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Magnetic structure of the disk corona

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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  1. 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

  2. 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!

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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

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

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

  10. Helical QSL (t=238) Magnetic field lines Launch footpoints

  11. 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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