Reconstruction of a Flux Transfer Event Based on Observations from Five THEMIS Satellites

Home , Flux transfer event

Reconstruction of a Flux Transfer Event Based on

Observations From Five THEMIS Satellites

A. T. Y. Lui

JHU/APL, Laurel, MD 20723-6099, USA

D. G. Sibeck

NASA/GSFC, Greenbelt, MD, USA

T. Phan

Space Sciences Laboratory, University of California, Berkeley, CA, USA

10 V. Angelopoulos

IGPP/UCLA, Los Angeles, CA, USA

J. P. McFadden

Space Sciences Laboratory, University of California, Berkeley, CA, USA

K.-H. Glassmeier

TUBS, Braunschweig, Germany

Abstract. We investigate a flux transfer event (FTE) observed by

THEMIS near the duskside magnetopause using the reconstruction

technique based on solving the Grad-Shafranov equation as developed

20 previously by Sonnerup et al. [2006]. THEMIS D detected the FTE with

the largest core magnetic field. THEMIS B and C observed deep troughs

in the magnetic field associated with the FTE. THEMIS A and E sensed

only slightly altered magnetic field from their surroundings. Two-

dimensional reconstruction maps of magnetic field and plasma pressure

are generated by combining observations from all five THEMIS satellites.

These reconstructed maps show distinct differences between a magnetic

island and an FTE in terms of vector potential and the derived plasma

parameters. Furthermore, the resulting maps show also asymmetry in these

parameters between the magnetosheath and magnetospheric sides of the

30 FTE. This asymmetry contributes partially to the different characteristics

of the FTE seen by the five THEMIS satellites in addition to the different

impact parameters of these satellites with respect to the FTE center.

1. Introduction

The most recent magnetospheric mission from NASA is THEMIS, an acronym for

Time History of Events and Macroscopic Interactions during Substorms [Angelopoulos et

al., 2008; Sibeck and Angelopoulos, 2008]. The primary objective of THEMIS is to

resolve the controversy on the substorm initiation location in the magnetotail by placing

40 five satellites with identical instruments aligned along the tail axis to determine

incontrovertibly the propagation direction of substorm disturbances in the magnetotail.

Due to a launch delay of the mission, the planned separation of the five satellites along

the tail axis was postponed for nearly one year. A decision was made to utilize this coast

phase to have the five satellites placed in the ‘beads on a string’ configuration. Thus, a

unique opportunity arises to probe magnetospheric structures in the near-Earth space with

nearby multipoint measurements.

In this coast phase, Sibeck et al. [2008] have identified a flux transfer event (FTE)

near the dusk magnetopause on 2007 May 20. During this interval, one THEMIS satellite

(THEMIS D) detected the FTE with a strong core magnetic field, while two another

50 THEMIS satellites (THEMIS B and C) detected a crater FTE in which the strong core

magnetic field is bounded by deep troughs in magnetic field strength. FTEs with this

signature are called crater FTEs. The two remaining THEMIS satellites (THEMIS A and

E) detected only slight magnetic field strength increase. Assisted by the MHD simulation

result of the event, Sibeck et al. [2008] have proposed that these different signatures of

FTE arise from different impact parameters with respect to the center of the FTE by the 4

different satellites. THEMIS D had a very low impact parameter while THEMIS B and C

had moderate impact parameters. THEMIS A and E had large impact parameters.

Lui et al. [2008] have reconstructed the plasma parameters around the FTE event

detected by THEMIS D using the Grad-Shafranov (GS) reconstruction technique

60 developed previously [Sonnerup and Guo, 1996; Hau and Sonnerup, 1999; Hu and

Sonnerup, 2001, 2003; Teh and Hau, 2004, 2007; Hasegawa et al., 2004, 2005, 2006,

2007; Sonnerup et al., 2004, 2006]. They have benchmarked their reconstruction results

with a theoretical model as well as with actual IRM magnetopause crossing data

previously investigated by Hau and Sonnerup [1999]. From this procedure, Lui et al.

[2008] have extended the observed magnetic field and plasma pressure of the FTE from

THEMIS D to a two-dimensional plane. In addition, current densities associated with the

FTE have been deduced in this two-dimensional plane. The result indicates that the axial

current density had a peak value > 40 nA/m2 with significant current densities (up to ~25

nA/m2) on the plane perpendicular to its axis.

