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The Structure of Magnetic Clouds in the Inner Heliosphere: An Approach
Through Grad-Shafranov Reconstruction
Qiang Hu, Charlie J. Farrugia, V. Osherovich, Christian Möstl,
Jiong Qiu and Bengt U. Ö. Sonnerup
ILWS Workshop 2011
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Coronal Mass Ejection (CME)
(Moore et al. 2007)
Simultaneous multi-point in-situ measurements of an Interplanetary CME
(ICME) structure(Adapted from STEREO/IMPACT website, http://sprg.ssl.berkeley.edu/impact/instruments_boom.html)
3in-situ spacecraft data
Cylindrical flux-rope model fit (Burlaga, 1995; Lepping et al., 1990, etc.)
Modeling of Interplanetary CME
4x: projected s/c pathx: projected s/c path
-VHT
Grad-Shafranov Reconstruction method: derive the axis orientation (z) and the cross section of locally 2 ½ D structure from in-situ single spacecraft measurements (e.g., Hu and Sonnerup 2002).
•Main features:
- 2 ½ D
- self-consistent
- non-force free
- flux rope boundary definition
- multispacecraft
actual result:actual result:
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• Output:1. Field configuration2. Spatial config.3. Electric Current.4. Plasma pressure p(A).5. Magnetic Flux :
- axial (toroidal) flux t= Bzxy- poloidal flux p=|Ab - Am|*L
• Relative Helicity:Krel=2L A’· Bt dxdy
A’=Bzz^
GS Reconstruction of ICME Flux Ropes (1D2D)
• Ab
Am
ACE Halloween event (Hu et al. 2005)
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• Relative magnetic helicity (Webb et al. 2010):
Bz(x,y)
rKr/AU: 3.5x1023 Wb2
Kr/AU (Hu and Dasgupta, 2005):
3.4x1023 Wb2
ˆ2 ' , ' ', 'r t zVK dV B A B A B B z
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poloidal or azimuthal magnetic flux P:
the amount of twist along the field lines
The helical structure, in-situ formed flux rope, results from magnetic reconnection.
toroidal or axial magnetic flux t
Longcope et al (2007)
ribbons
poloidal flux P
reconnection flux r
reconnection
3D view: one scenario of flux rope formation3D view: one scenario of flux rope formation3D view: one scenario of flux rope formation3D view: one scenario of flux rope formation
(Gosling et al. 1995)
(Moore et al. 2007)
Credit: ESA
reconnection
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• Comparison of CME and ICME fluxes (independently measured for 9 events; Qiu et al., 2007):
- flare-associated CMEs and flux-rope ICMEs with one-to-one correspondence; - reasonable flux-rope solutions satisfying diagnostic measures; - an effective length L=1 AU (uncertainty range 0.5-2 AU) .
GS method
Leamon et al. 04
Lynch et al. 05
P ~ r
• GS Reconstruction of Locally Toroidal Structure
(Freidberg 1987)
Z
R
O
A torus of arbitrary cross section
s/c
Sun
O’
O
Z’R
r
t
(r, t) plane projection
r’
R s/c path
O (O’)Z’.
(R, ) plane projection
(R, , Z) axes (Z: rotation axis; : torus axis):
Search grid on (r,t) plane
Boundary of the torus
Acknowledgement: Dr. J. Luhmann of UCB/SSL, and Dr. Antoinette Galvin of the University of New Hampshire, and NASA CDAWeb.
• The GS reconstruction map for the case w/o (left window) and w/ (right) Te contribution, respectively
• The GS reconstruction map for the case w/o (left window) and w/ (right) Te contribution, respectively
Concluding Remarks
• Quantitative CME-ICME comparison provides essential insight into the underlying mechanism(s)
• Also provides validation of data analysis methods/results
• Torus-shaped geometry provides an alternative view of MC flux rope; will complement the existing analysis
• The effect of Te is limited to contribution to the plasma and pressure; it is the gradient of pressure that matters