Fig' 4a' Current J, J, min var coords and J, relative curlometer error, magnetic forces pressure and

1
Cluster observations of flux rope structure in
the near-tail
P. D. Henderson1, C. J. Owen1, I. V. Alexeev1, J.
Slavin2, A. N. Fazakerley1, E. Lucek3, and H.
Reme4
1Mullard Space Science Laboratory, University
College London, Holmbury St. Mary, Dorking, UK,
RH5 6NT 2Laboratory for Extraterrestrial Physics,
NASA GSFC, Greenbelt, MD, USA, 20771 3Space and
Atmospheric Physics, Imperial College London, UK,
SW7 2BZ 4Centre d'Etude Spatiale des
Rayonnements, Toulouse, France
Abstract An investigation of the 2003 Cluster
tail season has revealed small flux ropes in the
near-tail plasma sheet of Earth. Few examples
were found with a strong core field, most tending
to be magnetic loop structures either without, or
with small core fields. Two flux ropes are
detailed in this poster, observed on the 2nd
October and on the 13th August 2003. The flux
rope observed on the 2nd October was travelling
Earthward and duskward at 160 kms-1. The axis
was close to the intermediate variance direction
of the magnetic field. Throughout the flux rope,
but more significant in the outer sections, J ? B
was large. The components of J ? B suggest that
the magnetic force is acting to expand the flux
rope, i.e. directed away from the centre of the
flux rope. The flux rope observed on the 13th
August was travelling tailward at 200 kms-1. The
axis was directed close to the maximum variance
direction of the magnetic field. J ? B was larger
in the outer sections of the flux rope than in
the centre. This flux rope was also under
expansive magnetic pressure forces from J ? B,
i.e. directed away from the centre of the flux
rope. The observations of a large J ? B signature
in the outer sections of the flux ropes may be
explained if they are being observed at an
intermediate stage in their evolution from
creation by reconnection at multiple X lines near
the Cluster apogee towards the force-free like
configuration often observed further down the
tail. The centre of the flux ropes may contain
older reconnected flux at a later evolutionary
stage and may therefore be more force-free.
Fig. 5a and 5b. Observations from 13th august
flux rope in the same format as Fig. 4.
Fig. 5b schematically shows the results shown
graphically in Fig. 5a. The current circulates
around the axis with the multi-spacecraft timings
showing this to be the maximum variance
direction. This flux rope is magnetic pressure
dominated, with the large pressure acting away
from the flux rope centre. Magnetic tension is
small, and acts somewhat towards the flux rope
centre. Again, J ? B acts away from the flux rope
centre, i.e. acting to make the flux rope expand.
J ? B is larger in the outer sections of the flux
rope. The electron pressure is again reduced
inside the flux rope suggesting a compressional
force from the plasma.
Introduction Flux ropes have been interpreted as
evidence for multiple X line reconnection (MXR)
in the near-tail associated with substorms (e.g.
Slavin et al., 2003). In MXR, instead of creating
one single X line in the tail, the conditions
required for reconnection can be satisfied in
numerous places, creating a number of X lines.
Given an IMF BY component which penetrates into
the tail, flux ropes can be created between the X
lines. Reconnection propagates out to open field
lines in the lobe, eventually leading to one
single magnetotail X line that produces Alfvenic
jets in the Earthward and tailward directions.
The newly-formed flux ropes are embedded in these
flows and thus move away from the point at which
they were created. These flux ropes are
characterised by a bipolar BZ signature, caused
by the magnetic structure moving past the
spacecraft and often have a large increase in the
magnitude of B caused by a strong core field.
Events with a south-then-north (north-then-south)
signature are seen to move Earthward (tailward),
and are usually embedded in fast plasma flows
Slavin et al. (2003).
Fig. 3a and 3b. Cluster FGM, CIS and PEACE
observations from 2nd October and 13th August
2003. The flux ropes, bipolar BZ signatures with
corresponding increases in B, are embedded in
fast plasma flows observed from CIS. A high
plasma ion ß and large differential energy flux
of 1keV electrons from CIS and PEACE respectively
show that Cluster was deep in the plasma sheet.
Minimum variance analysis gives the minimum
variance direction in the X Y direction, the
intermediate variance direction in the X Y Z
direction, consistent with the ambient plasma
velocity and assumed direction of the core
magnetic field respectively. Multi-spacecraft
timings show that the intermediate variance
direction is close to the axis direction of the
flux rope. In Fig. 3b, at 030000 UT, a small
enhancement in B can be seen along with a small
north-then-south bipolar BZ signature. A large
negative deflection in BY suggests that the core
field is in the Y direction. CIS ion moments
show that the ambient plasma is moving mainly in
the X direction, at 200 kms-1. Minimum
variance analysis gives the minimum variance
direction in the X direction. However, the
maximum variance direction lies along the Y
direction. If this is the direction of the axis,
this flux rope is not consistent with a simple
force-free picture. Multi-spacecraft timings show
that the maximum variance direction is indeed
close to the axis direction of the flux
rope. Fig. 4b schematically shows the results
shown graphically in Fig. 4a. The current
circulates around the axis, shown to be the
intermediate variance direction by
multi-spacecraft timing. Magnetic pressure acts
away from
The mechanism for the creation of these
structures is important for the study of the
break-up of current sheets near substorm onset.
The flux ropes reported on here are not
force-free, indeed tending to be less force-free
in the outer sections of the flux rope than in
the centre. As is the case for those seen in the
distant tail, the cores of these flux ropes would
perhaps be expected to relax into the constant a
force-free flux rope state, the lowest energy
state of a helical magnetic field, after some
time. If the process responsible for the creation
of these flux ropes is multiple X point
reconnection and if it is occurring close to the
point where the flux ropes are observed, the flux
ropes might not have had time to fully relax into
this force-free state. However, as the flux in
the centre of the flux ropes would have
reconnected before that in the outer sections,
the central flux would have had more time to
begin the evolution towards a force-free
configuration. The outer sections would therefore
be expected to less force-free than the centre,
as observed in both flux ropes reported here.
Fig. 1. The topology of a force-free helical flux
rope. An cartoon spacecraft trajectory is marked,
along with the variance coordinate system that
would arise from a constant a force-free flux
rope.