70 In this paper, we extend the previous GS reconstruction based on observations from a

single THEMIS satellite to encompass observations from all five THEMIS satellites. The

GS reconstruction technique has been extended to analyze observations from four Cluster

measurements of magnetic islands near the magnetopause by Hasegawa et al. [2004,

2005]. Here, we extend the GS reconstruction technique even more, to encompass

observations from five satellites. Naturally, the complexity in producing composite

reconstruction maps increases with increasing number of satellites involved and thus is

not a trivial extension. The resulting reconstruction maps provide insights on the

observed FTE and the origin of the troughs in magnetic field seen in crater FTEs, which 5

have been reported and theorized previously by several researchers [Saunders et al.,

80 1984; Rijnbeek et al., 1987; Farrugia et al., 1987; Ding et al., 1991; Sibeck et al., 2008].

2. THEMIS observations

2.1 THEMIS D observations

The flux transfer event (FTE) observations that provide the basis for the GS

reconstruction reported here are exemplified by THEMIS D and C. Figure 1 shows the

plasma and magnetic field measurements from THEMIS D that indicate the encounter of

an FTE with an intense core magnetic field. The GSE coordinate system is used for these

parameters. During this interval, the satellite crossed the magnetopause from the

magnetosheath at the start of the interval to the magnetosphere at the end. The

90 magnetosheath region is indicated by the high plasma density, a relatively steady tailward

plasma flow of ~200 km/s and fluctuating southward magnetic field. The magnetospheric

region is indicated by the low plasma density, high and steady northward magnetic field,

and a nearly stationary state of the plasma. At ~2202 UT within this interval, the plasma

and magnetic field characteristics were quite distinct from both the magnetosheath and

the magnetosphere regions. A prominent feature with a strong Bz magnetic field

component accompanied by a much reduced tailward plasma flow was detected for

~1min. This structure is marked in Figure 1 by the region between the two vertical

dashed lines. A dipolar signature can be seen in both the Bx and By components associated

with this structure. These characteristics are commonly recognized as that of a FTE

100 [Russell and Elphic, 1978].

2.2 THEMIS C observations

THEMIS C was close to THEMIS D and detected the characteristics of a crater FTE

as shown in Figure 2. At about the same time when THEMIS D detected the high core

magnetic field of an FTE, THEMIS C detected a distinct feature with similar magnetic

field and plasma flow characteristics. The structure is marked in Figure 2 by the region

between the two vertical dashed lines. The only outstanding difference in characteristics

from that seen by THEMIS D in Figure 1 is the presence of two deep minima in magnetic

field strength bounding the core magnetic field. It can also be noted that the core

110 magnetic field is still high but is reduced substantially from that seen by THEMIS D.

This field strength difference indicates that THEMIS C did not encounter the FTE as

close to its center as THEMIS D. This inference is consistent with the presence of the

deep minima [Sibeck et al., 2008].

2.3 Observations from all THEMIS satellites

Figure 3 provides a brief overview of observations from all five THEMIS satellites

during this interval. It may be noted that observations from THEMIS B and C are very

similar at ~2202 UT except that the magnetic field minima seen at THEMIS B were very

pronounced without a clear indication of a peak in the magnetic field strength within it.

120 Although THEMIS A and E were both immersed well within the magnetosheath, there

was an enhancement of the magnetic field at ~2202 UT for both satellites due to the

passing of the FTE structure near the magnetopause. The locations of the five satellites in

the GSE coordinate system are also given in Figure 3.

3. GS reconstruction of THEMIS observations

3.1 Underlying principle for reconstruction

As discussed in Sonnerup et al. [2006] and Hasegawa et al. [2004, 2005],

reconstruction of plasma configuration from observations by a single satellite and

multiple satellites is based on solving the Grad-Shafranov (GS) equation assuming the

130 structure has a two-dimensional (2D) MHD equilibrium. The GS equation is

# "2 "2 & dP A % ( A t ( ), % 2 + 2 ( = )µ0 $ "x "y ' dA

2 where the transverse pressure is given by Pt = p + Bz /2µ0. The magnetic field vector B is ! related to the partial vector potential A(x,y) and the axial magnetic field Bz by B = "A(x, y)# zˆ + Bz(A)zˆ . The third dimension is considered as the invariant axis,

representing the direction along which the structure changes much more gradually in

! comparison to the variation on the plane perpendicular to it. The approach in solving the

GS equation is treating it as a spatial initial value problem. The transverse pressure and

the axial magnetic field component Bz are modeled by a combination of polynomial and

exponential functions of the partial vector potential A(x,y).

