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### Magnetic structureof 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

2D case: field line connectivity and topology

BP separtrix

field line

NP separtrix

field line

normal

field line

disk

- Flux tubes enclosing separatrices split at null pointsor "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!

Extra opportunity in 3D: squashing instead of splitting

- 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 notapplicable;
- other approach is required.

Nevertheless, thin QSLs are as importantas genuine separatrices for this process.

- 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.

(Titov, Hornig & Démoulin, 2002)

- 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.

Expansion-contraction factor K

- 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.

- 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.

What can we obtain with the help of Q and K?

- Identify the regions subject to boundary effects.
- Understand the effect of resistivity.
- Identify the reconnecting magnetic flux tubes.

Example (t=238)

Numerical MHD

log Q

From the initial B(r)

and vdsk(rdsk,t) only!

From the

computed B(r,t).

1 2

Exact ideal MHD

-10 0 10

Conclusions

Evolving Q and K distributions make possible:

- to identify the regions subject to boundary effects,
- to understand the effect of resistivity,
- to identify the reconnecting magnetic flux tubes (helical QSL).

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