cannot be the resultof dipole tilt effect. Since the averaged IMF By is less than 5 nT(Fig. 4b and e), such kind of enhancement of By component alsocannot be attributed to the IMF By penetration. The enhancedfield-aligned currents (FACs) system seems a plausible reason toexplain it. The FACs generally consists of region-1 (R1) and region-2 (R2) FACs (Mcpherron, 1995). The R1 FACs is closed with the lowlatitude boundary layers while R2 FACs is closed with the partialring current. The FACs at both hemispheres would converge into ordiverge from the equatorial plane. If the subsystems of FACs atboth hemispheres are identical, the induced By component in CSshould be canceled and vanished. However, if the FACs is domi-nant at one hemisphere, a net By component will be induced in theCS. Therefore, as being sketched in Fig. 9, the oberved By-excursionat both flanks in active times may favor the FACs enhancementwhich are northern-hemisphere dominant. It is interesting to notethat, Shi et al. (2010) statistically found the field-aligned currentsin magnetotail has the similar hemispheric-asymmetry, that is, theintensity of FACs in northern hemisphere is more intense than thatin the southern hemisphere.

Actually, we had checked the events of By-excursion at bothflanks. It is found, though the amount of events is limited (68 datapoints), all these events are only appeared in active times, and arerelated to the geomagnetic storm/substorm processes. Previousobservations also show the enhancement of FACs in low altitudeduring the period of storm/substorm (e.g., Wang et al., 2006,2010). Certainly, to confirm our interpretation, more cases ofBy-excursion are needed in the future.

3. Responses to solar wind parameters

In this section, wewill study the response of magnetic field to solarwind parameters, especially the solar wind dynamic pressure and theIMF By component. We should remind readers that since the IMF Bzcomponent can modulate the geomagnetic activity (e.g., Nishida,1975), that is, when IMF Bz is positive the geomagnetic activities isusually in quiet time, vice versa (see Fig. 4a and d), the response to IMFBz have been discussed actually to some extent in Section 2.2.3.

3.1. Effect of solar wind dynamic pressure

Many studies demonstrated that the enhanced dynamic pressureof solar wind, denoted by Pdy, can compress the magnetosphere,resulting in various global and dynamic changes in the magneto-sphere. The response of the magnetotail to the sudden variation ofsolar wind pressure has been studied extensively, and most of themfocused on the lobe magnetic field (e.g., Kawano et al., 1992; Collieret al., 1998; Huttunen et al., 2005, and references therein). There arefew studies concentrating on the response of magnetic field in tailCS, particularly for the long-term averaged period. Since the polarityof IMF Bz, as a key factor, controls the solar wind energy couplingwith the magnetosphere, here, we would check the discrepantresponse of magnetic field in tail CS to the Pdy under the positive/negative IMF Bz. For simplicity, the Pdy45 nPa is defined as higherpressure, while it is lower pressure when Pdyo5 nPa.

The upper panels of Fig. 10 show the response of the Bzcomponent in different regions to the lower Pdy and higher Pdyunder the negative IMF Bz. Similarly, the response under positiveIMF Bz are shown in the lower panels of Fig. 10. As seen in Fig. 10,regardless of the sign of IMF Bz, the Bz component in tail CS isgenerally enhanced during the higher Pdy period than that duringthe lower Pdy period, which is more evident at the dawn flankregion. The result of an enhanced Bz in tail CS during the higher

0

0.1

0.2

0.3P

roba

bilit

y of

−B

z Quiet time

DuskMidnightDawn

8 9 10 11 12 13 14 15 16 17 18 19 200

0.1

0.2

0.3

Radial distance (RE)

Pro

babi

lity

of −

Bz Active time

Fig. 7. The radial distribution of negative Bz occurrence probability at differentregions in quiet times (a) and active times (b).

Z.J. Rong et al. / Planetary and Space Science 103 (2014) 273–285 279

period is consistent with the previous case studies of the suddenPdy jump (e.g., Keika et al., 2008; Miyashita et al., 2010).

Miyashita et al. (2010) proposed possible reasons to explain theresponse of plasma sheet Bz component to the sudden enhancementof solar wind dynamic pressure. The enhancement of dynamicpressure may cause the compression of magnetotail in all directions.If the compression in dawn–dusk direction dominant, it would leadto the increase of Bz by squeezing the magnetic field lines.In contrast, if the north–south direction dominant, a decrease of Bzwould appear due to the more tail-like magnetic field line config-uration. However, the explanation is only built on several cases, itstill lacks the support of statistical study. Although the long-termaveraged variation of Pdy addressed here is temporally different fromthe 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, webelieve, is just like a sudden jump of Pdy following the same physicallogic. Therefore, here, in terms of the explanations of Miyashita et al.,our statistical results may favor the compression of higher Pdy isdominant in the dawn–dusk direction.

