Living Reviews in Solar Physics

"Topological Methods for the
Analysis of Solar Magnetic Fields"
Dana W. Longcope  

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1 Introduction
2 Field Lines and Null Points
2.1 Magnetic field lines
2.2 Physical significance of magnetic field lines
2.3 Magnetic discontinuities
2.4 Null points
2.5 Topological changes: Reconnection
3 Footpoints and Footpoint Mappings
3.1 Anchoring and line tying
3.2 Field extrapolation
3.3 Footpoint mapping as a dynamical constraint
3.4 Topological models of anchored fields
4 Magnetic Charge Topology Models
4.1 The photospheric field
4.2 Skeletons
4.3 Connectivity
4.4 Applications
5 Pointwise Mapping Models
5.1 Mapping discontinuities: Coronal fans and bald patches
5.2 Quasi-separatrix layers
6 Submerged Poles Models
6.1 The method
6.2 Comparisons with observations
6.3 Separatrices and QSLs
7 Coronal Null Points
8 Topology of the Heliospheric Magnetic Field
8.1 The solar wind
8.2 Open/closed boundaries
8.3 Magnetic clouds and coronal mass ejections
9 Conclusion
10 Acknowledgements
Open References References