Internal structure of a magnetic flux rope from Cluster observations



[1] We investigate a magnetic flux rope (MFR) observed by Cluster in the magnetotail during a substorm on 2001 August 22. The MFR was aligned with its principal axis closely along the dawn-dusk direction and had a small size of ∼2 RE with a total current of ∼0.8 MA. The four spacecraft traversed the MFR at different distances from its center based on the magnetic field signature. This fortuitous situation reveals the irregular magnetic field structure in its inner core, which is a feature reported here for the first time. At the leading edge, the y-component of the electric field was dawnward against the current density direction (dynamo action) and the x-component of the Lorentz force was Earthward. These parameters reversed in direction at its trailing edge (load).

1. Introduction

[2] Space plasmas are known to consist mostly of charged particles. Since the bulk motions of charged particles with opposite charge signs do not necessarily coincide, electric currents resulting from their differential motions are quite ubiquitous in space plasmas. One-dimensional current structures in terms of current sheets can often be detected. A notable example is the current sheets at low altitudes forming the famous Regions 1 and 2 field-aligned currents [e.g., Iijima and Potemra, 1976]. Two-dimensional current structures are also observed. These are current filaments embedded within a plasma medium, often referred to as magnetic flux ropes [e.g., Russell and Elphic, 1979], which can result from plasma instabilities such as the tearing instability [Sitnov et al., 1997], the cross-field current instability [Lui et al., 1991], and the ballooning instability [Roux et al., 1991; Cheng and Lui, 1998].

[3] Previous investigations of magnetic flux ropes (MFRs) are mostly based on observations from a single satellite. Plasma characteristics of MFRs have been established through statistical studies [e.g., Moldwin and Hughes, 1992]. Recent Cluster investigations have expanded our knowledge on MFRs [e.g., Slavin et al., 2003; Zong et al., 2004]. In particular, Nakamura et al. [2006] suggested that MFRs embedded within thin current sheets could play an essential role in the magnetotail dynamics.

[4] The internal structure of a MFR is often inferred from data of a single satellite traversing such a current structure. The general expectation is that a MFR consists of layers of helical magnetic field lines. In this paper, we investigate in detail a MFR encountered by the four Cluster satellites during one substorm interval on 2001 August 22 when these satellites traversed nearly simultaneously the MFR at different distances from its center. This fortuitous situation reveals the internal structure of the MFR, showing significant deviations of the expected helical nature of magnetic field lines within its inner core. Furthermore, the y-component of the electric field is found to be dawnward at the leading edge of the MFR (opposite to the y-component of the current density, thus acting as a dynamo) and duskward at its trailing edge (acting as a load).

2. Observations

2.1. Ground and Magnetotail Activity

[5] The AU index (upper curve) and the AL index (lower curve) monitoring the strengths of the auroral electrojets in the interval 0800–1400 UT on 2001 August 22 are shown in the top panel of Figure 1. A substorm expansion onset occurred at ∼0920 UT on this day. The substorm activity was also recorded by the IMAGE/FUV global imaging data as shown in the work of Lui et al. [2006]. The encounter of the MFR to be investigated in detail was at ∼0950 UT during the substorm expansion phase. The encounter took place before the AL index reached its peak for this substorm.

Figure 1.

(top) AU (upper trace) and AL (lower trace) indices on 2001 August 22. Vertical dashed line indicates the time when the MFR was encountered by the Cluster satellites; (middle) Relative spacing between the four Cluster satellites in the GSM XY- and YZ-planes; (bottom) Overview of Cluster measurements from SAMBA (C3) during the substorm expansion phase for the time interval 0930-10:30 UT on 2001 August 22. Vector components are in GSM coordinates except for Ey and -(VxB)y in the third panel of Figure 1 (bottom) that are in GSE coordinates. Labels on the right refer to the dashed curves in the panels.

[6] The relative spacing between the four Cluster satellites is shown in the middle panels of Figure 1. Based on the x-coordinates, the order of satellites in terms of proximity to the Earth is C1 (RUMBA), C2 (SALSA), C3 (SAMBA), and C4 (TANGO). In terms of proximity to the midnight meridian the order of the four satellites is C4, C1, C2, and C3. The satellite C3 was south of the other satellites with a separation distance of <2000 km.

