Magnetic Field Extrapolations in the Corona: Success and Future Improvements

Abstract

The solar atmosphere being magnetic in nature, the understanding of the structure and evolution of the magnetic field in different regions of the solar atmosphere has been an important task over the past decades. This task has been made complicated by the difficulties to measure the magnetic field in the corona, while it is currently known with a good accuracy in the photosphere and/or chromosphere. Thus, to determine the coronal magnetic field, a mathematical method has been developed based on the observed magnetic field. This is the so-called magnetic field extrapolation technique. This technique relies on two crucial points: (i) the physical assumption leading to the system of differential equations to be solved, (ii) the choice and quality of the associated boundary conditions. In this review, I summarise the physical assumptions currently in use and the findings at different scales in the solar atmosphere. I concentrate the discussion on the extrapolation techniques applied to solar magnetic data and the comparison with observations in a broad range of wavelengths (from hard X-rays to radio emission).

arXiv commentAccepted in Solar Physics

References in corpus (63)

• Optimization code with weighting function for the reconstruction of coronal magnetic fields
• Preprocessing of vector magnetograph data for a non-linear force-free magnetic field reconstruction
• Evolution of Magnetic Field and Energy in A Major Eruptive Active Region Based on SDO/HMI Observation
• A Critical Assessment of Nonlinear Force-Free Field Modeling of the Solar Corona for Active Region 10953
• Non-linear force-free field modeling of a solar active region around the time of a major flare and coronal mass ejection
• Generalized Squashing Factors for Covariant Description of Magnetic Connectivity in the Solar Corona
• The Sun's Global Photospheric and Coronal Magnetic Fields: Observations and Models
• Sympathetic Partial and Full Filament Eruptions Observed in One Solar Breakout Event
• Magnetic Reconnection along Quasi-Separatrix Layers as a Driver of Ubiquitous Active Region Outflows
• Solar Magnetic Tracking. I. Software Comparison and Recommended Practices
• A Comparative Study of Confined and Eruptive Flares in NOAA AR 10720
• Multiwavelength Observations of Small-Scale Reconnection Events triggered by Magnetic Flux Emergence in the Solar Atmosphere
• Magnetic Energy and Helicity Budgets in the Active-Region Solar Corona. II. Nonlinear Force-Free Approximation
• Evidence of Magnetic Helicity in Emerging Flux and Associated Flare
• An optimization principle for the computation of MHD equilibria in the solar corona
• Free Magnetic Energy in Solar Active Regions above the Minimum-Energy Relaxed State
• Spatial analysis of solar type III events associated with narrow band spikes at metric wavelengths
• Testing magnetofrictional extrapolation with the Titov-Démoulin model of solar active regions
• A new view of quiet-Sun topology from Hinode/SOT
• A self-consistent nonlinear force-free solution for a solar active region magnetic field
• Extrapolation of the solar magnetic field within the potential-field approximation from full-disk magnetograms
• Can We Improve the Preprocessing of Photospheric Vector Magnetograms by the Inclusion of Chromospheric Observations?
• Including stereoscopic information in the reconstruction of coronal magnetic fields
• Spatially and Spectrally Resolved Observations of a Zebra Pattern in Solar Decimetric Radio Burst
• Nonlinear force-free models for the solar corona I. Two active regions with very different structure
• Guiding Nonlinear Force-Free Modeling Using Coronal Observations: First Results Using a Quasi Grad-Rubin Scheme
• Nonlinear force-free magnetic field extrapolations: comparison of the Grad-Rubin and Wheatland-Sturrock-Roumeliotis algorithm
• A Practical Approach to Coronal Magnetic Field Extrapolation Based on the Principle of Minimum Dissipation Rate
• A Quantitative Model of Energy Release and Heating by Time-dependent, Localized Reconnection in a Flare with a Thermal Loop-top X-ray Source
• Motions of Hard X-ray Sources During an Asymmetric Eruption