In contrast to the Bz enhancement, no evident response of By tothe higher dynamic pressure is found (not shown here).

3.2. Correlationship between CS By and IMF By

Numerous statistical surveys have demonstrated that theupstream IMF By component is the primary driver of the Bycomponent in magnetotail CS (Petrukovich, 2011, and the refer-ences therein), though sometimes the sign of CS By oppositing tothat of IMF By is noticed (Petrukovich, 2009; Rong et al., 2012). It isfound the IMF By penetration coefficient in the CS increasestowards 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 earth-ward enhancement of the penetration coefficient within�30oXo�10RE with the Geotail dataset. However, the higherpenetration coefficient does not necessarily imply the correlationcoefficient is better, and it is still unclear whether there is anydiscrepancy about the penetration and correlation coefficientunder different IMF Bz sign. With the joint dataset, we would liketo re-examine the radial dependance of the correlation betweenCS By and IMF By.

Since the By component is apt to be controlled by the dipole tiltangle at both flank regions (Petrukovich, 2011) and sensitive to theenhanced current system (including the FAC-2) in the innermagnetotail, the correlation analysis is focused around the

−40

−20

0

20

40

By(n

T)

Quiet time

8<r<10 RE

−40

−20

0

20

40

−40

−20

0

20

40

By(n

T)

−40

−20

0

20

40

90 110 130 150 170 190 210 230 250 270−40

−20

0

20

40

By(n

T)

Azimuthal angle (degree)

−40

−20

0

20

40

−40

−20

0

20

40

By(n

T)

Active time

−40

−20

0

20

40

Geo

dipo

le ti

lt an

gle

(deg

ree)

−40

−20

0

20

40

By(n

T)

−40

−20

0

20

40

Geo

dipo

le ti

lt an

gle

(deg

ree)

90 110 130 150 170 190 210 230 250 270−40

−20

0

20

40

By(n

T)

Azimuthal angle (degree)

−40

−20

0

20

40

Geo

dipo

le ti

lt an

gle

(deg

ree)

10<r<15 RE

15<r<20 RE

Fig. 8. The azimuthal distribution of By component( red lines) and dipole tilt angle (blue dotes) within different radial scopes. (For interpretation of the references to color inthis figure legend, the reader is referred to the web version of this article.)

Fig. 9. The sketched diagram to illustrate the induced By component by theenhanced FACs system at the nothern hemisophere during the active time.

Z.J. Rong et al. / Planetary and Space Science 103 (2014) 273–285280

0

10

20

30

40

50B

z(nT)

Dusk flank Midnight region

Lower pressureHigher pressure

8 9 10 11 12 13 14 15 16 17 18 19 20

r(RE)

Dawn flank

8 9 10 11 12 13 14 15 16 17 18 19 20

r(RE)

−IMF Bz

8 9 10 11 12 13 14 15 16 17 18 19 200

10

20

30

40

50

Bz(n

T)

r(RE)

+IMF Bz

Fig. 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 panelsare plotted for the conditions of negative IMF Bz while the lower panels is for the positive IMF Bz. (For interpretation of the references to color in this figure legend, the readeris referred to the web version of this article.)

−50−40−30−20−10 0 10 20 30 40 50−50

−40

−30

−20

−10

0

10

20

30

40

50

By (n

T)

Whole data

c.c.=0.61

By=0.51*IMFBy+0.3

15<r<20 RE

−50−40−30−20−10 0 10 20 30 40 50−50

−40

−30

−20

−10

0

10

20

30

40

50

IMF By (nT)

By (n

T)

c.c.=0.49

By=0.67*IMFBy−1.22

10<r<15 RE

−30 −20 −10 0 10 20 30−30

−20

−10

0

10

20

30−IMF Bz

c.c.=0.39

By=0.40*IMFBy+0.42

−30 −20 −10 0 10 20 30−30

−20

−10

0

10

20

30

IMF By (nT)

By (n

T)

c.c.=0.41

By=0.63*IMFBy−0.76

−30 −20 −10 0 10 20 30−30

−20

−10

0

10

20

30+IMF Bz

c.c.=0.50

By=0.53*IMFBy+0.34

−30 −20 −10 0 10 20 30−30

−20

−10

0

10

20

30

IMF By (nT)

By (n

T)

c.c.=0.63

By=0.85*IMFBy−1.57

Fig. 11. The scattering plots of IMF By versus CS By component around the midnight region. The upper panels are for the outer CS region (15rro20RE), while lower panelsare for the inner CS region (10rrr15RE). The line in each panel represents the least-square line.

