1. 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

2. 2 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 )

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

4. 4 x: projected s/c path - V HT 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:

5. 5 Output: 1.Field configuration 2.Spatial config. 3.Electric Current. 4.Plasma pressure p(A). 5.Magnetic Flux  ： - axial (toroidal) flux  t =  B z  x  y - poloidal flux  p =|A b - A m |*L 6.Relative Helicity: K rel =2L  A’· B t dxdy  A’=B z z ^ GS Reconstruction of ICME Flux Ropes ( 1D  2D) Ab Ab AmAm ACE Halloween event (Hu et al. 2005)

6. 6 Relative magnetic helicity ( Webb et al. 2010 ): B z (x,y) r Kr/AU: 3.5 x 10 23 Wb 2 Kr/AU ( Hu and Dasgupta, 2005 ): 3.4 x 10 23 Wb 2

7. 7 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 formation (Gosling et al. 1995) (Moore et al. 2007) Credit: ESA reconnection

8. 8 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

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

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

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

12. (Farrugia et al. 2011) Sun Wind ST-AST-B

13. 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) ~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+B z /2  0 fitting 2

17. Event 2005/10/30 00:00:00 - 2005/11/02 00:00:00 DOY 303-306 ~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. … Fully 3D? zr R Sun GS equation: (R. H. Weening, 2000) A torus of arbitrary cross section?