THIN CURRENT SHEETS IN THE MAGNETOTAIL OBSERVEDBY CLUSTER

R. NAKAMURA1,∗, W. BAUMJOHANN1, A. RUNOV1 and Y. ASANO1,2

1Space Research Institute, Austrian Academy of Sciences, Austria; 2Now at: Tokyo Institute ofTechnology, Japan

(∗Author for correspondence: E-mail: rumi.nakamura@oeaw.ac.at)

(Received 31 October 2005; Accepted in final form 23 December 2005)

Abstract. The dynamics of the current sheet is one of the most essential elements in magnetotail

physics. Particularly, thin current sheets, which we define here as those with a thickness of less than

several ion inertia lengths, are known to play an important role in the energy conversion process in the

magnetotail. With its capability of multi-point observation, Cluster succeeded to obtain the current

density continuously and therefore identify structures of thin current sheets. We discuss characteristics

of the thin current sheets by showing their temporal evolution and the spatial structures based on several

Cluster observations.

Keywords: magnetotail, current sheet, plasma sheet, reconnection, cluster

1. Introduction

The dynamics of the tail current sheet is key to understanding the energy conversionprocesses in the Earth’s magnetosphere. During substorms, a thin current sheet isformed where plasma instabilities can develop leading to reconnection and currentdisruption, depending on how thin a current sheet can evolve for different configu-rations of the tail. The consequences of these instabilities are the formation of thecurrent into the ionosphere and the acceleration of the plasmas, the latter observedas fast plasma flows. These tail current sheet disturbances involve processes withdifferent spatial scales. For example, in spite of the global substorm disturbance, theinitial onset region is considered to be concentrated in a very localized region withinthe thin current sheet. Reconnection involves processes from MHD scales down tothe electron scale. The multi-scale properties and the interplay of the ionosphereand the magnetosphere characterize the magnetotail’s dynamical processes.

Cluster traversed the magnetotail covering regions Earthward of 19 RE duringthe past four summer seasons: July to early November in 2001−2004. The four-spacecraft observations enable us to differentiate spatial from temporal disturbancesand provide a chance to obtain essential parameters, such as current density orspatial scale of the flow and field disturbances unambiguously and continuously.The tetrahedron scale varied between 4000 and 250 km during these years so thatcharacteristics at different scales can be identified. In this paper, we highlight severalCluster studies on thin current sheet observations.

Space Science Reviews (2006) 122: 29–38

DOI: 10.1007/s11214-006-6219-1 C© Springer 2006

30 R. NAKAMURA ET AL.

2. Dynamical Current Sheet

In order to study how a thin current sheet is formed and how it leads to differentplasma instabilities, it is important to monitor the evolution of the current sheetthickness. Even though Cluster monitors only “four points” in space, by fittingthe data to a current sheet model, Cluster can obtain local estimates of the currentsheet scale continuously. In particular, when the magnetic current sheet is one-dimensional with homogeneous plasma flow, the Harris current sheet model canbe applied. This method is most reliable when the spacecraft separation coversa good portion of the current sheet. During summer 2001, the tetrahedron scalewas about 2000 km, which means that the distances among the different spacecraftalong the vertical direction to the current sheet were between a couple of hundredkilometers up to 2000 km. This separation then enabled to cover current sheets withhalf-thickness of about 1 RE down to several hundreds of kilometers.

Nakamura et al. (2002) reported a Cluster observation in the plasma sheet witha significant thinning of the current sheet associated with a high-speed Earthwardflow of 900 km/s. The Harris sheet model was applied to investigate dynamicalchanges of the tail current sheet. In a Harris sheet, the magnetic field is representedby BX (z) = BLtanh(z − z0)/L where BL is the lobe field outside the current sheet,z0 is the location of the neutral sheet and L is the half-thickness of the currentsheet. Simultaneous measurements from three spacecraft allow to estimate the threeparameters and to compare the estimated model BX at the location of the fourthspacecraft with the actual data to check the validity of the estimation. By using thefour-spacecraft magnetic field data and using a Harris-type current sheet model,thickness and strength of the current sheet is obtained as shown in Figure 1a. Itwas estimated that the thickness of the current sheet, L , changes from about 1 RE

before the flow observation, down to 400 km, i.e., close to the ion inertial length.

