Magnetic Structure and Electron Flow at a Northward Interplanetary
Magnetic Field Reconnection Line

D. E. Wendel^1^, P. H. Reiff^1^, A. Fazakerley^2^, E. Lucek^3^, M. L.
Goldstein^4^

^1^ *Rice University, Houston, TX 77005, USA*

^2^ *Mullard Space Science Laboratory, Holmbury St. Mary, Dorking, UK*

^3^ *The Blackett Laboratory, Imperial College, London, UK*

^4^ *Goddard Space Science Center, Laboratory for Solar and Space
Physics, Greenbelt, MD* *20771, USA*

Date submitted: August 24, 2005

# 

# 

On March 18, 2002, the Cluster four-satellite suite traveled from the
earth's northern mantle into the magnetosheath. During this time, the
IMAGE spacecraft observed a long-lived proton emission northward of the
auroral zone. The Cluster electron and magnetic field data suggest
Cluster passed within 1 km of an active reconnection line, entering the
ion diffusion region and the edge of the electron diffusion region. We
present the first *in situ* discovery of the instantaneous structure,
velocity, orientation, and size of a reconnecting current layer.

94.30.Di, 52.35.Vd, 95.30.Qd

# 1. Introduction

Collisionless magnetic reconnection is a fundamental process that occurs
in many natural and artificial plasmas, including both solar flares and
small-scale heating of the solar corona. True collisionless reconnection
is difficult to study in either laboratory experiments (where the
scaling is not appropriate) or theoretical models (where numerical
diffusion provides the resistivity). We look to the magnetosphere as a
natural laboratory to provide us with data on this crucial process of
large-scale reconnecting fields. On the sunward side of the Earth's
field boundary, the magnetopause, the terrestrial field points
northward, favoring magnetic reconnection with a southward directed
interplanetary magnetic field (IMF). However, when the IMF is northward,
it drapes over the earth\'s magnetopause in a roughly anti-parallel
orientation over the magnetic tail lobes in a manner that also allows
reconnection near the earth's magnetic cusp region. When the IMF lies
nearly due North, it can reconnect with tail lobe fields near both
cusps, creating closed field lines (Reiff and Burch \[5\]). There has
been increasing indirect evidence that this occurs (Fuselier, Petrinec,
and Trattner \[2\]). Direct *in situ* multi-point observations of a
reconnection site provide a rare opportunity to investigate the
steadiness and spatial structure of such reconnection. For the first
time we can directly evaluate the length and time scales associated with
ion and electron demagnetization and the role these and the resulting
current structures play in the global reconnection rate.

The Cluster satellites, launched in 2000, are four spacecraft that fly
in close formation to investigate turbulence in the Earth's vicinity.
The instruments onboard include ion and electron spectrometers and a
magnetometer. In an earlier analysis of the Cluster magnetopause
crossing on March 18, 2002, Phan *et al.* \[4\] claimed discovery of an
x-line crossing at approximately 14:56 UT, based on an ion moment
reversal detected by Cluster. While we agree with the assertion that
Cluster passes through an active x-line, we disagree with this location
of the x-line. In this paper we will examine this event\'s Cluster PEACE
electron moments and FGM magnetic field data to locate the true x-line
and, for the first time, determine its stability, motion, and magnetic
structure by way of instantaneous multi-point measurements.

# 2. Magnetic Field Evidence for Reconnection

On March 18, 2002, from 14:54 to 15:05 UT Cluster passed from the
northern tail lobe through the magnetopause and into the magnetosheath,
moving primarily along the noon-midnight meridian toward the sun (see
Fig. 1). It passed through 81![](media/image1.wmf) latitude and 14 MLT.
Phan *et al.* \[4\] magnetically mapped the ionospheric footprint of the
spacecraft to within error, the location of a long-lasting (5.5 hour)
northern reconnection spot observed simultaneously in FUV emissions by
the IMAGE spacecraft (Frey, et al*.,* \[1\]). Phan, et al*.*, \[4\] note
that the velocities there meet the Walèn criterion.

In Fig. 2, we present the Cluster-1 FGM (Flux Gate Magnetometer)
magnetic field data for the interval during Cluster\'s magnetopause
crossing. The average magnetosphere fields are roughly anti-parallel to
the average magnetosheath fields, but in the magnetopause, the GSE
magnetic field components B~x~ and B~z~ simultaneously change sign
several times, suggesting Cluster touches or crosses a magnetic x-line
on multiple occasions. The B~x~-B~z~ null near 15:00 UT presents the
smallest values observed and thus the closest possible approach to an
x-line. Because the magnetopause has about a 67![](media/image1.wmf)tilt
from GSE x, we perform all further analysis in a coordinate system
aligned with the magnetopause. The guide field By is not zero, however,
making this an x-line and not a true null point.

