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

• Recent modeling and comparison of flux-rope flux and helicity contents (Kazachenko et al. 2011)

• 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

(Farrugia et al. 2011)

Sun

Wind ST-AST-B

Acknowledgement: Dr. J. Luhmann of UCB/SSL, and Dr. Antoinette Galvin of the University of New Hampshire, and NASA CDAWeb.

•Effect of Te (2007/01/13 00:00:00 - 2007/01/17 00:00:00 DOY 013-017)

<Te/Tp>~12<>~0.24

• The GS reconstruction map for the case w/o (left window) and w/ (right) Te contribution, respectively

• The corresponding Pt(A)=p+Bz/20 fitting2

Event 2005/10/30 00:00:00 - 2005/11/02 00:00:00 DOY 303-306

<Te/Tp>~4<>~1

• The GS reconstruction map for the case w/o (left window) and w/ (right) Te contribution, respectively

• The corresponding Pt(A) fitting

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

… Fully 3D?

z r

RSun

])2[(]/)/1[(

02

02

2

d

dGG

d

dpr

zr

rrr

GS equation:(R. H. Weening, 2000)

A torus of arbitrary cross section?