3. Non-Harris Current Sheet

Although the Harris current sheet model is convenient to obtain the characteristicscale of the current sheet, it is often the case that the tail current sheet structurecannot be expressed with the Harris current sheet model. In fact, in the vicinity ofthe thin Harris-type current sheet shown in Figure 1a, there were also signatures ofenhanced current density off the center of the neutral sheet, which was most likelydue to a bifurcated current sheet. Note that in such a case, i.e., if the current sheetdeviates from the Harris-type current sheet, no reasonable output can be obtainedfrom the model fitting causing lack of points in the two bottom panels in Figure 1a.If we interpret these changes due to observation of spatial profiles of the currentsheet associated with an X-line, the current sheet structure and the possible locationof Cluster can be illustrated as Figure 1b. The changes in the spacecraft locationrelative to the X-line for different sequences of the flow possibly come from the

THIN CURRENT SHEETS 31

102

103

104

L[km]

0

20

40

18:36 18:45 18:48

j [nA/m2]

-20

0

20

BX' [nT]

SC1-3

SC2-4

(1) (2) (3) 18:39

-0.3

0Z' [RE]

VX' [km/s]

Cluster 2001/08/12

0

500

1000

C3

C4C1

C2

thin current

sheet

thin current

sheet

Vx

t1

t2

t3

Z

-Xtail

Earth

ba

Figure 1. (a) X component of the ion flow and the magnetic field, location of the neutral sheet,

half-thickness of the current sheet and the current density, from the top to the bottom. The curves

in the top two panels are data while the symbols in the two bottom panels are the results from the

Harris current sheet model. The vertical lines indicates the start of the three sequences, t1, t2, t3 of

the fast-flow event (adapted from Nakamura et al., 2002). (b) Schematic of the current sheet for the

sequence of the fast flows, t1 (thicker weak current sheet), t2 (thin current sheet), and t3 (bifurcated

current sheet).

temporal/spatial evolution of the reconnection centered tailward of the spacecraft.As will be discussed later, statistical studies (Asano et al., 2005a; Runov et al.,2005b) have demonstrated that a significant portion of the thin current sheets haveprofile of the off-equatorial current sheet.

Figure 2 shows the distribution of the statistical result of the current density (fromAsano et al., 2005) for relatively thin current sheets whose thickness is a few times ofthe ion inertial length, and the peak current density is more than 5 nA/m2. Here, thedawn-to-dusk component of the current density in the neutral sheet region, jy(NS),is plotted against the current density in the off-equatorial region, jy(OE). The solidline shows jy(NS) = jy(OE), and the dashed line shows the theoretical ratio ofjy(OE)/jy(NS) in a Harris-type current sheet jy(z) = jy(NS)/cosh2(z/L), where Lis the current sheet thickness. To determine the Harris current sheet profile, jy(OE)is used at |Bx/BL | = 0.45 and therefore, the ratio will be 1/ cosh2(atanh(0.45)).Although, the main part of the data exists in the region jy(NS) > jy(OE), whichindicates that a center-peaked current sheet is more frequently observed, quite anumber of cases when bifurcated current sheets ( jy(NS) < jy(OE)) were observed(17% occurrence frequency). The occurrence of the bifurcated current sheet had asignificant relationship to fast flows: While the bifurcated current sheet appearedonly in 6% of the samples without any fast flows within the ±15-min interval, the

32 R. NAKAMURA ET AL.

-5

0

5

10

15

20

25

-5 0 5 10 15 20 25

j y(O

ute

r P

S)

[nA

m-2

]

j y (Inner PS) [nA m-2

]

Harris ratio(bx=0.45/bx=0)

Figure 2. Distribution of jy in the neutral sheet and in the off-equatorial plasma sheet. Theoretical

ratio in the Harris-type current sheet is shown by a dashed line (from Asano et al., 2005a).

occurrence frequency associated with fast flows was 48%. The non-Harris currentsheet signature observed in Figure 1 is therefore a quite common case.

Another interesting point in Figure 2 is that jy(OE) frequently becomes smallerthan that expected from the theoretical ratio derived from the Harris model. Thisresult indicates the formation of a very concentrated current in the center, embeddedin a larger current sheet whose current density is small. Either stronger peak near theequator or peak(s) at region away from the equator, the current density distributionin Figure 2 indicates that a simple Harris current sheet is not easily realized inthe tail during thin current sheet intervals. As we will discuss in more detail later,the current sheet profile obtained from rapid current sheet crossing events (Runovet al., 2005b) also supports this conclusion.

