Reconstruction of the Coronal Magnetic Field Using the Cese-MHD Method

Jiang, Chaowei; Feng, Xueshang; Fan, Yaofu; Xiang, Changqing

doi:10.1088/0004-637x/727/2/101

Cited by 42 publications

(46 citation statements)

References 48 publications

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“…At t = 0 a potential field extrapolation is used to fill the coronal volume, and after each update of the normal field and velocities on the boundary, the system is allowed to relax to a new equilibrium. The boundary velocities are derived from either (a) local correlation tracking methods [2,3,9], (b) imposed density perturbations proportional to the horizontal magnetic field magnitude at the surface [10,11], or (c) by the method of MHD characteristics [27].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Testing the Accuracy of Data-driven MHD Simulations of Active Region Evolution

Leake

Linton

Schuck

2017

ApJ

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Models for the evolution of the solar coronal magnetic field are vital for understanding solar activity, yet the best measurements of magnetic field lie at the photosphere, necessitating the development of coronal models which are "data-driven" at the photosphere. We present an investigation to determine the feasibility and accuracy of such methods. Our validation framework uses a simulation of active region (AR) formation, modeling the emergence of magnetic flux from the convection zone to the corona, as a ground-truth dataset, to supply both the photospheric information, and to perform the validation of the data-driven method. We focus our investigation on how the datadriven model accuracy depends on the temporal frequency of the driving data. The Helioseismic and Magnetic Imager on NASA's Solar Dynamics Observatory produces full-disk vector magnetic field measurements at a 12 minute cadence. Using our framework we show that ARs that emerge over 25 hours can be modeled by the data-driving method with only ∼1% error in the free magnetic energy, assuming the photospheric information is specified every 12 minutes. However, for rapidly evolving features, under-sampling of the dynamics at this cadence leads to a strobe effect, generating large electric currents and incorrect coronal morphology and energies. We derive a sampling condition for the driving cadence based on the evolution of these small-scale features, and show that higher-cadence driving can lead to acceptable errors. Future work will investigate the source of errors associated with deriving plasma variables from the photospheric magnetograms as well as other sources of errors such as reduced resolution and instrument bias and noise.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Testing the Accuracy of Data-driven MHD Simulations of Active Region Evolution

Leake

Linton

Schuck

2017

ApJ

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“…-Vertical integration: the method consists in propagating the boundary conditions into the corona from the bottom boundary, layer by layer Cuperman, Ofman, and Semel, 1989, 1990a, 1990bWu et al, 1990;Démoulin, Cuperman, and Semel, 1992;Song et al, 2006Song et al, , 2007. -MHD evolutionary techniques: based on the low plasma-β MHD equations, an initial configuration including electric currents is relaxed to a nonlinear force-free state owing to resistivity, also know as stress-and-relax models (Yang, Sturrock, and Antiochos, 1986;Mikic, Barnes, and Schnack, 1988;Schnack et al, 1990;McClymont and Mikic, 1994;Roumeliotis, 1996;Valori, Kliem, and Keppens, 2005;Valori, Kliem, and Fuhrmann, 2007;Valori et al, 2010;Jiang et al, 2011). -Optimization: the basic principle is to minimise a functional containing the force-free constraint as well as the solenoidal constraint to relax an initial configuration towards a nonlinear force-free state (Wheatland, Sturrock, and Roumeliotis, 2000;Wiegelmann, 2004;Wiegelmann et al, 2005Wiegelmann et al, , 2008Wiegelmann, Inhester, and Sakurai, 2006;Inhester and Wiegelmann, 2006;Wiegelmann and Neukirch, 2006;Tadesse, Wiegelmann, and Inhe 2009;Mysh'yakov and Rudenko, 2009;Wiegelmann and Inhester, 2010;Fuhrmann et al, 2011).…”

Section: Nonlinear Force-free Fieldmentioning

confidence: 99%

Magnetic Field Extrapolations into the Corona: Success and Future Improvements

Régnier

2013

Sol Phys

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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).