• Nonlinear force-free coronal magnetic field modelling and preprocessing of vector magnetograms in spherical geometry
• Optimization approach for the computation of magnetohydrostatic coronal equilibria in spherical geometry
• Time Evolution of Coronal Magnetic Helicity in the Flaring Active Region NOAA 10930
• First nonlinear force-free field extrapolations of SOLIS/VSM data
• Evolution of Hard X-ray Sources and Ultraviolet Solar Flare Ribbons for a Confined Eruption of a Magnetic Flux Rope
• Modeling X-ray Loops and EUV "Moss" in an Active Region Core
• Achieving Self-Consistent Nonlinear Force-free Modeling of Solar Active Regions
• Reconstructing the Local Twist of Coronal Magnetic Fields and the Three-Dimensional Shape of the Field Lines from Coronal Loops in EUV and X-Ray Images
• Nonlinear Force-Free Magnetic Field Fitting to Coronal Loops with and without Stereoscopy
• How to use magnetic field information for coronal loop identification?
• A Nonlinear Force-Free Magnetic Field Approximation Suitable for Fast Forward-Fitting to Coronal Loops. I. Theory
• Bootstrapping the Coronal Magnetic Field with STEREO: I. Unipolar Potential Field Modeling
• Segmentation of Loops from Coronal EUV Images
• Nonlinear force-free reconstruction of the global solar magnetic field: methodology
• Re-flaring of a Post-Flare Loop System Driven by Flux Rope Emergence and Twisting
• A comparison of preprocessing methods for solar force-free magnetic field extrapolation
• A Magnetostatic Grad-Rubin Code for Coronal Magnetic Field Extrapolations
• Flows at the Edge of an Active Region: Observation and Interpretation
• Understanding the white-light flare on 2012 March 9 : Evidence of a two-step magnetic reconnection
• Seismic Emissions from a Highly Impulsive M6.7 Solar Flare
• Nonlinear force-free modelling: influence of inaccuracies in the measured magnetic vector
• A Nonlinear Force-Free Magnetic Field Approximation Suitable for Fast Forward-Fitting to Coronal Loops. III. The Free Energy
• Coronal Alfven speeds in an isothermal atmosphere I. Global properties
• The free energy of NOAA active region AR 11029
• Constraining 3D Magnetic Field Extrapolations Using The Twin Perspectives of STEREO
• The Force-Free Electrodynamics Method for the Extrapolation of Coronal Magnetic Fields from Vector Magnetograms
• Study on two Methods for Nonlinear Force-free Extrapolation Based on Semi-Analytical Field
• Solar Magnetic Carpet I: Simulation of Synthetic Magnetograms
• Magnetic Energy Storage and Current Density Distributions for Different Force-Free Models
• Solar Magnetic Carpet II: Coronal Interactions of Small-Scale Magnetic Fields
• Gyrokinetic electron acceleration in the force-free corona with anomalous resistivity
• Reversed Drifting Quasi-periodic Pulsating Structure in an X1.3 Solar Flare on 2005 July 30
• Study of the three-dimensional shape and dynamics of coronal loops observed by Hinode/EIS

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• A new approach to the maser emission in the solar corona
• Comparison of Two Coronal Magnetic Field Models for Reconstructing a Sigmoidal Solar Active Region With Coronal Loops
• Magnetohydrodynamic modeling of solar coronal dynamics with an initial non-force-free magnetic field
• The role of asymmetries in coronal rain formation during thermal non-equilibrium cycles
• On the Area Expansion of Magnetic Flux-Tubes in Solar Active Regions
• A Study of Pre-flare Solar Coronal Magnetic Fields: Magnetic Energy and Helicity
• Optimizing Global Coronal Magnetic Field Models Using Image-Based Constraints
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• Analytical Three-dimensional Magnetohydrostatic Equilibrium Solutions for Magnetic Field Extrapolation Allowing a Transition from Non-force-free to Force-free Magnetic Fields
• Magnetohydrostatic modelling of stellar coronae
• The effect of spatial sampling on magnetic field modeling and helicity computation
• Toward a fast and consistent approach to model solar magnetic fields in multiple layers
• Effect of Size of the Computational Domain on Spherical Nonlinear Force-Free Modeling of Coronal Magnetic Field Using SDO/HMI Data
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