4. Current Sheet Flapping

Spacecraft traversing the magnetotail plasma sheet frequently observe rapid large-amplitude variations of the magnetic field. These variations, interpreted as up–downoscillation of the current sheet, are known as current sheet flapping motion. Theresults are presented in Figure 6. The velocity of this flapping motion may exceed100 km/s, although it was predominantly low, between 30 and 70 km/s (Runovet al., 2005a). The flapping may be caused either by the solar wind impact or byinternally generated large-scale waves in the current sheet. The Cluster tetrahedronconfiguration allows determining the normal velocity of the flapping current sheetby multi-point timing analysis. Sergeev et al. (2004) studied characteristics of suchcurrent sheet motion statistically. Figure 3a presents the distributions of Y and ZGSM components of the current sheet normals calculated by a timing analysis for

THIN CURRENT SHEETS 33

0

0

Nz

01

NY0

Nzslow flows

BBFs

8 < Ygsm < 15 -15 < Ygsm < -8

<Y

DAWNDUSK

<

Z

a

b

Figure 3. (a) Distributions of Y- and Z-components of the current sheet normals for subset of dusk-

side and dawn-side crossings during July–November 2001. (b) Interpretation scheme summarizing

the statistical results (from Sergeev et al., 2004).

58 rapid crossings (when the crossing time scale did not exceed 300 s) betweenJuly and November 2001 (from Sergeev et al., 2004) plotted for dawn-side anddusk-side sectors separately.

The results show a strong tendency for the normals to point outward, duskwardon the dusk-side and toward dawn on the dawn-side of the plasma sheet, indicatingwaves propagating outward from the midnight sector. Hence, the source of rapidflapping waves is localized in the central (near-midnight) sector of the magnetotail.A simple interpretation scheme summarizing the results is presented in Figure 3boscillation. These systematic propagation direction suggests that the oscillation isunlikely to be solar wind origin. Furthermore, although the observations indicatesome characteristic of kink-like wave, the dawnward propagation direction indicatesit is difficult to explain with an ion–ion kink mode where the phase velocity is nearthe ion bulk fluid velocity (Sergeev et al., 2004).

5. Structure of the Flapping Current Sheet

Being an interesting phenomenon itself, flapping provides a possibility to probethe internal structure of the current sheet. Here we show an example of currentsheet structure, reconstructed using four-point magnetic field measurements dur-ing an episode of intensive flapping. The method of reconstruction is based onlinear gradient estimation. It is supposed that during flapping the current sheet issimply translated without any change of its structure and the streamline derivative

34 R. NAKAMURA ET AL.

-4 -3 -2 -1 0 1 2 3 4

Z*, 1000 km

2

6

10

14

18

-10

0

10

20

30

J

, n

A/m

m2

B

, nT

l

a

b

c

d

a

bc

d

a

b c d

Figure 4. Left: Sketch of Cluster observations of Hall magnetic fields and current sheet structure

around the reconnection region based on four current sheet crossings indicated with a–d along the

spacecraft trajectory shown with a dashed line (from Runov et al., 2003). Right: Reconstructed current

sheet structures for current sheet crossings a–d. The upper panel shows the cross-tail current profile,

jm whereas the lower panel shows the maximum variance component, Bl , plotted against the estimated

distance from the neutral sheet by integrating the translation velocity along the normal direction of

the current sheet (after Runov et al., 2005a).

dB/dt = ∂B/∂t + (U · ∇)B = 0. Then, integration of the translation velocity pro-jected onto the local current sheet normal Un = ∂ Bx/∂t/∇n Bx during the crossinggives an estimate for the vertical scale Z∗ (see Runov et al., 2005a).

Current sheet profiles obtained using this method for a set of rapid current sheetcrossings during a passage of X-line is shown in Figure 4 (adapted from Runovet al., 2003, 2005a). Current sheet structures reconstructed from the magnetic fieldare shown in the right panels, whereas the obtained current sheet structure relative tothe X-line is illustrated in the left panel. A thin current sheet with a half-thickness ofabout one ion gyroradius was found for the crossing closest to the X-line (crossingb), whereas the outer crossings showed bifurcated current sheet profiles (crossings aand d). Changes in the curvature of the field for the different current sheet crossingsillustrated in the figure were consistent with an X-line motion from Earthward totailward of the spacecraft. Furthermore, a consistent feature of the field disturbanceassociated with Hall-current at both sides of the X-line was identified, confirmingthat the spacecraft traversed the ion diffusion region.