140

3.2 Reconstruction procedure

We have adopted the procedure documented in Hau and Sonnerup [1999] in the

previous work to reconstruct two-dimensional maps of plasma parameters based on

observations from a single satellite [Lui et al., 2008]. Our previous analysis indicates that

a well-defined coordinate system can be obtained through minimum variance analysis

and deHoffman Teller transformation. The results show the existence of a moving frame 8

in which the FTE fits well as a relatively steady state structure. Thus, the observed

structure has properties satisfying the assumptions for GS reconstruction. In this

approach, As recognized by Hasegawa et al. [2006], different branches of the function are

150 used to model parameters associated with the magnetosheath and with the

magnetosphere. These different branches are connected, indicating more definitely than

before on the basis of the vector potential map that the FTE is indeed a union of these two

regions [Lui et al., 2008].

For the composite reconstruction performed in this study, we adopt mostly the

procedure documented in Hasegawa et al. [2006] with some slight modifications. First,

since THEMIS D encountered the FTE close to its center, we adopt the coordinate system

for the composite reconstruction to be that used in our earlier work. Therefore, the axes

for the reconstruction are X=(0.5268, –0.7761, 0.3466), Y=(0.7366, 0.6203, 0.2694), and

Z=(–0.4241, 0.1134, 0.8985) in GSE coordinates. We shall refer to this coordinate system

160 as the GS coordinate system. Observations from each satellite are then used individually

to perform the reconstruction before producing a composite reconstruction with

observations from all five satellites. Second, since the derived partial vector potential

A(x,y) from each satellite satisfies the GS equation whereas any combination of these

separate A(x,y) does not necessarily satisfy the GS equation, we minimize the width of

the transition region in producing the partial vector potential A(x,y) for the entire region

by adopting a top-hat function bordered by cosine edges. More specifically, the edge

function is given by

f (x) = 0.5 [1+ cos(x /d)],

where x is the distance from the top-hat edge and d is the width of the edge. This function

170 allows gradual tapering of A(x,y) at the transition boundary between adjacent GS

solutions. Since an arbitrary constant can be added to A(x,y) without causing any change

in the derived parameters of magnetic field components and plasma pressure, the

continuity of A(x,y) at the interfaces of two adjacent reconstructions is achieved by

adding the average difference of the A(x,y) from the two reconstructions at the relevant

interface.

3.3 Comparison between observed and modeled parameters

The accuracy in the reconstruction results is reflected by the accuracy in reproducing

the observed values of Pt and the magnetic field components. Figure 4a shows the

180 comparison between the observed and modeled Pt for these five satellites. Similarly,

Figure 4b shows the comparison between observed and modeled magnetic field

components for these five satellites. For the Pt graph, different symbols are used for each

satellite. For the magnetic field graph, different symbols are used to denote different

components. The plots indicate that there is good agreement between the observed values

of Pt and the magnetic field components. For a more quantitative comparison, we have

performed linear fits to these parameters. The correlation coefficients and the slopes of

these fits are given in the figure. For the Pt parameter, the correlation coefficient and

slopes are 0.9905 and 0.9768±0.0055, respectively. For the magnetic field components,

the correlation coefficient and slopes are 0.9978 and 0.9779±0.0047, respectively. The

190 values of these parameters are close to unity, indicating very good matches in general 10

between the observed and modeled values of both Pt and the magnetic field components

for the reconstruction.

3.4 Reconstruction from individual satellite data

The reconstruction map of A(x,y) from each of five satellites is shown in Figure 5.

The observed magnetic field vectors on the GS XY-plane along the satellite path in the

GS coordinate system are given by the arrows along the X-axis in each panel.

Transforming the satellite locations to the GS coordinate system indicates that THEMIS

B and C were below THEMIS D in terms of their Y-coordinates whereas THEMIS A and

200 E were above THEMIS D. The almost vertical orientation of arrows in the THEMIS D

panel reinforces the notion that THEMIS D indeed passed very close to the center of the

FTE. THEMIS B and C detected significant deviations of the isocontours from the

horizontal direction. The deviations appear from the higher Y-coordinates in the

reconstruction maps of THEMIS B and C, consistent with the fact that they were below

THEMIS D. The deviations in THEMIS C were larger than that in THEMIS B. This is

also consistent with the fact that THEMIS C was closer to THEMIS D than THEMIS B

was. The deviations of the isocontours from the horizontal direction were less in

THEMIS A and E in comparison. Furthermore, they appear from below, which is

consistent with the fact that THEMIS A and E were above THEMIS D on the GS XY-

210 plane. The various degrees of deviation in the isocontours for these satellites are

consistent with the observed perturbations in magnetic field shown in Figure 3.

