Extrapolation of a nonlinear force-free field containing a highly twisted magnetic loop

Valori, G.; Kliem, B.; Keppens, Rony

doi:10.1051/0004-6361:20042008

Cited by 105 publications

(88 citation statements)

References 33 publications

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“…Thus, as in Valori et al (2005), it is confirmed that the magnetofrictional method can reconstruct field lines that wind around a flux rope axis more than one time. In this regard the nonlinear extrapolation differs in principle from linear extrapolations, which limit the number of field line turns in the computed field to about 1/2 for realistic magnetogram sizes, due to the upper limit on the force-free parameter inherent in linear fields (Kliem et al, in preparation; see also Leka et al 2005).…”

Section: Stable Equilibriasupporting

confidence: 61%

“…The implementation of magnetofrictional extrapolation used in this paper was described in detail in Valori et al (2005Valori et al ( , 2007, so that we can restrict ourselves here to a short outline of the method and its recent improvements. Our formulation of the method consists in a pseudo-temporal evolution of an initial field subject to the equation…”

Section: Extrapolation Methodsmentioning

confidence: 99%

“…(1) by applying it to the flux rope equilibrium constructed by Titov & Démoulin (1999, hereafter TD). This configuration describes structures that emerge from the solar interior already twisted and that carry a net current (e.g., Lites et al 1995;Leka et al 1996;Wheatland 2000), and it is in this sense complementary to the one in Valori et al (2005), which represents the case of an originally potential field twisted solely by photospheric displacements. The relevance of the TD equilibrium as a model for solar active regions and eruptive configurations has been demonstrated by many investigations (e.g., Zarro et al 2000;Kliem et al 2004;Török & Kliem 2005;Schrijver et al 2008b;McKenzie & Canfield 2008).…”

Section: Introductionmentioning

confidence: 99%

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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: Stable Equilibriasupporting

confidence: 61%

Section: Extrapolation Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Valori¹,

Kliem

Török³

et al. 2010

A&A

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“…This approach is sometimes called the "force-free model" (FFM), even though the field in this model is never exactly force-free anywhere (Mikić et al 1988;Ortolani & Schnack 1993). In the context of force-free magnetic field extrapolations this method is also known as the stress-and-relax method (Valori et al 2005). …”

Section: Introductionmentioning

confidence: 99%

Surface appearance of dynamo-generated large-scale fields

Warnecke

Brandenburg

2010

A&A

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Aims. Twisted magnetic fields are frequently seen to emerge above the visible surface of the Sun. This emergence is usually associated with the rise of buoyant magnetic flux structures. Here we ask how magnetic fields from a turbulent large-scale dynamo appear above the surface if there is no magnetic buoyancy. Methods. The computational domain is split into two parts. In the lower part, which we refer to as the turbulence zone, the flow is driven by an assumed helical forcing function leading to dynamo action. Above this region, which we refer to as the exterior, a nearly force-free magnetic field is computed at each time step using the stress-and-relax method. Results. Twisted arcade-like field structures are found to emerge in the exterior above the turbulence zone. Strong current sheets tend to form above the neutral line, where the vertical field component vanishes. Time series of the magnetic field structure show recurrent plasmoid ejections. The degree to which the exterior field is force free is estimated as the ratio of the dot product of current density and magnetic field strength to their respective rms values. This ratio reaches values of up to 95% in the exterior. A weak outward flow is driven by the residual Lorentz force.

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“…These methods have been elsewhere reviewed (see Aly & Amari 2007;Wiegelmann 2008;Schrijver et al 2006), and we only reiterate that they can be divided into three main classes: optimization methods (Wiegelmann 2004), which use all the photospheric data and try to determine the field by minimizing a cost function; magnetohydrodynamics relaxation methods (Valori et al 2005;Mikic & McClymont 1994) and Grad-Rubin methods (Sakurai 1981;Amari et al 1999;Wheatland 2007). An important difference between optimization and the Grad-Rubin methods is related to the way in which the photospheric data are used.…”

Section: Introductionmentioning

confidence: 99%

Observational constraints on well-posed reconstruction methods and the optimization-Grad-Rubin method

Amari

Aly

2010

A&A

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Context. Grad-Rubin type methods are interesting candidates for reconstructing the force-free magnetic field of a solar coronal region. As input these methods, however, require the normal component B n of the field on the whole boundary of the numerical box and the force-free function α on the part of the boundary where B n > 0 (or B n < 0), while observations provide data only on its lower photospheric part. Moreover, they introduce an unpleasing asymmetry between the opposite polarity parts of the boundary, and certainly do not take full advantage of the available data on α. Aims. We address these issues resulting from observations. We present a possible way to supply the missing information about B n and α on the non-photospheric sides of the box, and to use more effectively the data provided by the measurements. Methods. We introduce the optimization-Grad-Rubin method (OGRM), which is in some sense midway between optimization methods and the standard Grad-Rubin methods. It is based on an iterative scheme in which the α used as a boundary condition is imposed to take identical values at both footpoints of any field line and to be as close as possible to the α provided by the measurements on the photosphere. The degree of "closeness" is measured by an "error functional" containing a weight function reflecting the confidence that can be placed on the observational data. Results. The new method is implemented in our code XTRAPOL, along with some technical improvements. It is thus tested for two specific choices of the weight function by reconstructing a force-free field from data obtained by perturbing in either a random or a non-random way boundary values provided by an exact solution.

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Extrapolation of a nonlinear force-free field containing a highly twisted magnetic loop

Cited by 105 publications

References 33 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

Surface appearance of dynamo-generated large-scale fields

Observational constraints on well-posed reconstruction methods and the optimization-Grad-Rubin method

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