1. SDO-meeting Napa, 25.-28.03. 2008 Wiegelmann et al: Nonlinear force-free fields 1 A brief summary about nonlinear force-free coronal magnetic field modelling for SDO T. Wiegelmann and J.K. Thalmann Solar magnetic field vector measured in photosphere with SDO/HMI. Extrapolate field into the corona. Low-β coronal plasma => Nonlinear force-free fields

2. SDO-meeting Napa, 25.-28.03. 2008 Wiegelmann et al: Nonlinear force-free fields 2 NonLinear Force-Free Fields Compute initial a potential field (Requires only B n on bottom boundary) Iterate for NLFFF-field, Boundary conditions: - B n and J n for positive or negative polarity on boundary (Grad-Rubin method) - Magnetic field vector B x B y B z on boundary (MHD-relaxation, Optimization method) Equivalent

3. SDO-meeting Napa, 25.-28.03. 2008 Wiegelmann et al: Nonlinear force-free fields 3 -Minimize L numerically. -Boundary condition: Photospheric B-field vector. -Noise and inconsistencies in vector magnetograms require preprocessing.

4. SDO-meeting Napa, 25.-28.03. 2008 Wiegelmann et al: Nonlinear force-free fields 4 Coronal Magnetic Field Nonlinear Force-free code Preprocessing tool Vector magnetogram H-Alpha Image Chromospheric Magnetic Field Optional

5. SDO-meeting Napa, 25.-28.03. 2008 Wiegelmann et al: Nonlinear force-free fields 5 Magnetic energy builds up and is releases during flare Plan: Study flaring ARs with higher time cadence with SDO Evolution of a flaring active region (Thalmann & Wiegelmann A&A 2008, Data from Solar Flare Telescope, Japan)

6. SDO-meeting Napa, 25.-28.03. 2008 Wiegelmann et al: Nonlinear force-free fields 6 Outlook: Self-consistent B-Field and Plasma model Force-free code Vector magnetogram MHS code Force-free magnetic field -Length+shape of loops -Magnetic field strength -Electric current density compare STEREO images Plasma along magnetic loops Scaling laws Artificial images LOS-integration Tomography Self-consistent equilibrium

7. SDO-meeting Napa, 25.-28.03. 2008 Wiegelmann et al: Nonlinear force-free fields 7