Magnetic structure of the disk corona
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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, 200 5 Princeton. 2D case : field line connectivity and topology. BP separtrix

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Magnetic structure of the disk corona

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Magnetic structure of the disk corona

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


Magnetic structure of the disk corona

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!


Magnetic structure of the disk corona

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.


Magnetic structure of the disk corona

Squashing factor Q

  • 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.


    Magnetic structure of the disk corona

    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

    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

    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


    Example t 2381

    Example (t=238)

    Numerical MHD

    K

    -1 0 1

    Exact ideal MHD

    -10 0 10


    Example t 2382

    Example (t=238)

    Numerical MHD

    log Q

    K

    1 2

    -1 0 1

    Exact ideal MHD

    -10 0 10


    Helical qsl t 238

    Helical QSL (t=238)

    Magnetic field lines

    Launch footpoints


    Conclusions

    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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