Z.J. Rong et al. / Planetary and Space Science 103 (2014) 273–285 281

midnight region (1501oφo2101) within the radial scale 10rro20RE, according to the sign of IMF Bz.

In Fig. 11, for the outer region (15rro20RE, upper panels) andinner region (10rro15RE, lower panels), the scattering plots ofIMF By and CS By for the whole dataset (left column), the negativeIMF Bz (middle column), and the positive IMF Bz (right column) areshown respectively. In each panel, the derived correlation coeffi-cient (c.c.) and the penetration coefficient of IMF By (the ratio of CSBy to IMF By) are given. It is clear for the whole dataset from Fig. 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 enhancedpenetration coefficient are comparable to that reported byPetrukovich (2009). However, from Fig. 11a and b, the sampledIMF By range are quite different between the inner CS and outer CSevents. For Fig. 11a, the range of IMF By is��20 to �40 nT,whereas most samples of IMF By are dropped into |IMF By|o10 nT.The difference of statistical correlation (correlation coefficient andthe penetration coefficient) might be induced follow a logical trainof thought due to the different sample range of IMF By. To furthercheck the discrepancy of “IMF By penetration” under differentpolarity of IMF Bz for the same IMF By range, the samples of IMF Byat both regions are confined to |IMF By|o10 nT. The correlationanalysis under the interval of positive and negative IMF Bz, areplotted in the middle and right column of Fig. 11 respective.

It is clear from Fig. 11, at the both regions for |IMF By|o10 nT,the CS By is worse correlated with IMF By (c.c. �0.4), and thepenetration coefficient is lower (it is �0.4/�0.63 for the outer/inner region) when IMF Bz is negative. Whereas, it has bettercorrelation (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 thepenetration coefficient of IMF By.

It is believed that, in contrast to the þ IMF Bz, during the intervalof –IMF Bz, the magnetotail plasma convection is enhanced, themagnetotail flux ropes and magnetic reconnection are appearedmore frequently. The strength of By component in magnetotail wouldincrease significantly due to the compression by the enhancedearthward convection (Hau and Erickson, 1995). The core field ofmagnetotail flux rope (By is the proxy) is usually much stronger thanthe 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 quadrupole polarity is induced (e.g., Runov etal., 2003; Borg et al., 2005), while some plasma instabilities, e.g.Weibel instability (e.g., Baumjohann et al., 2010), may occur simul-taneously to generate the By component. Therefore, a scenario couldbe depicted: during the interval of –IMF Bz, some internal processes,i.e. enhanced convection, flux ropes, magnetic reconnection, andplasma instabilities etc. which could enhance or even generate the Bywith sign opposite to IMF By, would occur more frequently, so that itmay lower the correlation coefficient and penetration of IMF By.However, our analysis presented here is preliminary, and it requiresfurther investigation.

4. Discussion

There are several points which deserve to be discussed morethoroughly.

(1) Our results revealed that the magnetic field strength Bmin andthe Bz component at the magnetotail current sheet center ofentire tail width enhance prominently as radial distancedecreasing down to r�11.5RE independent of the activity state.It implies that the earthward plasma flow embedding in CSwould start significantly diversion by the enhanced magneticfield 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 mergingthe observation of Bz component by many earlier satellites, e.g.ISEE1, AMPTE/CCE, IMP 8, Rostoker and Skone (1993) have derivedan empirical formula for the radial dependence of the Bzcomponent, which is expressed as Bz ¼ 7:8e�0:4xþ 125302x�4.By test (not shown here), we find this formula is more suitable todescribe the quiet time Bz profile for the midnight region.We find that, around the midnight region, the Bz in active times isevidently larger than that in quiet times beyond r�8RE. Incontrast, within ro8.8RE, Fairfield et al. (1987) found the mag-netic field strength in CS decreased in active times (indicated bythe increased Kp index). Therefore, combining with the results ofFairfield et al., one can reaches a conclusion that Bz in active timesis larger than that in quiet times beyond r48RE, but smallerwithin ro8RE. Accordingly, one can reasonably infer that anenhanced duskward current is developed around r�8–9RE inactive times.

