Living Reviews in Solar Physics

"Solar Force-free Magnetic Fields"
Thomas Wiegelmann and Takashi Sakurai 

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1 Introduction
2 Linear Force-Free Fields
2.1 How to obtain the force-free parameter α
3 Analytic or Semi-Analytic Approaches to Nonlinear Force-Free Fields
3.1 Low and Lou’s (1990) equilibrium
3.2 Titov–Démoulin equilibrium
4 Azimuth Ambiguity Removal and Consistency of Field Measurements
4.1 How to derive vector magnetograms?
4.2 Quantitative comparison of ambiguity removal algorithms
4.3 Ambiguity removal algorithm
4.4 Summary of automatic methods
4.5 Derived quantities, electric currents, and α
4.6 Consistency criteria for force-free boundary conditions
4.7 Preprocessing
5 Nonlinear Force-free Fields in 3D
5.1 Magnetic helicity
5.2 Energy principles
5.3 Maximum energy
5.4 Stability of force-free fields
5.5 Numerical stability investigations
6 Numerical Methods for Nonlinear Force-free Fields
6.1 Upward integration method
6.2 Grad–Rubin method
6.3 MHD relaxation method
6.4 Optimization approach
6.5 Boundary-element methods
6.6 Comparison of methods and the NLFFF consortium
6.7 Application of nonlinear force-free codes
7 Summary and Discussion
8 Acknowledgements
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