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Amari, T.; Aly, J. J.; Luciani, J. F.; Boulmezaoud, Tahar Zamène; Mikić, Z.

doi:10.1023/a:1004966830232

Cited by 191 publications

(193 citation statements)

References 21 publications

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“…The particular case of α = 0 yields a potential field, which is inadequate for many purposes, since it does not contain any free energy to power coronal activity. Therefore, it is necessary to proceed beyond the linear approximation and to solve the nonlinear extrapolation problem, permitting α(x) to vary across the field (Sakurai 1981;McClymont et al 1997;Amari et al 1999). The nonlinearity means that such extrapolation requires a numerical approach.…”

Section: Introductionmentioning

confidence: 99%

Testing magnetofrictional extrapolation with the Titov-Démoulin model of solar active regions

Valori¹,

Kliem

Török³

et al. 2010

A&A

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We examine the nonlinear magnetofrictional extrapolation scheme using the solar active region model by Titov and Démoulin as test field. This model consists of an arched, line-tied current channel held in force-free equilibrium by the potential field of a bipolar flux distribution in the bottom boundary. A modified version with a parabolic current density profile is employed here. We find that the equilibrium is reconstructed with very high accuracy in a representative range of parameter space, using only the vector field in the bottom boundary as input. Structural features formed in the interface between the flux rope and the surrounding arcade -"hyperbolic flux tube" and "bald patch separatrix surface" -are reliably reproduced, as are the flux rope twist and the energy and helicity of the configuration. This demonstrates that force-free fields containing these basic structural elements of solar active regions can be obtained by extrapolation. The influence of the chosen initial condition on the accuracy of reconstruction is also addressed, confirming that the initial field that best matches the external potential field of the model quite naturally leads to the best reconstruction. Extrapolating the magnetogram of a Titov-Démoulin equilibrium in the unstable range of parameter space yields a sequence of two opposing evolutionary phases, which clearly indicate the unstable nature of the configuration: a partial buildup of the flux rope with rising free energy is followed by destruction of the rope, losing most of the free energy.

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Section: Introductionmentioning

confidence: 99%

Testing magnetofrictional extrapolation with the Titov-Démoulin model of solar active regions

Valori¹,

Kliem

Török³

et al. 2010

A&A

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“…Based on the above assumption, the coronal magnetic field is modeled with a nonlinear force-free field (NLFFF) extrapolation Valori et al 2005;Wiegelmann 2004;Wheatland 2004;Wheatland & Régnier 2009;Tadesse et al 2009;Wheatland & Leka 2011;Amari & Aly 2010;Wiegelmann et al 2012;Jiang & Feng 2012). From a mathematical point of view, appropriate boundary condition for force-free modeling are the vertical magnetic field B n and the vertical current J n prescribed only for one polarity of B n (Amari et al 1997(Amari et al , 1999(Amari et al , 2006. A direct use of these boundary conditions is implemented in Grad-Rubin codes (Amari et al 1999).…”

Section: Introductionmentioning

confidence: 99%

“…From a mathematical point of view, appropriate boundary condition for force-free modeling are the vertical magnetic field B n and the vertical current J n prescribed only for one polarity of B n (Amari et al 1997(Amari et al , 1999(Amari et al , 2006. A direct use of these boundary conditions is implemented in Grad-Rubin codes (Amari et al 1999). Wheatland & Régnier (2009) and Wheatland & Leka (2011) implemented the use of B + n and B − n solution together with an error approximation to derive consistent solutions.…”

Section: Introductionmentioning

confidence: 99%

Full-disk nonlinear force-free field extrapolation of SDO/HMI and SOLIS/VSM magnetograms