# 3. Instantaneous X-Line Derivatives and Location

The four Cluster spacecraft lie on the corners of a tetrahedron, to
allow instantaneous measurement of the curl of the magnetic field,
yielding the "curlometer" current evaluated at the centroid of the array
(shown as spacecraft 0 in some of the plots). We choose times when the
centroid (average) field exhibits a minimum B~x~ and B~z~ to determine
the instantaneous spatial gradients of the fields by way of a
multi-spacecraft least squares fit of ![](media/image2.wmf). An
inversion of the Taylor expansion for the B~x~ and B~z~ components
yields the spacecraft distance from the x-line. We assume that the line
is nearly along the y-direction (hence ![](media/image3.wmf)for a
spacecraft crossing the x-line):

> ![](media/image4.wmf)
>
> \(1\)

B~i~ is evaluated at the x-z position of each spacecraft at closest
approach to minimum B~x~ and B~z~. We choose the spacecraft with minimum
measured Bxz to allow us to infer that spacecraft's distance to the
x-line; from that,. we calculate the x-line position as a function of
time.

# 4. Spatial and Temporal Structure of Reconnecting Magnetic Fields

Figures 3a-3b are statistical maps of B~x~ and B~z~ at the positions of
all spacecraft (including the centroid) relative to the x-line in a 30-s
time window around the 15:00 UT crossing. The positions of the
spacecraft relative to the x-line are determined from the Taylor
expansion of the previous section, while the magnetic field values come
from the .25-s data. These maps allows us to fit the magnitude and
distance parameters B~o~ and ![](media/image5.wmf), respectively, of a
Harris sheet model, e.g.,

![](media/image6.wmf), (2)

shown by the red curve in the figures. The Harris sheet is general
enough to describe the x-line positions and velocities at larger
distances where the Taylor expansion may be invalid. Note that in both
figures the statistics favor a pronounced linear fit through the origin,
which we exploit to remove the uncertainty in the gradient used in the
Taylor expansion of the preceding section. Thus the final positions of
the spacecraft relative to the x-line follow from a second iteration.

The fit to B~x~ gives an absolute current sheet thickness, since we have
derived it in the x-line frame of reference. If the operational
definition of the current sheet thickness is full-width at half-maximum,
then the value of ![](media/image5.wmf) = 50 km in Fig. 3a implies a
current sheet thickness of 100 km. The fit to the B~z~(x) data in Fig.
3b yields a significant asymptotic reconnection B~z~ of approximately 10
nT. Such a normal field would produce a polar cap potential drop of
about 77 kV, given a polar cap width of 3 Earth radii and an
anti-sunward solar wind speed of 400 km/s.

The estimated x-line positions (x~xl~, z~xl~) allow us to estimate and
remove the x-line velocity. The spacecraft frame x-line velocity is
necessary to derive an accurate current sheet width from the centroid's
spatial gradient estimations, and to determine the steadiness and
spatial continuity of the reconnection site. From measurements of x-line
positions and times at the crossing near 15:00 UT, a least-squares fit
of the x-line velocity estimates a moderate rate tailward and earthward
of v~x~ = .8 km/s and v~z~ = -6 km/s. Cluster 2 penetrates as close as
at least 1 km from the x-line and Cluster 4 within about 3.5 km. The
x-line continues to jitter at later crossings: at 15:01, the x-line
slides away from earth at a rate v~x~ = -2 km/s, v~z~ = 7.6 km/s; at
15:02, the x-line moves inward again at v~x~ = 7.2 km/s, v~z~ = -10.4
km/s and Cluster is on the sheath side of the fields; and at 15:03, it
sweeps very rapidly back toward earth at v~x~ = 7.4 km/s, v~z~ = - 44
km/s---note the steepness of the magnetic field gradient at that time.
The motion is consistent with a single, oscillating x-line, but we
cannot rule out the possibility that we encounter multiple x-lines from
a tearing-mode instability.

Figures 4a-4d are frames selected from a movie modeling the spacecraft
motion relative to the x-line near 15:00 UT, in the x-line reference
frame. We include a model of the zeroth-order x-line magnetic fields, in
red and blue. Black arrows represent magnetic field vectors at each
spacecraft, including "Cluster 0," the average magnetic field values at
the centroid. The sun is to the left.