The reconstruction maps of Pt (left column) and Bz (right column) for each of the five

satellites are shown in Figure 6. It can be seen that the FTE is quite prominently seen in 11

the reconstruction maps of Pt and Bz for THEMIS D. THEMIS C was closest to THEMIS

D and detected an edge of the FTE, more obvious in the Pt panel and less so in the Bz

panel. There were very little indications of the FTE effect from the reconstruction maps

of the other three THEMIS satellites.

3.5 Composite reconstruction of data from all five THEMIS satellites

220 The results of the composite reconstruction are given in Figure 7. The contours for

the partial vector potential, axial magnetic field component, transverse and plasma

pressures are in steps of 0.01175 T-m, 5 nT, and 0.05 nPa, respectively. Since THEMIS

D traversed the FTE closest to its center, we adopt the X-axis of the composite

reconstruction map to be along the THEMIS D path. In the GS coordinate system,

THEMIS B has the lowest Y-coordinate and thus its data are used as the starting point of

the composite reconstruction. The horizontal straight lines in these maps indicate paths of

the five satellites in the GS coordinate system. Labels of each satellite are given on the

right side of the reconstruction map for the partial vector potential A(x,y), which shows

THEMIS D crossing very close to the center of the FTE structure as mentioned before.

230 Just above the FTE are several nearly parallel isocontours which probably mark the

transition from the magnetospheric boundary layer to the magnetosheath proper. Above

these isocontours is a magnetic island structure that lies slightly below the paths of

THEMIS A and E. The FTE shows more prominently in the Pt, Bz, and Pr maps than in

the A(x,y) map. On the other hand, the magnetic island seen prominently in the A(x,y)

map does not have a similar prominence in these other maps. This finding suggests a

clear distinction between a magnetic island and an FTE event. 12

4. Summary and Discussion

We have developed independently the technique to perform the Grad-Shafranov

240 reconstruction from multiple satellite observations following similar procedures

documented previously [Sonnerup and Guo, 1996; Hau and Sonnerup, 1999; Hasegawa

et al., 2004, 2005; Sonnerup et al., 2006 and references therein]. We apply the technique

to the FTE detected by the THEMIS satellites near the dusk magnetopause on 2007 May

20 [Sibeck et al., 2008]. Significant differences exist in the observed plasma parameters

from these five THEMIS satellites.

Two-dimensional maps of plasma parameters are first reconstructed individually for

each THEMIS satellite. These results are presented to show how the FTE influence is

seen in the reconstruction maps from each satellite located at different distances from the

center of the FTE. This is followed by combining measurements from all five THEMIS

250 satellites to produce two-dimensional composite reconstruction maps of plasma

parameters of the FTE and its surroundings. The composite results show some interesting

features that have not been noted before. First, a magnetic island in the magnetosheath

region appears quite prominently in the A(x,y) map but is not conspicuous in the maps of

the Bz component, the transverse pressure Pt, and the plasma pressure Pr. On the other

hand, the FTE is less conspicuous in the A(x,y) map but stands out prominently in the

maps of other parameters. This is partly due to the different branches of the functions

modeling the Pt and the Bz component. Second, from the A(x,y) and Bz maps, the

magnetic field troughs bounding the FTE are due to extrusions of the weak Bz region

adjacent to the magnetosheath region. Third, the FTE exhibits asymmetric structures with 13

260 respect to the transition region between the magnetosphere proper and the magnetosheath

proper, especially in the Bz and Pr maps. This asymmetry contributes partially to the

different signatures seen by these five THEMIS satellites during the FTE encounter.

Acknowledgements

This work was supported by the NASA contract NAS5-02099 to University of

California, Berkeley, by the NSF grant ATM-0630912 and NASA grant NNX07AU74G

to The Johns Hopkins University Applied Physics Laboratory, and by the German

Ministerium für Wirtschaft und Technologie and the Deutsches Zentrum für Luft- und

270 Raumfahrt under grant 50QP0402 to the FGM Lead Investigator Team at the Technical

University of Braunschweig.

References

Angelopoulos, V., et al. (2008), First results from the THEMIS mission, Space Sci. Rev.,

submitted.

Hasegawa, H., B. U. Ö Sonnerup, M. W. Dunlop, A. Balogh, S. E. Haaland, B. Klecker,

G. Paschmann, B. Lavraud, I. Dandouras, and H. Rème (2004), Reconstruction of

two-dimensional magnetopause structures from Cluster observations: verification

of method, Ann. Geophys, 22,1251-1266.