[7] An overview of magnetotail activity from Cluster observations at ∼19 RE downstream distance for the period 0930–1030 UT is shown in the bottom panels of Figure 1. The measurements shown are from C3. The plasma data were obtained by CIS/HIA [Rème et al., 2001]. The electric field and magnetic field measurements on Cluster were taken by EFW [Gustafsson et al., 1997] and FGM [Balogh et al., 2001], respectively. Several plasma flow reversals were seen. For example, plasma flow reversed from tailward to sunward at ∼0940 UT, from sunward to tailward at ∼0944 UT, from tailward to sunward at ∼0954 UT, from sunward to tailward at ∼1002 UT, and from tailward to sunward at ∼1003 UT. The number density was rather low at the time of most of the flow reversals, suggesting that the flow reversals took place in a low plasma density environment. The y-component of the electric field reversed sign many times within the time interval of these plasma flow reversals. The temporal profile of the Bx component of the magnetic field indicates that the satellite crossed from the northern magnetotail to the southern magnetotail during this 1-hr interval. Several abrupt increases in the Bz component indicative of dipolarizations were also seen during this interval. Not all these abrupt Bz increases are dipolarizations. One of them signifies a MFR.

2.2. Close Up View of the Magnetic Flux Rope

[8] A close up look at the Cluster measurements from all satellites including the current density and the Lorentz force around the MFR encounter is shown in Figure 2. The time span in this figure is only 2 min. The coordinates are GSM except for Ey, which is in GSE instead. The top two panels show the three components of current density and Lorentz force, respectively. The other panels show the data from all four Cluster satellites. A clear bipolar signature in the Bz component, which is a distinct characteristic of MFR, was seen in all satellites almost simultaneously. The MFR in the time interval bracketed by the vertical dashed lines was embedded in tailward flowing plasma with southward magnetic field. In terms of zero crossing of the Bz component, the order is C1, C2, C3, and C4. This is the exact sequence in terms of proximity to the Earth, suggesting that the structure was encountered first by the satellite closest to Earth and followed in order by satellites at further downstream distances. This timing sequence is consistent with a tailward moving MFR during this interval, in good agreement with the occurrence of tailward plasma flow in the MFR interval. From the duration of the bipolar signature and the flow magnitude, the size of this MFR is estimated to be ∼2 RE across and a total current of ∼0.8 MA.

Figure 2.

Plasma parameters associated with the encounter of the magnetic flux rope by Cluster satellites at ∼0950 UT on 2001 August 22. Vertical dashed lines bracket the time interval of the encounter.

[9] Just before the start of the Bz bipolar signature at 09:49:45 UT, the Bx component and the total magnetic field magnitude from the four satellites showed major differences in strength. These major differences suggest that the four different satellites encountered MFR at different distances from its center. The order from the largest field strength to the smallest one is C3, C2, C1, and C4. Therefore, this sequence also gives the depth of penetration into the MFR from the outer edge to the inner core. It may also be noted that Ey was initially negative and subsequently became positive during the MFR interval. The Ey turned negative again for the two outer traversals (C3 and C2).

[10] There was a noticeable enhancement of current density in the y-component near the center crossing of the MFR. The enhanced value was similar to those after 09:50:40 UT when the neutral sheet was located within the Cluster constellation based on the Bx component, i.e., close to the current density at the neutral sheet. This enhancement coincided with the enhancement of z-component of the Lorentz force. Within this brief enhancement interval, the x-component of the Lorentz force reversed from earthward to tailward.

[11] Although not shown, the number density ratio of oxygen ions over protons during the MFR interval has also been examined for the three satellites that have plasma data from CIS/CODIF. There was no indication of any significant increase in this density ratio within the MFR interval, suggesting that there was no significant enhancement of ionospheric ions within the MFR.

2.3. Variation of Plasma Parameters Within the Magnetic Flux Rope

[12] We have performed the minimum variance analysis on the Cluster magnetic field data. The results for the C3 (furthest from the MFR core) and C4 (closest to the MFR core) are shown in Figure 3. The coordinate L corresponds to the largest variance and N to the smallest variance. For C3, L = (0.31, 0.08, −0.95), M = (−0.86, 0.45, −0.24), and N = (−0.41, −0.89, −0.21) in GSM coordinates. The corresponding ratios of eigenvalues are λM/λN = 2.8 and λL/λN = 12.4. For C4, in GSM L = (−0.50, 0.001, 0.87), M = (0.46, 0.84, 0.27), and N = (−0.73, 0.54, −0.42). The corresponding ratios of eigenvalues are λM/λN = 1.6 and λL/λN = 10.0. The LMN profiles for C3 conform well to the signatures of MFR and the orientation of N in C3 indicates that the MFR axis was mainly along the y-direction. The LMN profiles for C4 show substantial deviations from the MFR signatures, indicating the internal magnetic structure of this MFR to be rather complicated. Although different magnetic signatures can result from crossings of MFR at different impact parameter values, there is still a systematic trend for the profile of the magnetic component with intermediate variance as modeled by Moldwin and Hughes [1991], which is significantly different from the observed profile. Therefore, the complexity in the inner core cannot be attributed to a satellite path with a different impact parameter from the ones at the outer edge of the MFR.