(2) Our results demonstrate that the radial profile of Bmin or Bzdisplays a clear dawn–dusk asymmetry, i.e. the magnitude ofBmin or Bz at the dawn flank region is larger than that in thedusk flank and midnight region, which is more evident duringquiet times within 9oro20RE. This may imply the CS thick-ness in the dawn flank region is usually larger than that in themidnight and dusk flank region. In addition, in Section 2.3, thedistribution of negative Bz during active times consistentlyshows a similar asymmetry. Actually, the asymmetry has beenalso noticed in previous studies (Fairfield, 1986; Rong et al.,2010, 2011). With the ISEE1's measurement within�20rXr�6RE, |Y|r7RE, the derived current density in CSare found stronger within �3oYo6RE displaying evidentdawn–dusk asymmetry. It is also noticed that the fast flow inthe near-earth magnetotail based on THEMIS-D observationare strongly localized in the local time sector 21:00–01:00(McPherron et al., 2011). The tail dawn–dusk asymmetrymight be causally associated with the dawn–dusk asymmetricdistribution of auroral substorm onset (Frey et al., 2004; seethe discussion of Rong et al., 2011). The reasons for theasymmetry are unclear, a summary of the possible reasons isgiven by Vlasova et al. (2002). Recent simulation demonstratethat the asymmetry is probably regulated by the spatialvariation in ionospheric conductance (Zhang et al., 2012).

(3) As we mentioned above, in the dusk region, a local minimum inBz is presented within 10.5oro12.5RE in active time (seeFigs. 5e and 6a). Previous theoretical studies (e.g., Hau et al.,1989; Erickson, 1992) predicted that the 2-D force-balancedmagnetic field models with constant entropy would exhibit alocal Bz minimum in the inner plasma sheet by the steadyadiabatic earthward convection (Hau et al., 1989; Hau, 1991;Erickson, 1992). The local Bz minimum is noticed at r�12RE in aSMC event model (Sergeev et al., 1994, 1996), and it is supportedby indirect observational evidence from the pre-midnight sectorof the near-Earth plasma sheet (Saito et al., 2010). Considering allthese facts, it seems the spatial features of local Bz minimumexhibited in our survey satisfy that one as being predicted in theconvection theory. We had checked the plasma data, IMFconditions, the geomagnetic field data at ground stations andthe quick look of AE plots associated with the local Bz minimumin dusk region. It is found most of the data points are actuallyrelated with the southern IMF and higher long duration (largerthan 4 h) AE index but no substorm signatures, which satisfiesthe typical characteristics of SMC. Hence, our observation resultssupport that the local minimum Bz in the inner plasma sheet isbrought by the earthward convection. We should remember thatthe Bz minimum does not contradict the enhanced Bz as we

Z.J. Rong et al. / Planetary and Space Science 103 (2014) 273–285282

found in Section 2.2.3. The Bz minimum is located within10.5oro12.5RE in the dusk region, while the enhanced Bzduring active times appears mainly around the midnight region.

(4) The radial profile revealed here cannot be simply reproduced bythe empirical models. Besides of the comparison with dipole fieldin Fig. 5, the radial profile of Bz from T01 model (Tsyganenko,2002) is shown in Fig. 12 for the further comparison. The duskflank, midnight region, and the dawn flank are simply corre-sponded to the meridians with azimuthal angleφ¼1201,φ¼1801,and φ¼2401 respectively. For the quiet time, Dst, IMF By, and IMFBz are set to zero; while for the active time, Dst¼�30 nT, IMFBy¼0 nT, IMF Bz¼�6 nT. The dynamic pressure for both states areset to Pdy¼2 nPa. Moreover, the solar wind speed �400 km/s,dipole tilt angle �01 are input for both activity states. Severalinconsistent aspects can be noticed from T01 model: (1) T01 doesnot show the evident dawn–dusk asymmetry (the minor Bzdifference between dawn and dusk in the inner magnetosphereas shown in Fig. 12 results from the dawn–dusk asymmetricpartial ring current); (2) The Bz in the midnight region is largerthan that at both flanks for r414.5RE in quiet times and r412REin active times (actually, T01 model only used data sunward ofX¼–15RE); while, our survey indicate Bz in the midnight is usuallyweaker than that at both flanks; (3) In active time, there is a widerdepression of Bz within 10oro18RE in the midnight region,while, our survey indicates that the depression of Bz is onlypresented within 10.5oro12.5RE for the dusk flank region.Hence, one should be careful when applying this model.

