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Extrapolation of coronal magnetic fields from photospheric measurements

Extrapolation of coronal magnetic fields from photospheric measurements. M. Fuhrmann* , G. Valori**, B. Kliem**, N. Seehafer* * Universität Potsdam; ** AIP. General Discussion. Assumption: force-free:  with

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Extrapolation of coronal magnetic fields from photospheric measurements

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  1. Extrapolation of coronal magnetic fields from photospheric measurements M. Fuhrmann*, G. Valori**, B. Kliem**, N. Seehafer* * Universität Potsdam; ** AIP

  2. General Discussion • Assumption: force-free:  with • Force-free condition holds above 400km • Measurements might be affected by non-magnetic effects • Extrapolation should take into account of plasma conditions

  3. The Method • MHD Relaxation: Magnetofrictional Relaxtion • Initialization:Potential Field (α=0): reprodruces the normal component of photospheric boundary of vector magnetogram • Stress:Overwrite the transversal component of the magnetic field • Relax: artificially evolve the field towards a nonlinear force-free state keeping fixed the boundary at z=0. MHD equations contain a friction term, dissipates the flow induced by lorentzforce  static equilibrium to

  4. Test case & Reality Low&Lou Bastille Event

  5. Preprocessing • Problems on real magnetograms • Force-free ? • Noise (lack of smootheness) • Hidden problems? • Philosophy: • Different mgms, close to the original one • Staying within given errorbars

  6. Force-freeness [Molodenskii (1969)] Magnetic-field Stress Tensor T with ext. forces F Force-free condition leads to some integral properties Smootheness Current Method: Laplacian Results not satisfactory Preprocessing: Minimization

  7. Quality of force-freeness

  8. Conclusions • Extrapolation successful, but on real cases lack of force-freeness (σJ ~ 10-1) • Preprocessing: • successful to make magnetogram force-free  better agreement with initial assumption  slightly better results, but not enough • Difficulties to smooth without flattening  have to find a better smoothing term!

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