Exact Green's function method of solar force-free magnetic-field computations with constant alpha. I - Theory and basic test cases

Chiu, Y. T.; Hilton, Henry H.

doi:10.1086/155111

Cited by 168 publications

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“…(1) is linear, and only the knowledge of the normal field component is needed as boundary condition for the extrapolation. The solution of the linear problem was given in closed form in Nakagawa & Raadu (1972), Chiu & Hilton (1977), and Seehafer (1978). Linear methods have several intrinsic limitations, the most severe one being that they cannot match most observed magnetograms closely because α is often found to vary strongly across active regions (e.g., Régnier et al 2002).…”

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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“…In the present work, we use linear force-free fields confined to half-space, computed using Green's function from Chiu & Hilton (1977). Such fields are less popular than linear force-free fields confined to a box (Alissandrakis 1981) because it takes much more computational time to build them.…”

Section: The Methodsmentioning

confidence: 99%

Direct Measurements of Magnetic Twist in the Solar Corona

Malanushenko

Yusuf

Longcope

2011

ApJ

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In the present work, we study the evolution of magnetic helicity in the solar corona. We compare the rate of change of a quantity related to the magnetic helicity in the corona to the flux of magnetic helicity through the photosphere and find that the two rates are similar. This gives observational evidence that helicity flux across the photosphere is indeed what drives helicity changes in the solar corona during emergence. For the purposes of estimating coronal helicity, we neither assume a strictly linear force-free field nor attempt to construct a nonlinear force-free field. For each coronal loop evident in extreme ultraviolet, we find a best-matching line of a linear force-free field and allow the twist parameter α to be different for each line. This method was introduced and its applicability discussed in Malanushenko et al. The object of this study is emerging and rapidly rotating AR 9004 over about 80 hr. As a proxy for coronal helicity, we use the quantity α i L i /2 averaged over many reconstructed lines of magnetic field. We argue that it is approximately proportional to the "flux-normalized" helicity H/Φ 2 , where H is the helicity and Φ is the total enclosed magnetic flux of the active region. The time rate of change of such a quantity in the corona is found to be about 0.021 rad hr −1 , which is comparable with the estimates for the same region obtained using other methods, which estimated the flux of normalized helicity to be about 0.016 rad hr −1 .

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“…Potential field and LFF field can be determined directly from the line-of-sight (LOS) component of magnetic field(e.g. MDI/SOHO) as input, and α has to be computed in LFF field from some additional data (Chiu & Hilton 1977;Seehafer 1978;Alissandrakis 1981;Gary 1989).…”

Section: Extrapolation Of Magnetic Fieldmentioning

confidence: 99%

The induced electric field distribution in the solar atmosphere

Chen¹,

Yang²,

Deng³

2013

Res. Astron. Astrophys.

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A method of calculating induced electric field is presented in this paper. Induced electric field in solar atmosphere is derived by the time variation of magnetic field when the charged particle accumulation is neglected. In order to get the spatial distribution of magnetic field, several extrapolation methods are introduced. With observational data from Helioseismic and Magnetic Imager (HMI) aboard the NASA's Solar Dynamics Observatory (SDO) on May 20th, 2010, we extrapolate the magnetic field to the upper atmosphere from the photosphere. By calculating the time variation of magnetic field, we can get the induced electric field. The derived induced electric field can reach a value of 10 2 V/cm and the average electric field has a maximum point at the layer of 360 km above the photosphere. The Monte Carlo statistics method is used to compute the triple integration of induced electric field.

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Exact Green's function method of solar force-free magnetic-field computations with constant alpha. I - Theory and basic test cases

Cited by 168 publications

References 0 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

Direct Measurements of Magnetic Twist in the Solar Corona

The induced electric field distribution in the solar atmosphere

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