Preface

Sakurai, Kunitomo

doi:10.1007/bf00226265

Cited by 47 publications

(61 citation statements)

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“…Brosius et al 1992) or Zeeman splitting from infrared lines (Lin et al 2000). Therefore methods to determine the topology and the geometry of the coronal magnetic field have been developed: the determination of the geometry of active region loops (height, inclination, radius, width) applying a dynamical stereoscopy method to coronal EUV observations (Aschwanden et al 1999a(Aschwanden et al , 1999b(Aschwanden et al , 2000, the reconstruction of the coronal magnetic field using photospheric measurements as boundary condition (see reviews by Sakurai 1989;Amari & Démoulin 1992).…”

Section: Introductionmentioning

confidence: 99%

3D Coronal magnetic field from vector magnetograms: non-constant-αforce-free configuration of the active region NOAA 8151

Régnier

Amari

Kersalé

2002

A&A

102

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Abstract. The Active Region 8151 (AR 8151) observed in February 1998 is the site of an eruptive event associated with a filament and a S-shaped structure, and producing a slow Coronal Mass Ejection (CME). In order to determine how the CME occurs, we compute the 3D coronal magnetic field and we derive some relevant parameters such as the free magnetic energy and the relative magnetic helicity. The 3D magnetic configuration is reconstructed from photospheric magnetic magnetograms (IVM, Mees Solar Observatory) in the case of a non-constant-α force-free (nlff) field model. The reconstruction method is divided into three main steps: the analysis of vector magnetograms (transverse fields, vertical density of electric current, ambiguity of 180• ), the numerical scheme for the nlff magnetic field, the interpretation of the computed magnetic field with respect to the observations. For AR 8151, the nlff field matches the coronal observations from EIT/SOHO and from SXT/Yohkoh. In particular, three characteristic flux tubes are shown: a highly twisted flux tube, a long twisted flux tube and a quasi-potential flux tube. The maximum energy budget is estimated to 2.6 × 10 31 erg and the relative magnetic helicity to 4.7 × 10 34 G 2 cm 4 . From the simple photospheric magnetic distribution and the evidence of highly twisted flux tubes, we argue that the flux rope model is the most likely to describe the initiation mechanism of the eruptive event associated with AR 8151.

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Section: Introductionmentioning

confidence: 99%

3D Coronal magnetic field from vector magnetograms: non-constant-αforce-free configuration of the active region NOAA 8151

Régnier

Amari

Kersalé

2002

A&A

102

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“…Therefor we can obtain a boundary value problem of (2.1-2.2), e.g., as described in Sakurai (1989). In general, the potential Ψ at any position r i , in space V can be determined from (Courant & Hilbert 1962):…”

Section: Methodsmentioning

confidence: 99%

“…The Green's function solution of the above boundary value problem was applied to practical solar magnetic field observations in early 1960s (Sakurai (1989)). Here, the magnetic field is, however, obtained from:…”

Section: Methodsmentioning

confidence: 99%

On the Coronal Current-Free Global Field Configuration

Yan¹

2004

Proc. IAU

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Abstract. A coronal current-free field model, which applies the asymptotic condition of no field at infinity and the boundary condition on the solar surface specified, is presented. Some Applications of the method to practical solar events indicate that the extrapolated global magnetic field structures effectively demonstrate the case for the disk signature of the radio CME and the evolution of the radio sources during the CME/flare processes.

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“…Although the force-free magnetic field equations take a disarmingly simple form, the nature of their solutions has not yet been understood (Priest 1994). Nevertheless, significant progress has been made in tackling this problem during the past half century (see review papers by, e.g., Aly 1989;Gary 1989;Sakurai 1989;McClymont et al 1997;Wang 1999;Yan 2003;Aschwanden 2004; see also the brief review on the linear force-free field in Démoulin & Priest 1992;Schmieder & Aulanier 2003;see Seehafer 1978 andAly 1992, for some important properties of the linear force-free field associated to the different geometry of the photosphere). Besides theoretical approaches, computational methods play an important role among these studies.…”

Section: Introductionmentioning

confidence: 99%

The GMRES method applied to the BEM extrapolation of solar force-free magnetic fields

Yan²,

Devel³

et al. 2007

A&A

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Context. Since the 1990's, Yan and colleagues have formulated a kind of boundary integral formulation for the linear or non-linear solar force-free magnetic fields with finite energy in semi-infinite space, and developed a computational procedure by virtue of the boundary element method (BEM) to extrapolate the magnetic fields above the photosphere. Aims. In this paper, the generalized minimal residual method (GMRES) is introduced into the BEM extrapolation of the solar forcefree magnetic fields, in order to efficiently solve the associated BEM system of linear equations, which was previously solved by the Gauss elimination method with full pivoting. Methods. Being a modern iterative method for non-symmetric linear systems, the GMRES method reduces the computational cost for the BEM system from O(N 3 ) to O(N 2 ), where N is the number of unknowns in the linear system. Intensive numerical experiments are conducted on a well-known analytical model of the force-free magnetic field to reveal the convergence behaviour of the GMRES method subjected to the BEM systems. The impacts of the relevant parameters on the convergence speed are investigated in detail. Results. Taking the Krylov dimension to be 50 and the relative residual bound to be 10 −6 (or 10 −2 ), the GMRES method is at least 1000 (or 9000) times faster than the full pivoting Gauss elimination method used in the original BEM extrapolation code, when N is greater than 12 321, according to the CPU timing information measured on a common desktop computer (CPU speed 2.8 GHz; RAM 1 GB) for the model problem.

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Preface

Cited by 47 publications

References 0 publications

3D Coronal magnetic field from vector magnetograms: non-constant-αforce-free configuration of the active region NOAA 8151

3D Coronal magnetic field from vector magnetograms: non-constant-αforce-free configuration of the active region NOAA 8151

On the Coronal Current-Free Global Field Configuration

The GMRES method applied to the BEM extrapolation of solar force-free magnetic fields

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