280 Hasegawa, H., B. U. Ö Sonnerup, B. Klecker, G. Paschmann, M. W. Dunlop, and H.

Rème (2005), Optimal reconstruction of magnetopause structures from Cluster

data, Ann. Geophys, 23,973-982. 14

Hasegawa, H., B. U. Ö Sonnerup, C. J. Owen, B. Klecker, G. Paschmann, A. Balogh, H.

Rème, and Y. Khotyaintsev (2006), The structure of flux transfer events

recovered from Cluster data, Ann. Geophys, 24, 603-618.

Hasegawa, H., R. Nakamura, M. Fujimoto, V. A. Sergeev, E. A. Lucek, H. Rème, and Y.

Khotyaintsev (2007), Reconstruction of a bipolar magnetic signature in an

earthward jet in the tail: Flux rope or 3D guide-field reconnection? J. Geophys.

Res., 112, A11206, doi:10.1029/2007JA012492.

290 Hau, L.-N. and B. U. Ö Sonnerup (1999), Two-dimensional coherent structures in the

magnetopause: Recovery of static equilibria from single-spacecraft data, J.

Geophys. Res., 104, 6899-6917.

Hu, Q. and B. U. Ö Sonnerup (2001), Reconstruction of magnetic flux ropes in the solar

wind, Geophys. Res. Lett., 28 (3), 467-470.

Hu, Q. and B. U. Ö Sonnerup (2003), Reconstruction of two-dimensional structures in the

magnetopause: Method improvements, J. Geophys. Res., 108, A11011,

doi:10.1029/2002JA009323.

Lui, A. T. Y., et al. (2008), Reconstruction of a magnetic flux rope from THEMIS

observations, Geophys. Res. Lett., in press.

300 Sibeck, D. G. and V. Angelopoulos (2008), THEMIS cience objectives and mission

phases, Space Sci. Rev., submitted.

Sibeck, D. G., M. Kuznetsolva, V. Angelopoulos, K.-H. Glassmeier, and J. P. McFadden

(2008), Crater FTEs: Simulation results and THEMIS observations, submitted,

Geophys. Res. Lett. 15

Sonnerup, B. U. Ö and M. Guo (1996), Magnetopause transects, Geophys. Res. Lett., 23,

3679-3682.

Sonnerup, B. U. Ö, H. Hasegawa, G. Paschmann (2004), Anatomy of a flux transfer

event seen by Cluster, Geophys. Res. Lett., 31, L11803,

doi:10.1029/2004GL020134.

310 Sonnerup, B. U. Ö, H. Hasegawa, W.-L. Teh, and L.-N. Hau (2006), Grad-Shafranov

reconstruction: An overview, J. Geophys. Res., 111, A09204,

doi:10.1029/2006JA011717.

Teh, W.-L. and L.-N. Hau (2004), Evidence for pearl-like magnetic island structures at

dawn and dusk side magnetopause, Earth Planets Space, 56, 681-686.

Teh, W.-L. and L.-N. Hau (2007), Triple crossings of a string of magnetic islands at

duskside magnetopause encountered by AMPTE/IRM satellite on 8 August 1985,

J. Geophys. Res., 112, A08207, doi:10.1029/2007JA012294. 16

Figure Captions

320 Figure 1. Plasma parameters near the dusk magnetopause measured by THEMIS D for

the flux transfer event on 2007 May 20: (a) the number density is given by the solid

line and the pressure is given by the dashed line; (b)-(d) the three components of the

plasma bulk flow, (e)-(h) the total magnitude and the three components of the

magnetic field.

Figure 2. Plasma parameters measured by THEMIS C for the flux transfer event on 2007

May 20.

Figure 3. A brief overview of plasma parameters observed by all THEMIS satellites for

the flux transfer event on 2007 May 20.

Figure 4. Comparison between the observed and modeled values for (a) the transverse

330 pressure and (b) the axial magnetic field component.

Figure 5. Two-dimensional maps of the partial vector potential for five THEMIS

satellites obtained from the GS reconstruction based on measurements from each

individual satellite.

Figure 6. Two-dimensional maps of the transverse plasma pressure and the axial

magnetic field component for the five THEMIS satellites reconstructed individually

based on measurements of each satellite.

Figure 7. Composite reconstruction maps of the partial magnetic vector potential, the

transverse pressure, the axial magnetic field component, and the plasma pressure

based on combined measurements from all five THEMIS satellites.

340 17

340

Figure 1 18

Figure 2 19

Figure 3 20

Figure 4 21

Figure 5 22

350

Figure 6 23

Figure 7