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“…Due to the lack of measurement data, the three-dimensional magnetic field in the solar corona is usually "extrapolated" or "reconstructed" in numerical ways from the photosphere surface data based on particular assumptions or models. Such techniques of modeling the coronal magnetic field have been developed (e.g., see review papers of Sakurai 1989;Mc-time scheme (CESE-MHD-NLFFF: Jiang et al 2011;Jiang & Feng 2012a, 2013. Now NLFFF models are widely used in the solar physics community for exploring the 3D coronal structure prior to and post solar eruptions and for understanding the influence of the magnetic topology on solar eruptions (e.g., Guo et al 2008;Sun et al 2012;Cheng et al 2014;Liu et al 2014;Xue et al 2016).…”

Section: Introductionmentioning

confidence: 99%

Comparison of Two Coronal Magnetic Field Models to Reconstruct a Sigmoidal Solar Active Region with Coronal Loops

Duan

Jiang

et al. 2017

ApJ

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Magnetic field extrapolation is an important tool to study the three-dimensional (3D) solar coronal magnetic field which is difficult to directly measure. Various analytic models and numerical codes exist but their results often drastically differ. Thus a critical comparison of the modeled magnetic field lines with the observed coronal loops is strongly required to establish the credibility of the model. Here we compare two different non-potential extrapolation codes, a non-linear force-free field code (CESE-MHD-NLFFF) and a non-forcefree field (NFFF) code in modeling a solar active region (AR) that has a sigmoidal configuration just before a major flare erupted from the region. A 2D coronal-loop tracing and fitting method is employed to study the 3D misalignment angles between the extrapolated magnetic field lines and the EUV loops as imaged by SDO/AIA. It is found that the CESE-MHD-NLFFF code with preprocessed magnetogram performs the best, outputting a field which matches the coronal loops in the AR core imaged in AIA 94 Å with a misalignment angle of ∼ 10 • . This suggests that the CESE-MHD-NLFFF code, even without using the information of coronal loops in constraining the magnetic field, performs as good as some coronal-loop forward-fitting models. For the loops as imaged by AIA 171 Å in the outskirts of the AR, all the codes including the potential-field give comparable results of mean misalignment angle (∼ 30 • ). Thus further improvement of the codes is needed for a better reconstruction of the long loops enveloping the core region. . Three magnetic field models often used include the potential field, linear force-free field (LFFF), and nonlinear force-free field (NLFFF). All these models are derived from a basic assumption that the Lorentz force in the corona vanishes in the case of extremely low plasma β (β is the ratio of the plasma pressure to the magnetic pressure) and quasi-static equilibrium of the coronal field. Consequently the electric current J = ∇ × B must be parallel to the magnetic field, i.e., J = αB where α is called the force-free parameter. In the potential field model, α = 0; in the LFFF, α is a constant; and in the NLFFF, α is variable in space. The earliest models were based on potential field (Altschuler & Newkirk 1969;Sakurai 1982) and LFFF (Seehafer 1978) that are extrapolated from only the data of line-of-sight (LoS) component of the photospheric field since the transverse components were not measured. Now both the LoS and transverse components of the photospheric magnetic field can be measured (e.g., Hoeksema et al. 2014) and information of the electric current passing through the photosphere can derived. Nonlinear force-free field (NLFFF) reconstructions, which are based on the vector magnetograms, are more robust than those earlier models, and employ several numerical schemes

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Reconstruction of the Coronal Magnetic Field Using the Cese-MHD Method

Cited by 42 publications

References 48 publications

Testing the Accuracy of Data-driven MHD Simulations of Active Region Evolution

Testing the Accuracy of Data-driven MHD Simulations of Active Region Evolution

Magnetic Field Extrapolations into the Corona: Success and Future Improvements

Comparison of Two Coronal Magnetic Field Models to Reconstruct a Sigmoidal Solar Active Region with Coronal Loops

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