During this thin current sheet interval on October 1, 2001, which was an X-lineevent during storm-time substorms, the O+ pressure and density were observed todominate those of H+ (Kistler et al., 2005). In such current sheets, the O+ ions wereobserved to execute Speiser-type serpentine orbits across the tail and were foundto carry about 5–10% of the cross-tail current (Kistler et al., 2005). This presenceof the O+ could possibly explain the observation of a relatively thick bifurcatedcurrent sheet, about 4000 km, even though it was close to the X-line.

THIN CURRENT SHEETS 35

Current sheet profiles using the rapid crossings observed between July andOctober 2001 were systematically studied by Runov et al. (2005b). It was foundthat the flapping motion of these current sheets was associated with kink-like waveson the sheet surface and quite often (57%) the current sheet was relatively thin, i.e.,had a half-thickness between 1 and 10 ion thermal gyroradii. There were quitea number of cases (45%) where the current density peak was off the equator,which suggest again the importance of non-Harris current distributions: Bifurcatedcurrent sheet or asymmetric current sheet although some asymmetry could be dueto temporal changes during the current sheet crossing.

6. Ion-Scale Thin Current Sheet

The closest separation of Cluster was reached in 2003, with a tetrahedron scale of250 km, enabling to determine the current density using the curlometer techniquewith a spatial resolution below the nominal ion inertia length. Characteristics of thincurrent sheet structures when the maximum current density exceeded 50 nA/m2 (in4 s average) was studied by Nakamura et al. (2004).

Figure 5 shows current sheet profiles presented in Nakamura et al. (2004) duringtwo rapid crossings (<10 s) of the current sheet plotted against the distance from theneutral sheet determined from the translation velocity as discussed in the previoussection. These crossings took place during high-speed flow intervals associated withBZ signatures indicating tailward of an X-line at 1843 UT (right) and Earthward ofan X-line at 1903 UT (left) on August 24, 2003. Thin current sheets tailward andEarthward of X-lines were observed when the full thickness of the current sheet

0

-1000 km 0 1000

0

60

z

-20

-1000 km 0 1000

0

60

nA/m2

z

-20

jy

jx

jy jxjx

jy

jx

Cluster

reconnection

region

Figure 5. Reconstructed current sheet profile for X and Y components of the current density structure

during two rapid crossings around 1843 UT (right) and 1903 UT (left) on August 24, 2003 near the

X-line as illustrated in the schematic below (based on Nakamura et al., 2004).

36 R. NAKAMURA ET AL.

had a scale of the ion inertia length, suggesting Cluster was located within theion diffusion region. In the profile of jy, fine structures indicating multi-peak (threepeak) current sheets were observed. At the tailward side of the X-line, the jx currentwas directed out from the X-line at the outer edge of the thin dawn-to-dusk currentsheet, while the jx current was directed into the X-line near the equator. The formercase possibly corresponds to the closure current of the Hall-current, whereas thelatter could be part of the Hall-current in the ion diffusion region.

The field-aligned current system closing the Hall-current near the reconnectionregion have been also inferred using electron moments. Cluster also succeeded tomeasure the field-aligned electron currents at the Earthward side of the reconnectionregion (Alexeev et al., 2005). In addition to confirming the inward (into the X-line)and outward (out from the X-line) field-aligned current at the PSBL and plasmasheet side, respectively, as predicted from the closure current of the Hall-current,their observations showed a layer of stronger inward current region on the interfacebetween the inward and outward currents. These different layers of field-alignedcurrents could be due to two nested diffusion regions possibly related to the effectof the heavy ions (Alexeev et al., 2005). For the same event, even finer structureswith a temporal scale less than 1 s were observed to be embedded in the inflowingfield-aligned beams (Asano et al., 2005b) based on the high-temporal resolutionmeasurement of the 500 eV field-aligned electrons. Properties of the multi-layer ofthin (electron) current sheets are therefore obtained both from the magnetic fielddisturbances and from the electron data.

