Direct Boundary Integral Formulation for Solar Non‐constant‐α Force‐free Magnetic Fields

Yan, Yihua; Li, Zhuheng

doi:10.1086/499064

Cited by 53 publications

(64 citation statements)

References 12 publications

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“…[8] For this reason, Yan [2005] and Yan and Li [2006] improved the BIE and proposed the direct boundary integral equation (DBIE) formulation, which represents the force-free field B i in W by direct integration of the observed magnetic field B 0 on the bottom boundary surface G,…”

Section: Introductionmentioning

confidence: 99%

“…In the geometry of DBIE, a mirror point of the field point i with respect to the boundary G is introduced to help eliminate the ∂B/∂n term in BIE [Yan and Li, 2006;. As an expense, the expressions of the reference function Y in equation (7) are more complex than the expression of Y in equation (6), and have different forms for different bottom boundary geometries (e.g., planar surface boundary or spherical boundary) [Yan, 2005;Yan and Li, 2006].…”

Section: Introductionmentioning

confidence: 99%

“…As an expense, the expressions of the reference function Y in equation (7) are more complex than the expression of Y in equation (6), and have different forms for different bottom boundary geometries (e.g., planar surface boundary or spherical boundary) [Yan, 2005;Yan and Li, 2006]. On the basis of DBIE formulation (7), Yan and Li [2006] devised an optimal algorithm to work out the NLFFF solution for the planar surface boundary situation. The computation is carried out point by point in the space W above the boundary G. At each field point, the magnetic field B i is calculated iteratively until the force-free constraint (2) is satisfied, then the NLFFF solution in the whole space can be obtained.…”

Section: Introductionmentioning

confidence: 99%

“…[9] But a careful analysis of the optimal algorithm proposed by Yan and Li [2006] shows that , in the original computational procedure of Yan and Li [2006], the iterative calculations only have good convergence properties at the field points with lower altitude (near the bottom boundary), while at the field points with higher altitude (away from the bottom boundary), the convergence properties are poor. This is due to an assumption in the original optimal algorithm of Yan and Li [2006] which is only valid at low altitudes [Rudenko and Myshyakov, 2009].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Nonlinear force-free field extrapolation of the coronal magnetic field using the data obtained by the Hinode satellite

Wang

Yan

2011

J. Geophys. Res.

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[1] The Hinode satellite can obtain high-quality photospheric vector magnetograms of solar active regions and the simultaneous coronal loop images in soft X-ray and extreme ultraviolet (EUV) bands. In this paper, we continue the work of and apply the newly developed upward boundary integration computational scheme for the nonlinear force-free field (NLFFF) extrapolation of the coronal magnetic field to the

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Nonlinear force-free field extrapolation of the coronal magnetic field using the data obtained by the Hinode satellite

Wang

Yan

2011

J. Geophys. Res.

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“…Hence the problem of reconstruction of 3D coronal magnetic field is reduced to the problem of solving linear force free field, with known constant a parameter and the photospheric vector magnetograph measurements as boundary data. Numerous effort has been put on extrapolating coronal magnetic fields, mostly based on FFF assumption [e.g., Amari et al, 2006;Gary, 1989;Wheatland et al, 2000;Wu et al, 1990;Yan and Li, 2006]. Meanwhile, non-force free field reconstruction started to emerge [e.g., Wiegelmann and Inhester, 2003].…”

Section: Introductionmentioning

confidence: 99%

A new approach to modeling non‐force free coronal magnetic field

Dasgupta

2006

Geophysical Research Letters

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[1] We propose a new approach to deriving the local threedimensional (3D) non-force free coronal magnetic field structure from photospheric vector magnetograph measurements. Based on the Principle of Minimum Dissipation Rate, a general non-force free magnetic field can be expressed as the superposition of two linear (constant-a) force free field. The parameter, a, for each of the two linear force free field, can be determined by optimizing the requirement that the recovered transverse magnetic field components as the superposition of the corresponding components of the two linear force free field agree with the observed ones at the photospheric level. A preliminary test case study of an analytic non-force free field model is presented to illustrate the method. We discuss the difficulties associated with the linear force free field extrapolation and the feasibility of our method.Citation: Hu, Q., and B. Dasgupta (2006), A new approach to modeling non-force free coronal magnetic field, Geophys. Res. Lett., 33, L15106,

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Variations of the 3‐D coronal magnetic field associated with the X3.4‐class solar flare event of AR 10930

Wang

Yan

et al. 2014

JGR Space Physics

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The variations of the 3-D coronal magnetic fields associated with the X3.4-class flare of active region 10930 are studied in this paper. The coronal magnetic field data are reconstructed from the photospheric vector magnetograms obtained by the Hinode satellite and using the nonlinear force-free field extrapolation method developed in our previous work (He et al., 2011). The 3-D force-free factor , 3-D current density, and 3-D magnetic energy density are employed to analyze the coronal data. The distributions of and current density reveal a prominent magnetic connectivity with strong negative values and strong current density before the flare. This magnetic connectivity extends along the main polarity inversion line and is found to be totally broken after the flare. The distribution variation of magnetic energy density reveals the redistribution of magnetic energy before and after the flare. In the lower space of the modeling volume the increase of magnetic energy dominates, and in the higher space the decrease of energy dominates. The comparison with the flare onset imaging observation exhibits that the breaking site of the magnetic connectivity and site with the highest values of energy density increase coincide with the location of flare initial eruption. We conclude that a cramped positive region appearing in the photosphere causes the breaking of the magnetic connectivity. A scenario for flare initial eruption is proposed in which the Lorentz force acting on the isolated electric current at the magnetic connectivity breaking site lifts the associated plasmas and causes the initial ejection.

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Direct Boundary Integral Formulation for Solar Non‐constant‐α Force‐free Magnetic Fields

Cited by 53 publications

References 12 publications

Nonlinear force-free field extrapolation of the coronal magnetic field using the data obtained by the Hinode satellite

Nonlinear force-free field extrapolation of the coronal magnetic field using the data obtained by the Hinode satellite

A new approach to modeling non‐force free coronal magnetic field

Variations of the 3‐D coronal magnetic field associated with the X3.4‐class solar flare event of AR 10930

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