5. Summary

This study has statistically surveyed the radial profile ofmagnetic field in the magnetotail current sheet within the region8oro20RE of the entire tail width based on the joint magneticfield dataset of Cluster and TC-1. Many related issues are addressedand compared with previous studies. The new contributions fromour study can be summarized as follows:

1. For the radial profile: it is found, basically independent ofgeomagnetic activity, the magnetic field strength Bmin and Bzcomponent are enhanced prominently as radial distance decreas-ing down to r�11.5RE. This feature cannot seen

simply from the models and no one had presented it explicitly asfar as we know. The strength of Bmin or Bz are weaker in themidnight and dusk flank than that in dawn flank displaying adawn–dusk asymmetry. Although the asymmetry has qbeennoticed in previous studies, the radial scale of asymmetry is onlypresented in our study, that is, the asymmetry is evidentat least within 9oro20RE in the quiet times, but 14oro20REin the active times. The occurrence probability of negativeBz in active times also shows the similar asymmetric distribution.

2. Features in active times: previous studies noticed that themagnitude of magntic field or the Bz component is strongerduring substorms (Huang and Frank,1994; Nakai et al.,1997,1999).However, from our study, this point is only valid in the midnightand dawn flank, but not for the dusk flank. Additionally, a local Bzminimum within 10.5oro12.5RE in the dusk region in activetimes is found statistically for the first time, which provideevidence for previous theoretical predictions. Our new findingsalso demonstrated that, the sharp positive-excursion/negative-excursion of By component at the dawn/dusk flank regions occursinside ro10RE in active times, which may imply that theenhancement of FACs that are northern-hemisphere dominantare developed in active times.

3. Responses to solar wind parameters: previous case studies (Keikaet al., 2008; Miyashita et al., 2010) of Pdy jump found the strongerBz component in plasma sheet may appear. Here, through astatistical survey for the first time, we explicitly confirm that theBz component is indeed generally stronger during the period ofhigher solar wind dynamic pressure. Although the CS By generallycorrelated with IMF By is well known, it has not been checkedwhether there is any difference for different polarities of IMF Bz.Here, we find the CS By is better correlated with IMF By, and thepenetration coefficient (the ratio of CS By to IMF By) is higherwhen IMF Bz is positive. In addition, we have confirmed theearthward enhancement of IMF By penetration coefficient, whichwas 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

8 10 12 14 16 18 200

5

10

15

20

25

30

35

40

45

50Quiet time

r (RE)

Bz (n

T)

Dst=0,Pdy=2 nPa,IMF By=0,IMF Bz=0

8 10 12 14 16 18 200

5

10

15

20

25

30

35

40

45

50Active time

r (RE)

Bz (n

T)

Dst=−30 nT,Pdy=2 nPa,IMF By=0,IMF Bz=−6 nT

Dusk flank(φ=120o)Midnight(φ=180o)Dawn flank(φ=240o)

Fig. 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 themeridians with azimuthal angle φ¼1201, φ¼1801, and φ¼2401.

Z.J. Rong et al. / Planetary and Space Science 103 (2014) 273–285 283

interface (http://omniweb.gsfc.nasa.gov) for providing the ClusterFGM data, TC-1 FGM data, and OMNI data, respectively. This workis supported by the Chinese Academy of Sciences (KZZD-EW-01-2),National Basic Research Program of China (973 Program) Grants2011CB811404 and 2011CB811405, the National Natural ScienceFoundation of China Grants 41104114, 41374180, 41321003,40974101, 41131066 and 41211120182, China Postdoctoral ScienceFoundation Funded Project 2012T50132, and the Research Fund forthe State Key Laboratory of Lithospheric Evolution. The work byM.W. Dunlop is partly supported by CAS visiting professorship forsenior international scientists Grant 2012T1G0018. The authorsthank the helpful discussions with H. Zhang, J.-H. Shue, P. Zhu, andH.V. Malova. Z.J. Rong would like to acknowledge the hospitality ofIRF, Kiruna, Sweden.

References

Angelopoulos, V., 2009. The THEMIS Mission. In: Burch, J.L., Angelopoulos, V.(Eds.), The THEMIS Mission. Springer, New York, pp. 5–34. http://dx.doi.org/10.1007/978-0-387-89820-9_2.

Artemyev, A.V., et al., 2013. Profiles of electron temperature and Bz along Earth'smagnetotail. 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 inflightperformance and initial results. Ann. Geophys. 19, 1207–1218.

Baumjohann, W., Paschmann, G., Nagai, T., 1992. Thinning and expansion of thesubstorm plasma sheet. J. Geophys. Res. 97, 17173–17175. http://dx.doi.org/10.1029/92JA01519.