Figure 3.

Magnetic field strength and components in the minimum variance coordinates for C3 (SAMBA) and C4 (TANGO).

[13] The irregular magnetic field structure near the MFR core is further illustrated in the leftmost column of Figure 4 where hodograms constructed from the values of the LM coordinates from all four satellites are shown. The hodogram order is arranged such that from top to bottom are from satellites at decreasing distances from the MFR center. It is seen that the hodograms indicate the expected helical magnetic structure for the outer two MFR traversals (Figure 4, first and second rows of plots) and irregular structure for the inner two MFR traversals (Figure 4, third and fourth rows of plots). The electric field and plasma flow structures within the MFR are shown in the middle and the rightmost columns of Figure 4, respectively. There was no plasma data from C2. In all satellites, Ey was negative in the initial interval of MFR but reversed to be positive in the later interval. Although not shown here, the electric field in the plasma rest frame, i.e., Ey′ = Ey + (ν × B)y, was also computed for the three satellites with plasma data. It is found that Ey′ was also negative at the leading edge of MFR and reversed to be positive at the trailing edge. Therefore, the leading edge of MFR was a dynamo (jyEy′ < 0, where jy is the y-component of the current density) and the trailing edge of MFR was a load (jyEy′ > 0). It may be noted that tailward flow was stronger closer to the inner core, which can also be noted from Figure 2. Since the tailward flow was very weak in the initial MFR interval and became much stronger later, this flow development suggests that Cluster encountered the MFR at the early stage of its formation.

Figure 4.

Vertical profiles of magnetic field hodogram, y-component of the electric field, and x-component of the plasma flow for the four Cluster satellites, arranged such that the panels (top to bottom) denote decreasing distance from the magnetic flux rope center.

3. Summary and Discussion

[14] Based on Cluster observations, we have examined a MFR during a substorm interval on 2001 August 22 when the four Cluster satellites were at a downstream distance of ∼19 RE in the magnetotail and traversed the structure at different distances from its center. The MFR had a small size of ∼2 RE with a total current of ∼0.8 MA and was not force-free. The lack of force-free for this MFR is consistent with the findings by Slavin et al. [2003] for another MFR detected by Cluster later on the same day. The significant features of this tailward moving MFR are illustrated in Figure 5: (1) the outermost layer of the MFR had the expected helical magnetic field lines while the innermost layer showed an irregular magnetic structure; (2) the electric field was dawnward at the leading edge and duskward at the trailing edge; (3) the product of jyEy′ is negative (i.e., dynamo) while it is positive at the leading edge (i.e., load) at the trailing edge; (4) the x-component of the Lorentz force was Earthward initially and became tailward later; and (5) the z-component of the Lorentz force was the largest component, pointing towards the neutral sheet. These results indicate that the internal structure of this MFR is more complicated than the simple picture of a uniformly helical magnetic field pattern within a MFR. This is the first report showing the complex nature of a MFR near its inner core.

Figure 5.

A schematic diagram to illustrate the various features of the magnetic flux rope based on the four Cluster satellites encountering the structure at different distances from its center.

[15] The presence of a dynamo at the leading edge of a MFR suggests that mechanical energy is converted into electric energy. Since initially the Lorentz force was directed Earthward while the MFR was moving tailward, the Lorentz force cannot be the driving force. The pressure gradient force, generally directed tailward and opposing the Lorentz force, is likely the required force.

[16] The complex nature in MFR inner core may give a clue to its formation mechanism. If magnetic reconnection acting at the two edges of the MFR is envisioned, then the inner core far from the reconnection sites should not be affected and thus no complex structure in the inner core is anticipated. However, if the MFR is a result of current filamentation from a current-driven or pressure-driven instability, such as the cross-field current instability or the ballooning instability, then its inner core is the center of the current filament from the nonlinear evolution of the instability and may be expected to have a complex magnetic structure. However, detailed investigations on the nonlinear evolution of these instabilities are needed to verify these expectations.


[17] This work was supported by the NSF grant ATM-0630912 and NASA grant NNG04G128G to the Johns Hopkins University Applied Physics Laboratory.