Tadesse

Wiegelmann

Inhester

et al. 2013

A&A

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Context. The magnetic field configuration is essential for understanding solar explosive phenomena, such as flares and coronal mass ejections. To overcome the unavailability of coronal magnetic field measurements, photospheric magnetic field vector data can be used to reconstruct the coronal field. Two complications of this approach are that the measured photospheric magnetic field is not force-free and that one has to apply a preprocessing routine to achieve boundary conditions suitable for the force-free modeling. Furthermore the nonlinear force-free extrapolation code should take uncertainties into account in the photospheric field data. They occur due to noise, incomplete inversions, or azimuth ambiguity-removing techniques. Aims. Extrapolation codes in Cartesian geometry for modeling the magnetic field in the corona do not take the curvature of the Sun's surface into account and can only be applied to relatively small areas, e.g., a single active region. Here we apply a method for nonlinear force-free coronal magnetic field modeling and preprocessing of photospheric vector magnetograms in spherical geometry using the optimization procedure to full disk vector magnetograms. We compare the analysis of the photospheric magnetic field and subsequent force-free modeling based on full-disk vector maps from Helioseismic and Magnetic Imager (HMI) onboard the solar dynamics observatory (SDO) and Vector Spectromagnetograph (VSM) of the Synoptic Optical Long-term Investigations of the Sun (SOLIS). Methods. We used HMI and VSM photospheric magnetic field measurements to model the force-free coronal field above multiple solar active regions, assuming magnetic forces to dominate. We solved the nonlinear force-free field equations by minimizing a functional in spherical coordinates over a full disk and excluding the poles. After searching for the optimum modeling parameters for the particular data sets, we compared the resulting nonlinear force-free model fields. We compared quantities, such as the total magnetic energy content, free magnetic energy, the longitudinal distribution of the magnetic pressure, and surface electric current density, using our spherical geometry extrapolation code. Results. The magnetic field lines obtained from nonlinear force-free extrapolation based on HMI and VSM data show good agreement. However, the nonlinear force-free extrapolation based on HMI data contain more total magnetic energy, free magnetic energy, the longitudinal distribution of the magnetic pressure, and surface electric current density than do the VSM data.

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“…Among these, the nonlinear force-free field has the most realistic description of A&A 527, A30 (2011) the coronal magnetic field. For a more complete review of existing methods for computing nonlinear force-free coronal magnetic fields, we refer to the review papers by Amari et al (1997), Schrijver et al (2006), Metcalf et al (2008), and Wiegelmann (2008). The magnetic field is not force-free in the photosphere, but becomes force-free roughly 400 km above the photosphere (Metcalf et al 1995).…”

Section: Introductionmentioning

confidence: 99%

Nonlinear force-free field extrapolation in spherical geometry: improved boundary data treatment applied to a SOLIS/VSM vector magnetogram

Tadesse

Wiegelmann

Inhester

et al. 2011

A&A

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Context. Understanding the 3D structure of coronal magnetic field is important to understanding: the onset of flares and coronal mass ejections, and the stability of active regions, and to monitoring the magnetic helicity and free magnetic energy and other phenomena in the solar atmosphere. Routine measurements of the solar magnetic field are mainly carried out in the photosphere. Therefore, one has to infer the field strength in the upper layers of the solar atmosphere from the measured photospheric field based on the assumption that the corona is force-free. Meanwhile, those measured data are inconsistent with the above force-free assumption. Therefore, one has to apply some transformations to these data before nonlinear force-free extrapolation codes can be applied. Aims. Extrapolation codes in Cartesian geometry for modelling the magnetic field in the corona do not take the curvature of the Sun's surface into account and can only be applied to relatively small areas, e.g., a single active region. Here we apply a method for nonlinear force-free coronal magnetic field modelling and preprocessing of photospheric vector magnetograms in spherical geometry using the optimization procedure. Methods. We solve the nonlinear force-free field equations by minimizing a functional in spherical coordinates over a restricted area of the Sun. We extend the functional by an additional term, which allows us to incorporate measurement errors and treat regions lacking observational data. We use vector magnetograph data from the Synoptic Optical Long-term Investigations of the Sun survey (SOLIS) to model the coronal magnetic field. We study two neighbouring magnetically connected active regions observed on May 15 2009. Results. For vector magnetograms with variable measurement precision and randomly scattered data gaps (e.g., SOLIS/VSM), the new code yields field models that satisfy the solenoidal and force-free condition significantly better as it allows deviations between the extrapolated boundary field and observed boundary data within the measurement errors. Data gaps are assigned an infinite error. We extend this new scheme to spherical geometry and apply it for the first time to real data.

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Untitled

Cited by 191 publications

References 21 publications

Testing magnetofrictional extrapolation with the Titov-Démoulin model of solar active regions

Testing magnetofrictional extrapolation with the Titov-Démoulin model of solar active regions

Full-disk nonlinear force-free field extrapolation of SDO/HMI and SOLIS/VSM magnetograms

Nonlinear force-free field extrapolation in spherical geometry: improved boundary data treatment applied to a SOLIS/VSM vector magnetogram

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