Baumjohann, W., 2002. Modes of convection in the magnetotail. Phys. Plasmas 9,3665–3667. http://dx.doi.org/10.1063/1.1499116.

Baumjohann, W., Nakamura, R., Treumann, R.A., 2010. Magnetic guide fieldgeneration in collisionless current sheets. Ann. Geophys. 28, 789–793. http://dx.doi.org/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, 19895–19903. http://dx.doi.org/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. http://dx.doi.org/10.1029/2005GL023794.

Büchner, J., Zelenyi, L.M., 1989. Regular and chaotic charged particle motion inmagnetotaillike field reversals: 1. Basic theory of trapped motion. J. Geophys.Res. 94 (A9), 11821–11842. http://dx.doi.org/10.1029/JA094iA09p11821.

Carr, C., et al., 2005. The Double Star magnetic field investigation: instrumentdesign, 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 ofinstrument performance and initial results. Adv. Space Res. 38, 1828–1833.

Collier, M.R., et al., 1998. Multispacecraft observations of sudden impulses in themagnetotail caused by solar wind pressure discontinuities: wind and IMP 8.J. Geophys. Res. 103 (A8), 17293–17305.

Davey, E.A., et al., 2012. Storm and substorm effects on magnetotail current sheetmotion. J. Geophys. Res. 117, A02202. http://dx.doi.org/10.1029/2011JA017112.

Erickson, G.M., 1992. A quasi‐static magnetospheric convection model in twodimensions. J. Geophys. Res. 97, 6505.

Escoubet, C.P., Fehringer, M., Goldstein, M., 2001. The Cluster mission. Ann. Geophys19, 1197–1200.

Fairfield, D., 1979. On the average configuraton of the geomagnetic tail. J. Geophys.Res. 84 (A5), 1950–1958.

Fairfield, D.H., 1986. The magnetic field of the equatorial magnetotail from 10 to40 RE. J. Geophys. Res. 91 (A4), 4238–4244. http://dx.doi.org/10.1029/JA091iA04p04238.

Fairfield, D.H., et al., 1987. The magnetic field of the equatorial magnetotail:AMPTE/CCE observations at ro8.8 RE. J. Geophys. Res. 92 (A7), 7432–7442.http://dx.doi.org/10.1029/JA092iA07p07432.

Fairfield, D.H., 1992. On the structure of the distant magnetotail: ISEE 3. J. Geophys.Res. 97 (A2), 1403–1410. http://dx.doi.org/10.1029/91JA02388.

Frey, H.U., Mende, S.B., Angelopoulos, V., Donovan, E.F., 2004. Substorm onsetobservations by IMAGE-FUV. J. Geophys. Res. 109, A10304. http://dx.doi.org/10.1029/2004JA010607.

Fujmoto, M., Terasawa, T., Mukai, T., 1998. The lower‐latitude boundary layer in thetail‐flanks. In: Nishida, A., Baker, D.N., Cowley, S.W.H. (Eds.), New Perspectiveson the Earth's Magnetotail. Geophysical Monograph Series, vol. 105. AGU,Washington, D. C, pp. 33–44.

Hameiri, E., Laurence, P., Mond, M., 1991. The ballooning instability in spaceplasmas. J. Geophys. Res. 96 (A2), 1513–1526. http://dx.doi.org/10.1029/90JA02100.

Hau, L.‐N., et al., 1989. Steady state magnetic field configurations for the Earth'smagnetotail. J. Geophys. Res. 94 (A2), 1303–1316. http://dx.doi.org/10.1029/JA094iA02p01303.

Hau, L.‐N., 1991. Effects of steady state adiabatic convection on the configuration ofthe near‐Earth plasma sheet: 2. J. Geophys. Res. 96 (A4), 5591–5596. http://dx.doi.org/10.1029/90JA02619.

Hau, L.-N., Erickson, G.M., 1995. Penetration of the interplanetary magnetic field Byinto Earth's plasma sheet. J. Geophys. Res. 100 (A11), 21,745–21,751. http://dx.doi.org/10.1029/95JA01935.

Huang, C.Y., Frank, L.A., 1994. Magnitude of BZ in the neutral sheet of themagnetotail. J. Geophys. Res. 99 (A1), 73–82. http://dx.doi.org/10.1029/93JA01752.

Huttunen, K.E.J., et al., 2005. Cluster observations of sudden impulses in themagnetotail 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 magnetotaillobe. J. Geophys. Res. 97 (A11), 17177–17182.