• Conclusions
• Conspicuously few well-formed flux ropes were
  found in the 2003 Cluster tail season.
• Both flux ropes investigated here were found not
  to be in a force-free configuration, demonstrated
  by the computation of the J ? B forces inside the
  flux ropes.
• J ? B was larger in the outer sections and
  magnetic pressure dominated in both flux ropes.
• Electron pressure was reduced inside the flux
  ropes suggesting a compressional force from the
  plasma.
• Flux rope axis do not always correspond to the
  intermediate variance direction of the magnetic
  field, in one case the axis is close to the
  maximum variance direction.
• Flux rope bipolar signatures were small and slow
  moving, determined with multi-spacecraft timing
  and CIS ion moments.
• Observation of a tailward moving flux rope at X
  (GSM) -18RE suggests that multiple X line
  reconnection must have occurred Earthwards of
  this point.

the flux rope centre with magnetic tension acting
towards the centre. This flux rope is magnetic
pressure dominated, with J ? B acting away from
the flux rope centre, i.e. acting to make the
flux rope expand. J ? B is larger in the outer
sections of the flux rope. The electron pressure
is reduced inside the flux rope suggesting a
compressional force from the plasma.
The simplest flux rope model is the force-free
flux rope (Fig. 1). This model represents the
minimum energy state for helical magnetic field
lines and could therefore represent the cores of
well developed, fully evolved flux ropes observed
in the deep tail.
Minimum variance analysis has previously been
used in an attempt to determine the orientation
of flux ropes. For the force-free model, a
variance analysis on the magnetic field gives an
intermediate variance direction which corresponds
to the axis of the flux rope. The minimum
variance direction will lie along the trajectory
(Fig. 1). In 2003 the separation of the Cluster
spacecraft was only 200 km. This small separation
means that the curolmeter technique (Dunlop et
al., 2002) can be used to determine the internal
current systems in small flux ropes observed in
the near-tail region. Multi-spacecraft timing can
also be used to probe the internal structure of
flux ropes. By noting the time at which different
spacecraft measure the same level of B, the
rotation of the flux rope can be observed. This
can then be used to determine the axis direction
of flux ropes (Fig. 2).
Fig. 4a. Current (J?, J, min var coords and
J), relative curlometer error, magnetic forces
(pressure and tension in min var coords),
electron pressure and magnetic field observations
(BZ and B) from 2nd October flux rope. Fig.
4b. Multi-spacecraft timing and curlometer
results, with the resolution of the magnetic
forces in variance space
Fig. 2. Multi-spacecraft timing from constant
flux surfaces. In this way, the axis direction
can be determined.
Results and discussion
In Fig. 3a, at 005200 UT, a large enhancement
in B can be seen along with a south-then-north
bipolar BZ signature. At this time enhancements
in BX (positive), BY (negative) and BZ (positive)
show that the flux rope core field should be
aligned in the X Y Z direction. CIS ion
velocity moments show that the ambient plasma is
moving Earthward ( 150 kms-1) and duskward (
150 kms-1).
References Dunlop, M. W., et al., Four-point
cluster application of magnetic field analysis
tools The Curlometer, J Geophys. Res., 107,
1384, 2002. Slavin, J. A., et al., Geotail
observations of magnetic flux ropes in the plasma
sheet, J. Geophys. Res., 108, 1015, 2003.