1. The Structure of Magnetic Clouds in the Inner Heliosphere: An ApproachThrough Grad-Shafranov Reconstruction Qiang Hu, Charlie J. Farrugia, V. Osherovich, Christian Möstl, Jiong Qiu and Bengt U. Ö. Sonnerup ILWS Workshop 2011

2. Coronal Mass Ejection (CME) 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) (Moore et al. 2007)

3. Modeling of Interplanetary CME Cylindrical flux-rope model fit (Burlaga, 1995; Lepping et al., 1990, etc.) in-situ spacecraft data

4. 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 ½D • self-consistent • non-force free • flux rope boundary definition • multispacecraft actual result: -VHT x: projected s/c path

5. GS Reconstruction of ICME Flux Ropes (1D2D) • Output: • Field configuration • Spatial config. • Electric Current. • Plasma pressure p(A). • Magnetic Flux ： • - axial (toroidal) flux • t= Bzxy • - poloidal flux • p=|Ab - Am|*L • Relative Helicity: • Krel=2L A’· Btdxdy • A’=Bzz Am • Ab ^ ACE Halloween event (Hu et al. 2005)

6. Relative magnetic helicity (Webb et al. 2010): Bz(x,y) r

7. 3D view: one scenario of flux rope formation poloidal or azimuthal magnetic flux P: the amount of twist along the field lines poloidal flux P (Moore et al. 2007) The helical structure, in-situ formed flux rope, results from magnetic reconnection. Longcope et al (2007) reconnection reconnection (Gosling et al. 1995) reconnection flux r Credit: ESA ribbons toroidal or axial magnetic flux t

8. GS method Leamon et al. 04 Lynch et al. 05 • 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) . P ~ r

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

10. GS Reconstruction of Locally Toroidal Structure R Z O A torus of arbitrary cross section (Freidberg 1987)

11. R s/c path  (R, , Z) axes (Z: rotation axis; : torus axis): s/c Z’ r R . r’ O (O’) O Z’ (R, ) plane projection O’   Sun t Boundary of the torus Search grid on (r,t) plane (r, t) plane projection

12. Sun torus-axis ( direction) at Wind Wind ST-B ST-A (Farrugia et al. 2011)

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

14. Effect of Te (2007/01/13 00:00:00 - 2007/01/17 00:00:00 DOY 013-017) <Te/Tp>~12 <>~0.24

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

16. The corresponding Pt(A)=p+Bz/20 fitting 2

17. Event 2005/10/30 00:00:00 - 2005/11/02 00:00:00 DOY 303-306 <Te/Tp>~4 <>~1

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

19. The corresponding Pt(A) fitting

20. 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

21. A torus of arbitrary cross section? z r R Sun GS equation: (R. H. Weening, 2000) … Fully 3D?