Kaymaz, Z., et al., 1994a. Magnetotail views at 33RE: IMP 8 magnetometerobservations. J. Geophys. Res. 99 (A5), 8705–8730. http://dx.doi.org/10.1029/93JA03564.

Kaymaz, Z., et al., 1994b. Interplanetary magnetic field control of magnetotailmagnetic field geometry: IMP 8 observations. J. Geophys. Res. 99 (A6),11113–11126. http://dx.doi.org/10.1029/94JA00300.

Keika, K., et al., 2008. Response of the inner magnetosphere and the plasma sheetto a sudden impulse. J. Geophys. Res. 113, A07S35. http://dx.doi.org/10.1029/2007JA012763.

King, J.H., Papitashvili, N.E., 2005. Solar wind spatial scales in and comparisons ofhourly wind and ACE plasma and magnetic field data. J. Geophys. Res. 110,A02104. http://dx.doi.org/10.1029/2004JA010649.

Liu, W.W., 1997. Physics of the explosive growth phase: ballooning instabilityrevisited. J. Geophys. Res. 102 (A3), 4927–4931. http://dx.doi.org/10.1029/96JA03561.

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. http://dx.

doi.org/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 theplasma sheet. J. Geophys. Res. 116, A00I33. http://dx.doi.org/10.1029/2010JA015923.

Miyashita, Y., et al., 2010. Plasma sheet changes caused by sudden enhancements ofthe solar wind pressure. J. Geophys. Res. 115, A05214. http://dx.doi.org/10.1029/2009JA014617.

Nagai, T., et al., 2005. Solar wind control of the radial distance of the magneticreconnection site in the magnetotail. J. Geophys. Res. 110, A09208. http://dx.doi.org/10.1029/2005JA011207.

Nakai, H., Kamide, Y., Russell, C.T., 1997. Statistical nature of the magnetotail currentin the near-Earth region. J. Geophys. Res. 102 (A5), 9573–9586. http://dx.doi.org/10.1029/97JA00136.

Nakai, H., Kamide, Y., Russell, C.T., 1999. Dependence of the near-Earth magnetotailmagnetic field on storm and substorm activities. J. Geophys. Res. 104 (A10),22701–22711. http://dx.doi.org/10.1029/1999JA900273.

Ness, N.F., 1965. The Earth's magnetotail. J. Geophys. Res. 70, 2989–3005. http://dx.doi.org/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.Panov, E.V., et al., 2010. Multiple overshoot and rebound of a bursty bulk flow.

Geophys. Res. Lett. 37, L08103. http://dx.doi.org/10.1029/2009GL041971.Petrukovich, A.A., et al., 2005. Cluster vision of the magnetotail current sheet on a

macroscale. J. Geophys. Res. 110, A06204. http://dx.doi.org/10.1029/2004JA010825.Petrukovich, A.A., et al., 2007. Thinning and stretching of the plasma sheet.

J. Geophys. Res. 112, A10213. http://dx.doi.org/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.

http://dx.doi.org/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. http://dx.doi.org/10.1002/jgra.50550.

Rong, Z.J., et al., 2010. Statistical survey on the magnetic field in magnetotail currentsheets: cluster observations. Chin. Sci. Bull. 55, 2542–2547. http://dx.doi.org/10.1007/s11434-010-3096-5.

Rong, Z.J., et al., 2011. Statistical survey on the magnetic structure in magnetotailcurrent sheets. J. Geophys. Res. 116, A09218. http://dx.doi.org/10.1029/2011JA016489.

Rong, Z.J., et al., 2012. Profile of strong magnetic field By component in magnetotailcurrent sheets. J. Geophys. Res. 117, A06216. http://dx.doi.org/10.1029/2011JA017402.

Rostoker, G., Skone, S., 1993. Magnetic flux mapping considerations in the auroraloval and the Earth's magnetotail. J. Geophys. Res. 98 (A2), 1377–1384. http://dx.doi.org/10.1029/92JA01838.

Runov, A., et al., 2003. Current sheet structure near magnetic X-line observed byCluster. Geophys. Res. Lett. 30 (11), 1579. http://dx.doi.org/10.1029/2002GL016730.

Z.J. Rong et al. / Planetary and Space Science 103 (2014) 273–285284

Saito, M.H., et al., 2010. Spatial profile of magnetic field in the near‐Earth plasmasheet prior to depolarization by THEMIS: feature of minimum B. Geophys. Res.Lett. 37, L08106. http://dx.doi.org/10.1029/2010GL042813.