# 5. Electron Flows

> The superposed-epoch electron moments in the x-line frame are depicted
> in Fig. 5 along with the derived magnetic field model there (purple
> arrows signify vectors with a negative y-component, and black arrows
> vectors with a positive y-component). There is a pattern of inflow and
> accelerated outflow at the x-line in the x-z plane. Moreover, the
> positive-y flows (corresponding to the negative-y reconnection current
> sheet) are centered within roughly 100 km of the x-line, consistent
> with the current sheet thickness estimate. The electron moments at the
> x-line give a current density on the order of J~y~ \~ 10^-6^ A/m^2^,
> the same order of magnitude as the current sheet density obtained by
> taking the instantaneous curl of the magnetic field measured by the
> four spacecraft (the "curlometer" current). (The ions are moving at \~
> 50 - 150 km/s in the region around the x-line). Furthermore, the
> Alfvén speed is roughly 276 km/s for the local ion density (\~
> 90/cm^3^), using an asymptotic magnetic field of 120 nT, while the
> electron flows are approximately 300-400 km/s within a few km of the
> inferred reconnection site. The first-order electron moments in the
> vicinity of the x-line are therefore consistent with the normal
> inflows and tangential outflows that define a reconnection region,
> with currents derived from the magnetic field data, and with the
> supra-Alfvénic speeds observed in the ion demagnetization region of
> reconnection simulations (Hesse, Birn, and Kuznetsova \[3\]).

**6. Electron and Ion Diffusion Regions**

The enhancements in B~y~ that just precede the magnetic nulls in B~x~
and B~z~ might result from Hall currents, which arise when the ions are
demagnetized but the electrons are not, as occurs inside the ion
diffusion region. A superposition of B~y~ and the curlometer current,
supports this conclusion (see Fig. 6). The position of Cluster 2 at the
edge of the discontinuity in B~y~ therefore suggests an ion diffusion
box with a half-width of about 110 km. Simulations put the Hall current
region to within about 10 ion skin depths![](media/image7.wmf) of the
x-line, where ![](media/image8.wmf) (Shay, Drake, and Rogers \[7\],
Hesse, Birn, and Kuznetsova \[3\]). Calculations of the ion skin depth
from measurements of ion density in the magnetopause yield
![](media/image7.wmf)= 24 km and an ion diffusion half-width of 240 km,
so that the distance we propose between Hall currents and the x-line lie
well within this limit.

> The second-order electron moments further support the proximity of a
> reconnection line. The electron skin depth for the density observed in
> the magnetopause is about 1 km, so our x-line distance measurements
> suggest we may not penetrate the electron diffusion region. However,
> when we pass within 1 km or 3.5 km of the x-line (as Cluster 2 and
> Cluster 4 do, respectively) we are close enough to at least view
> effects of partial demagnetization in the transition region. This is a
> transition region between the ion and electron diffusion regions that
> lies within an ion gyroradius of the reconnection site. In this and
> the electron diffusion region, the off-diagonal components of the
> electron pressure tensor in a field-aligned coordinate system arise
> from electrons departing from field-aligned gyrotropy. An earlier
> observation of a northward IMF reconnection line by the Polar
> spacecraft also observed such electron pressure shears, indicating
> entry into the electron diffusion region (Scudder *et al.* \[6\]).

From the electron second-order moments, the divergence term
![](media/image9.wmf) (Fig. 7) of the generalized Ohm's law reaches 15%
of the maximum Hall electric fields in the region around the x-line, a
strong indicator of the proximity of the electron diffusion region.
Reference \[4\] achieves a maximum reconnection E~y~ of .3v~A~B~0~,
where v~A~ and B~0~ are the asymptotic Alfvén speed and magnetic field,
respectively. This presents an order-of-magnitude estimate, as the
authors note that the value drops in time. For our asymptotic field and
density values of B~0~ ![](media/image10.wmf) 120 nT and n~p0~
![](media/image10.wmf) 9x10^7^/m^3^, .3v~A~B~0~ ![](media/image10.wmf)
10 mV/m, satisfyingly close to our pressure divergence contribution of
12 mV/m. Note that we calculate the pressure divergence instantaneously
by a least-squares estimate from data collected by all four spacecraft.

# 7. Conclusions

For the case of a northward IMF, we observe translating but otherwise
steady reconnection magnetic B~x~, B~z~ fields, and an induced B~y~,
that are consistent with an anti-parallel merging site twisting through
the out-of-plane (y) direction. The resulting potential field drop
mapped to the ionosphere is consistent with sunward convection flows. We
find that there is a steep interior field: the orientation of the lobe
and draping at the reconnection site is tilted at \~ 67
![](media/image1.wmf) from the GSE horizontal.

