1. Magnetic structure of the disk corona Slava Titov, Zoran Mikic, Alexei Pankin, Dalton Schnack SAIC, San Diego Jeremy Goodman, Dmitri Uzdensky Princeton University CMSO General Meeting, October 5-7, 2005 Princeton

2. 1 2D case: field line connectivity and topology normal field line NP separtrix field line BP separtrix field line Flux tubes enclosing separatrices split at null points or "bald-patch" points. They are topological features, because splitting cannot be removed by a continous deformation of the configuration. Current sheets are formed at the separatrices due to footpoint displacements or instabilities. All these 2D issues can be generalized to 3D!

3. 2 Differences compared to nulls and BPs: squashing may be removed by a continuous deformation, => QSL is not topological but geometrical object, metric is needed to describe QSL quantitatively, => topological arguments for the current sheet formation at QSLs are not applicable; other approach is required. Extra opportunity in 3D: squashing instead of splitting Nevertheless, thin QSLs are as important as genuine separatrices for this process.

4. 3 Definition of Q in coordinates: where a, b, c and d are the elements of the Jacobian matrix D and then Q can be determined by integrating field line equations. Geometrical definition: Infinitezimal flux tube such that a cross-section at one foot is curcular, then circle ==> ellipse: Q = aspect ratio of the ellipse ; Q is invariant to direction of mapping. Squashing factor Q (Titov, Hornig & Démoulin, 2002)

5. 4 Geometrical definition: Infinitezimal flux tube such that a cross-section at one foot is curcular, then circle ==> ellipse: K = lg(ellipse area / circle area); K is invariant (up to the sign) to the direction of mapping. Expansion-contraction factor K Definition of K in coordinates: where a, b, c and d are the elements of the Jacobian matrix D and then Q can be determined by integrating field line equations.

6. 5 What can we obtain with the help of Q and K? 1.Identify the regions subject to boundary effects. 2.Understand the effect of resistivity. 3.Identify the reconnecting magnetic flux tubes.

7. 6 Example (t=238) Exact ideal MHDNumerical MHD log Q 1 2 -10 0 10 From the initial B(r) and v dsk (r dsk,t) only! From the computed B(r,t).

8. 7 Example (t=238) Exact ideal MHDNumerical MHD K -1 0 1 -10 0 10

9. 8 Example (t=238) Exact ideal MHDNumerical MHD log Q 1 2 -10 0 10 K -1 0 1

10. 9 Helical QSL (t=238) Magnetic field linesLaunch footpoints

11. 10 Conclusions Evolving Q and K distributions make possible: 1.to identify the regions subject to boundary effects, 2.to understand the effect of resistivity, 3.to identify the reconnecting magnetic flux tubes (helical QSL).