Grad-Shafranov reconstruction of a bipolar Bz signature in an earthward jet in the tail

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Grad-Shafranov reconstruction of a bipolar Bz
signature in an earthward jet in the tail

• Hiroshi Hasegawa
• ISAS/JAXA
• _at_Uppsala (2007/02/14)

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Observation of bipolar Bz
to - Bz (GSM) in the mid- to distant-tail
along with tailward flows studied in
association with substorms (Ieda et al., 1998,
etc.)
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Earthward moving flux rope? - to Bz often
seen in the near-tail (from Geotail and Cluster
observations).
Slavin et al. (2003)
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Superposed epoch analysis
Core By field Observed along with earthward
flows (BBFs)
Slavin et al. (2003)
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Models for bipolar Bz in earthward flows
Vz
Multiple X-line reconnection (forming magnetic
flux ropes) (e.g., Slavin et al., 2003)
Transient reconnection (e.g., Sergeev et al.,
1992) Localized reconnection under guide-field
By (Shirataka et al., 2006)
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2002-08-13 Cluster event (2200-2400 UT)
Studied by Amm et al. (2006) associated with a
substorm (onset at 2250 UT)
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2002-08-13 Cluster event (2312-2318 UT) -/ Bz
embedded in an earthward flow C3 exactly at
the center of the current sheet C1, 2, 4 on
the northern side Separation 4000 km
Bx
Bz
Vx
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Grad-Shafranov reconstruction technique (Hau
Sonnerup, 1999) (A spatial initial value
problem) Assumptions Plasma structures are in
magnetohydrostatic equilibria (time-independent).
Magnetic field tension balances with force from
the gradient of total (magnetic plasma)
pressure.
2-D (no spatial gradient in the z
direction) Grad-Shafranov (GS) equation (e.g.,
Sturrock, 1994)
Pt, p, and Bz are functions of A alone (constant
on same field lines).
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Reconstruction procedure
A 2D structure
Reconstruction plane
Y
Spatial integration
Y
VST_X
X
X
VST (VHT) (in the x-z plane)
Lx VST_X T (analyzed interval) X axis SC
trajectory in the x-y plane
Z (invariant axis)
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Spatial initial value problem
(Sonnerup Guo, 1996)
Grad-Shafranov equation
spatial integration in -/ y direction
(2nd order Taylor exp.)
(1st order Taylor exp.)
GS eq.
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z
x
cc 0.961
Roughly circular flux rope Flux rope with
half width of 1 Re Strong core field (mostly
By)
VHT (237, 27, 23) km/s in GSM i (-0.999,
0.042, 0.005) j (-0.022, -0.621, 0.784) k
(0.036, 0.783, 0.621)
Consistent with multiple X-line models?
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3D-MHD simulation of localized reconnection with
guide-field (Shirataka et al., 2006)
guide-fieldBy0
The Northern hemisphere
2Ry
The plane of the equator
2Ry 3 Re
The Southern hemisphere
Slavin et al. 2003
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Results
Reproducing the southward magnetic field
Shirataka et al. (2006)
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Results
Virtual S/C obs. in the MHD run
Bz z0
11.25Re
By04nT, 2Ry3.0Re
t135s
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Virtual observation vs real data
What will be reconstructed, when applied to the
simulation data in which no flux rope is created?
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Virtual spacecraft observations _at_ (x,y,z)
(11.25, 0, 0), (11.25, 0, 1), (11.25, 1,
0), (11.25, 2, 0) Re Applied to the interval T
105 195 s (A suitable model may be
determined if the separation is 2Re. )
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GS map recovered from virtual observation
Map recovered from data sampled at (x,y,z)
(11.25, 0, 0) Re
A flux rope, which does not really exist in the
simulation, is reconstructed erroneously.
Z(GS) (0.000, 0.996, 0.087)
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Map recovered from data sampled at (x,y,z)
(11.25, 1, 0) Re
The presence of a flux rope-like structure in
GS maps does not necessarily mean that it exists
in reality. But, are GS results totally
meaningless?
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Map recovered from data sampled at (x,y,z)
(11.25, 0, 0) Re
Simulation result at the time when Bz reversal is
at x11.25 Re (in the same plane)
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Map recovered from data sampled at (x,y,z)
(11.25, 1, 0) Re
Simulation result at the time when Bz reversal is
at x11.25 Re (in the same plane)
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Which model is more reasonable (for the Cluster
event)? CL event Roughly circular Pressure
minimum at the core
Simulation result Elongated in the x
direction Enhanced P at the front
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Summary The GS method cannot accurately recover
the magnetic topology. One must be cautious
about interpretation of model-based (force-free,
or GS model) results. It seems possible to
get some information on the basic structure
(shape, pressure distribution, etc.) in the
reconstruction plane. The Cluster bipolar Bz
event on 2001-08-13 is most likely explained by a
flux rope (multiple X-line reconnection). A
suitable separation distance for discriminating
models is a few Re (comparable to the jet width).