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Magnetic structure of the disk corona

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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.

Squashing factor Q

- Geometrical definition:
- Infinitezimal flux tube such that a cross-section at one foot is curcular, then circle ==> ellipse:

(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:

- 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.

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

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

Numerical MHD

K

-1 0 1

Exact ideal MHD

-10 0 10

Numerical MHD

log Q

K

1 2

-1 0 1

Exact ideal MHD

-10 0 10

Magnetic field lines

Launch footpoints

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).