Figure 6 shows another event with series of current sheet crossings presented byNakamura et al. (2004) when the entire current sheet had a comparable thicknessto that shown in Figure 5. The event occurred during a substorm expansion phase,but in a stagnant plasma sheet without any high-speed flows. In contrast to theprevious example, the interval was during cold and dense plasma sheet, whenthe plasma sheet density exceeds 2/cm−3. The ion inertia length was thereforeless than about 160 km. Interestingly, there are again features of a three-peak andbifurcated current sheet as well as off-equatorial centered current sheet. Althoughthese structures took place in several hundreds-km scale, the mechanism responsibleto produce this structure are larger scale ones exceeding the ion scale such as thosefor the rapid current sheet crossing cases identified during 2001 by Runov et al.(2005b). In fact during the time interval shown in Figure 6, the entire current sheetwas about 1000–1500 km (6–10 ion scales) thick with some persistent structuresuch as a local minimum around 200 km north existing at least for about 3 min(about 120 ion gyro times). This relatively “long time” and “large-scale” profile ismixed also with very sharp peaks, profiles below the ion scale, as clearly shown,for example, in the current density profile of crossing b. The example shown inFigure 6 therefore suggests that multi-scale processes seem to be involved in theseobserved thin tail current sheets. Note that the conclusions on the thin currentsheets are yet based on preliminary studies and need confirmation and furtherstudies.

THIN CURRENT SHEETS 37

-1000 0 1000

0

30

60

-1000 0 1000-1000 0 1000 -1000 0 1000 -1000 0 1000

Bx´

Bz´

jx´jy´jz´divB

By´

jy

z´ km z´z´ kmz´z´

Bx´

Bz´

jx´jy´jz´

By´

0

60

120

divB

-40

0

40

-40

0

40

-40

0

40

-60

0

60

-40

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40

-40

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-40

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60

20:09 20:13 20:14 UT

0

20:13

nA

/m2

nT

nT

nT

nA

/m2

020

nA

/m2

nT

nT

nT

nA

/m2

a b c

a b c d e

d e 20031001 Cluster FGM

Figure 6. Top panels: Three components of the magnetic field and current density and divergence of Bduring multiple current sheet crossings (indicated by a–e) between 2009 and 2014 UT, October 1, 2003.

Tilted coordinates are used to make the X and Z component parallel (and maximum variance direction)

and normal to the current sheet plane, respectively using the current sheet crossing parameters indicated

by dashed line. Bottom panels: Reconstructed current sheet profiles of the tail current during the

crossings a–e. Current sheet orientation are obtained separately for each of the crossings (based on

Nakamura et al., 2004).

7. Conclusions

The four Cluster spacecraft enabled to obtain temporal and spatial characteristicsof the tail current sheet with thickness down to ion inertia length. Depending on thesize of the Cluster tetrahedron and motion of the current sheet, different analysistechniques can be applied using four-point observations to monitor temporal changeof the current sheet thickness, characteristic motion of the current sheet, and spatialstructure of the current sheet.

Although its mechanism is still not well-explained, up-and-down motion of thecurrent sheet helped to reveal the detailed structure of the current sheet. Both therapid current sheet crossings diagnostics discussed in Sections 5 and 6 as well aspure spatial analysis discussed in Section 2 and 3 came to the conclusion that thecurrent sheet often deviates from the Harris-type current sheet profile. These includebifurcated current sheet, off-equatorially centered current sheet, three-peaks currentsheets or embedded spikes.

Some of these current sheet features are most likely related to Hall-physics inthe vicinity of the reconnection regions. On the other hand, cases were also foundwhen both the structures below the ion-scale and a larger relatively stable currentsheet profile were standing out within a current sheet. These examples suggest thatmulti-scale processes may be involved in the thin tail current sheets, which requiresfurther detailed studies to confirm their temporal and spatial characteristics.

38 R. NAKAMURA ET AL.

Acknowledgements

The authors thank B. Klecker, V. A. Sergeev, A. Balogh, H. Reme, L. M. Kistler,C. Mouikis, G. Paschmann, C. J. Owen, A. Fazerkerley, T. Nagai, M. Fujimoto, I.Shinohara, M. Volwerk, Z. Voros, T. L. Zhang, K. Torkar, T. Takada for helpfuldiscussions; P. Escoubet, H. Laakso and all the Cluster mission and instrumentteams for the successful mission; and E. Georgescu, G. Laky, H. U. Eichelberger,G. Leistner, CDAWeb, CSDS, GCDC, ACDC for great help in data processing. Thework at IWF was partly supported by INTAS 03-51-3738 Grant.

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