Sanny, J., McPherron, R.L., Russell, C.T., Baker, D.N., Pulkkinen, T.I., Nishida, A., 1994.Growth-phase thinning of the near-Earth current sheet during the CDAW6 substorm. J. Geophys. Res. 99, 5805.

Sergeev, V.A., 1987. Penetration of the By component of the interplanetary magneticfield (IMF) into the tail of the magnetosphere. Geomagn. Aeron. 27, 612–615.

Sergeev, V., et al., 1994. Hybrid state of the tail magnetic configuration duringsteady convection events. J. Geophys. Res. 99 (A12), 23571–23582. http://dx.doi.org/10.1029/94JA01980.

Sergeev, V.A., Pellinen, R.J., Pulkkinen, T.I., 1996. Steady magnetospheric convec-tion: a review of recent results. Space Sci. Rev. 75, 551–604. http://dx.doi.org/10.1007/BF00833344.

Sharma, A.S., et al., 2008. Transient and localized processes in the magnetotail: areview. Ann. Geophys. 26, 955–1006.

Shen, C., et al., 2003. Analyses on the geometrical structure of magnetic field in thecurrent sheet based on cluster measurements. J. Geophys. Res. 108 (A5), 1168.http://dx.doi.org/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. http://dx.doi.org/10.1029/2005JA011584.

Shi, J.K., et al., 2010. South–north asymmetry of field-aligned currents in themagnetotail observed by cluster. J. Geophys. Res. 115, A07228. http://dx.doi.org/10.1029/2009JA014446.

Shiokawa, K., Baumjohann, W., Haerendel, G., 1997. Braking of high-speed flows inthe 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 themagnetopause size and shape. J. Geophys. Res. 102 (A5), 9497–9511. http://dx.doi.org/10.1029/97JA00196.

Slavin, J.A., et al., 1987. Magnetic configuration of the distant plasma sheet: ISEE-3observations. In: Lui, A.T.Y. (Ed.), Magnetotail Physics. JHU Press, Baltimore,pp. 59–64.

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. http://dx.doi.org/10.1029/97JA03621.

Tsyganenko, N.A., 2002. A model of the near magnetosphere with a dawn–duskasymmetry, 2, parameterization and fitting to observations. J. Geophys. Res. 107(A8), http://dx.doi.org/10.1029/2001JA000220.

Tsyganenko, N.A., Fairfield, D.H., 2004. Global shape of the magnetotail currentsheet as derived from geotail and polar data. J. Geophys. Res. 109, A03218. http://dx.doi.org/10.1029/2003JA010062.

Tsyganenko, N.A., Sitnov, M.I., 2007. Magnetospheric configurations from ahigh-resolution data-based magnetic field model. J. Geophys. Res. 112, A06225.http://dx.doi.org/10.1029/2007JA012260.

Vasyliunas, V.M., et al., 1982. Scaling relations governing magnetospheric energytransfer. Planet. Space Sci. 30 (4), 359–365.

Vlasova, N.A., Sosnovets, E.N., Chuchkov, E.A., 2002. A study of long-term strongdawn–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-phaseplasma sheet: the geotail observations. J. Geophys. Res. 109, A12201. http://dx.doi.org/10.1029/2004JA010590.

Wang, H., et al., 2006. Field-aligned currents observed by CHAMP during theintense 2003 geomagnetic storm events. Ann. Geophys. 24, 311–324.

Wang, H., et al., 2010. Substorm time ionospheric field-aligned currents asobserved by CHAMP. Chin. J. Geophys. 53, 339–346. http://dx.doi.org/10.1002/cjg2.1502.

Wing, S., et al., 1995. A large statistical study of the entry of interplanetarymagnetic 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 steadymagnetospheric convection: results of RCM-E simulations. J. Geophys. Res. 115,A00I11. http://dx.doi.org/10.1029/2010JA015731.

Zhang, B., et al., 2012. Magnetotail origins of auroral Alfvénic power. J. Geophys.Res. 117, A09205. http://dx.doi.org/10.1029/2012JA017680.

Zhang, L.Q., et al., 2009. Convective bursty flows in the near-Earth magnetotailinside 13 RE. J. Geophys. Res. 114, A02202. http://dx.doi.org/10.1029/2008JA013125.

Zhang, Y.C., et al., 2008. Relationship between the magnetic flux ropes inmagnetotail and interplanetary magnetic field. Chin. J. Space Sci. 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. http://dx.doi.org/10.1002/2013JA019511.

Z.J. Rong et al. / Planetary and Space Science 103 (2014) 273–285 285