We use distance-to-x-line estimates to assess the x-line motion, and
determine that it is consistent with a single, steady x-line wavering
across the spacecraft at speeds in the range of ![](media/image10.wmf) 6
to 45 km/s. However, we cannot rule out encounters with multiple x-lines
from a tearing mode instability. Resistance to slippage at a tailward
location adjacent to the magnetosheath is consistent with Phan *et
al.*'s \[4\] observation of a plasma depletion layer (PDL) at the same
time and location. Fuselier, Petrinec and Trattner \[2\] have found that
a larger magnetic field and lower density in a PDL produces sub-Alfvénic
flow adjacent to the magnetopause, which is consistent with a relatively
steady x-line position. Analysis of the magnetic field gradients shows
that at least one of the Cluster spacecraft comes within 1 km of the
x-line. This means we have passed through at least the outflow and the
ion diffusion regions, the current sheet, and perhaps the electron
partial demagnetization region, on our way through the magnetopause.
Statistical fitting of a Harris sheet model yields a current sheet
thickness estimate of approximately 100 km. We infer an ion diffusion
region that is at least as large as roughly 220 km thick, on the basis
of detecting the edge of the Hall current region at the perpendicular
electron flows. This estimate agrees with a Hall zone within
10![](media/image7.wmf) of the x-line, as predicted by the theoretical
simulations. The off-diagonal pressure components and the pressure
gradients are sympathetic with proximity to the electron diffusion
region. The pressure shear terms attain values about 15% of the diagonal
pressure values near the x-line. In the absence of Cluster electric
field data, we compare the pressure divergence contribution to E~y~ with
the magnitude of the Hall term in Ohm's law, presumed significant in the
ion diffusion region, as well as simulation estimates of E~y~. The 12
mV/m pressure divergence reaches 15% of the maximum Hall term magnitudes
in the region, and agrees well with simulation estimates by Hesse, Birn,
and Kuznetsova \[3\]. Very near the x-line the electron flow becomes
aligned with the electric field, suggesting that Cluster might have
reached the electron diffusion layer.

We believe Phan *et al.* \[4\] detected an ion flow reversal at 14:56 UT
which is not due to an x-line traversal, since the magnetic fields and
electron moments are inconsistent with an x-line structure at that time.
We have modeled several later true x-line crossings based on the
magnetic field structure and electron flows.

Acknowledgements

The authors thank Steven Schwartz for his calibrated electron moments
and advice. This research is supported in part by NASA under grant
NAG5-13219.

1.  H. U. Frey, T. D. Phan, S. A. Fuselier, and S. B. Mende, Nature
    **426**, 533 (2003).

2.  S. A. Fuselier, S. M. Petrinec, and K.J. Trattner, Geophys. Res.
    Lett. **27***,* 473 (2000).

3.  Michael Hesse, Joachim Birn, and Masha Kuznetsova, J. Geophys. Res.
    **106**, 3721 (2001).

4.  T. D. Phan *et al.*, Geophys. Res. Lett. **30***,* 1509 (2003).

5.  P. H. Reiff and J. L. Burch, J. Geophys. Res., **90**, 1595 (1985).

6.  J.D. Scudder, F. S. Mozer, N.C. Maynard, and C. T. Russell, J.
    Geophys. Res. **107***,* 1294 (2002).

7.  M. A. Shay, J. F. Drake, and B. N. Rogers, Geophys. Res. Lett.
    **26***,* 2163 (1999).

**FIG. 1.** Cluster passes from the northern tail lobe through the
magnetopause and into the magnetosheath, moving primarily along the
noon-midnight meridian toward the sun.

**FIG. 2.** Cluster-1 FGM magnetic field data for the interval during
Cluster\'s magnetopause crossing. The green curve is the B~y~ component
in the GSE coordinate system, the blue curve B~x~ and the red curve
B~z~.

**FIG. 3a-3b.** A statistical map of B~x~ as a function of z (above )
and B~z~ as a function of x (below) (the centroid is included). The
figures include all times in a 30 s interval around 15:00 UT.

**FIG. 4a-4d (top to bottom).** Frames from a movie modeling the
spacecraft motion relative to the x-line near 15:00 UT, in the x-line
reference frame. We include a model of the zeroth-order x-line magnetic
fields, in red and blue. The magnetic field vectors at each spacecraft
are depicted as black arrows. The centroid, denoted by "Cluster 0," is
included as a data point.

**FIG. 5**. Superposed epoch electron flow vectors (black and purple
arrows) near the x-line at 15:00 UT. Purple arrows signify vectors with
a negative y-component, and black arrows vectors with a positive
y-component.

**FIG. 6.** The large curlometer currents measured in the z direction
(and, to a lesser extent, in the x direction) of discontinuities in the
magnetic field data strengthens the case for Hall currents.

**FIG. 7.** The pressure divergence contribution to the electric field
E~y~ at 15:00 UT (located by the purple asterisk) attains a value that
is 15% of the Hall electric field contribution.

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