Gauge-Invariant Helicity for Force-Free Magnetic Fields in a Rectangular Box

Rudenko, G. V.; Myshyakov, I. I.

doi:10.1007/s11207-011-9743-4

Cited by 22 publications

(19 citation statements)

References 11 publications

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“…Methods applying the DeVore gauge are applications of the method in Valori et al (2012) that differ only in the details of the numerical implementation. In the following, different FV methods are identified by the gauge they employ (DeVore or Coulomb), followed by the initial of the author of the reference article describing its implementation (e.g., Coulomb GR labels the Coulomb method described in Rudenko and Myshyakov (2011)), see Table 2.…”

Section: Helicity Computation Methodsmentioning

confidence: 99%

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Magnetic Helicity Estimations in Models and Observations of the Solar Magnetic Field. Part I: Finite Volume Methods

et al. 2016

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Magnetic helicity is a conserved quantity of ideal magneto-hydrodynamics characterized by an inverse turbulent cascade. Accordingly, it is often invoked as one of the basic physical quantities driving the generation and structuring of magnetic fields in a variety of astrophysical and laboratory plasmas. We provide here the first systematic comparison of six existing methods for the estimation of the helicity of magnetic fields known in a finite volume. All such methods are reviewed, benchmarked, and compared with each other, and specifically tested for accuracy and sensitivity to errors. To that purpose, we consider four groups of numerical tests, ranging from solutions of the three-dimensional, force-free equilibrium, to magneto-hydrodynamical numerical simulations. Almost all methods are found to produce the same value of magnetic helicity within few percent in all tests. In the more solar-relevant and realistic of the tests employed here, the simulation of an eruptive flux rope, the spread in the computed values obtained by all but one method is only 3 %, indicating the reliability and mutual consistency of such methods in appropriate parameter ranges. However, methods show differences in the sensitivity to numerical resolution and to errors in the solenoidal property of the input fields. In addition to finite volume methods, we also briefly discuss a method that estimates helicity from the field lines' twist, and one that exploits the field's value at one boundary and a coronal minimal connectivity instead of a pre-defined three-dimensional magnetic-field solution.

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Section: Helicity Computation Methodsmentioning

confidence: 99%

“…The Coulomb GR method is described in Rudenko and Myshyakov (2011). A distinctive feature of the algorithm is that the Coulomb GR method defines the reference potential field in terms of vector potential B p = ∇ × A p , rather than using Eqs.…”

Section: Coulomb Grmentioning

confidence: 99%

Magnetic Helicity Estimations in Models and Observations of the Solar Magnetic Field. Part I: Finite Volume Methods

et al. 2016

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“…This is far from trivial, since it often involves the computation of the magnetic vector potential that has to satisfy specific gauge properties (Rudenko and Myshyakov 2011;Thalmann et al 2011;Valori et al 2012a;Yang et al 2013). So far, these models have not been applied to real solar cases, but have been tested by the use of semianalytic force-free magnetic field solutions.…”

Section: Relation To Flare Productivitymentioning

confidence: 99%

The magnetic field in the solar atmosphere

Wiegelmann

Thalmann

Solanki

2014

Astron Astrophys Rev

176

125

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This publication provides an overview of magnetic fields in the solar atmosphere with the focus lying on the corona. The solar magnetic field couples the solar interior with the visible surface of the Sun and with its atmosphere. It is also responsible for all solar activity in its numerous manifestations. Thus, dynamic phenomena such as coronal mass ejections and flares are magnetically driven. In addition, the field also plays a crucial role in heating the solar chromosphere and corona as well as in accelerating the solar wind. Our main emphasis is the magnetic field in the upper solar atmosphere so that photospheric and chromospheric magnetic structures are mainly discussed where relevant for higher solar layers. Also, the discussion of the solar atmosphere and activity is limited to those topics of direct relevance to the magnetic field. After giving a brief overview about the solar magnetic field in general and its global structure, we discuss in more detail the magnetic field in active regions, the quiet Sun and coronal holes.

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“…There are several practical ways to compute magnetic helicity either using a finite volume method (Rudenko & Myshyakov 2011;Thalmann et al 2011;Valori et al 2012;Yang et al 2013;Rudenko & Anfinogentov 2014;Moraitis et al 2014), a twist number method (Guo et al 2010(Guo et al , 2013, a helicity-flux integration method (Chae 2001;Pariat et al 2005;Liu & Schuck 2012), or a connectivity-based method (Georgoulis et al 2012). These methods differ in their input magnetic field and in the way to calculate the magnetic helicity.…”

Section: Introductionmentioning

confidence: 99%

Magnetic Helicity Estimations in Models and Observations of the Solar Magnetic Field. III. Twist Number Method

Guo

Pariat

Valori

et al. 2017

ApJ

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We study the writhe, twist and magnetic helicity of different magnetic flux ropes, based on models of the solar coronal magnetic field structure. These include an analytical force-free Titov-Démoulin equilibrium solution, non forcefree magnetohydrodynamic simulations, and nonlinear force-free magnetic field models. The geometrical boundary of the magnetic flux rope is determined by the quasi-separatrix layer and the bottom surface, and the axis curve of the flux rope is determined by its overall orientation. The twist is computed by arXiv:1704.02096v1 [astro-ph.SR] 7 Apr 2017 -2 -the Berger-Prior formula that is suitable for arbitrary geometry and both forcefree and non-force-free models. The magnetic helicity is estimated by the twist multiplied by the square of the axial magnetic flux. We compare the obtained values with those derived by a finite volume helicity estimation method. We find that the magnetic helicity obtained with the twist method agrees with the helicity carried by the purely current-carrying part of the field within uncertainties for most test cases. It is also found that the current-carrying part of the model field is relatively significant at the very location of the magnetic flux rope. This qualitatively explains the agreement between the magnetic helicity computed by the twist method and the helicity contributed purely by the current-carrying magnetic field.

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Gauge-Invariant Helicity for Force-Free Magnetic Fields in a Rectangular Box

Cited by 22 publications

References 11 publications

Magnetic Helicity Estimations in Models and Observations of the Solar Magnetic Field. Part I: Finite Volume Methods

Magnetic Helicity Estimations in Models and Observations of the Solar Magnetic Field. Part I: Finite Volume Methods

The magnetic field in the solar atmosphere

Magnetic Helicity Estimations in Models and Observations of the Solar Magnetic Field. III. Twist Number Method

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