Evolution of field line helicity during magnetic reconnection

Russell, A. J. B.; Yeates, Anthony R.; Hornig, G.; Wilmot-Smith, A. L.

doi:10.1063/1.4913489

Cited by 51 publications

(87 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The behaviour has interesting points of comparison with the fully three-dimensional relaxation situation studied by Smiet et al (2015): in particular, the two-stage character of the relaxation process, and the fact that a Taylor state does not emerge from it. The one-dimensional model presented here is of course computationally far more economical, and the details are easier to visualise.…”

Section: Discussionmentioning

confidence: 99%

Magnetic relaxation and the Taylor conjecture

Moffatt

2015

J. Plasma Phys.

View full text Add to dashboard Cite

A one-dimensional model of magnetic relaxation in a pressureless low-resistivity plasma is considered. The initial two-component magnetic field b(x, t) is strongly helical, with non-uniform helicity density. The magnetic pressure gradient drives a velocity field that is dissipated by viscosity. Relaxation occurs in two phases. The first is a rapid initial phase in which the magnetic energy drops sharply and the magnetic pressure becomes approximately uniform; the helicity density is redistributed during this phase but remains non-uniform, and although the total helicity remains relatively constant, a Taylor state is not established. The second phase is one of slow diffusion, in which the velocity is weak, though still driven by persistent weak non-uniformity of magnetic pressure; during this phase, magnetic energy and helicity decay slowly and at constant ratio through the combined effects of pressure equalisation and finite resistivity. The density field, initially uniform, develops rapidly (in association with the magnetic field) during the initial phase, and continues to evolve, developing sharp maxima, throughout the diffusive stage. Finally it is proved that, if the resistivity is zero, the spatial mean (b · ∇ × b)/b 2 is an invariant of the governing one-dimensional induction equation.

show abstract

Section: Discussionmentioning

confidence: 99%

Magnetic relaxation and the Taylor conjecture

Moffatt

2015

J. Plasma Phys.

View full text Add to dashboard Cite

show abstract

“…Some preliminary tests have been presented in Yang et al (2016). Alternatively, one may use the method of the field line helicity (Yeates & Hornig 2014Russell et al 2015) to study the helicity flux distribution per field line. This method distinguishes the internal topology of a magnetic flux rope, and its integration over a cross section provides the total magnetic self-helicity.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…Its local density in an arbitrary volume does not have a physical meaning, because the vector potential depends on the distribution of the field in the entire volume, and because adding a gauge function to any vector potential would arbitrarily change the local helicitydensity values. However, magnetic helicity does have a local density per elementary flux tube, namely, the field line helicity defined as the integral of A along a magnetic field line (Yeates & Hornig 2014Russell et al 2015). Besides the relative magnetic helicity in Equation (1), there are some other expressions and interpretations of the magnetic helicity (Jensen & Chu 1984;Hornig 2006;Low 2006Low , 2011Longcope & Malanushenko 2008;Prior & Yeates 2014).…”

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

View full text Add to dashboard Cite

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.

show abstract

“…In Wilmot-Smith et al (2011) a similar field, embedded in a cylindrical tube, was shown to split into two force-free flux ropes of opposing twist through reconnection, entirely contrary to the Taylor relaxation hypothesis. An explanation for this phenomenon was proposed recently by Russell et al (2015) though it is beyond the scope of the discussion here.…”

Section: B4 Braidmentioning

confidence: 99%

Twisted versus braided magnetic flux ropes in coronal geometry

Prior

Yeates

2016

A&A

Self Cite

View full text Add to dashboard Cite

Aims. Sigmoidal structures in the solar corona are commonly associated with magnetic flux ropes whose magnetic field lines are twisted about a mutual axis. Their dynamical evolution is well studied, with sufficient twisting leading to large-scale rotation (writhing) and vertical expansion, possibly leading to ejection. Here, we investigate the behaviour of flux ropes whose field lines have more complex entangled/braided configurations. Our hypothesis is that this internal structure will inhibit the large-scale morphological changes. Additionally, we investigate the influence of the background field within which the rope is embedded. Methods. A technique for generating tubular magnetic fields with arbitrary axial geometry and internal structure, introduced in part I of this study, provides the initial conditions for resistive-MHD simulations. The tubular fields are embedded in a linear force-free background, and we consider various internal structures for the tubular field, including both twisted and braided topologies. These embedded flux ropes are then evolved using a 3D MHD code. Results. Firstly, in a background where twisted flux ropes evolve through the expected non-linear writhing and vertical expansion, we find that flux ropes with sufficiently braided/entangled interiors show no such large-scale changes. Secondly, embedding a twisted flux rope in a background field with a sigmoidal inversion line leads to eventual reversal of the large-scale rotation. Thirdly, in some cases a braided flux rope splits due to reconnection into two twisted flux ropes of opposing chirality -a phenomenon previously observed in cylindrical configurations. Conclusions. Sufficiently complex entanglement of the magnetic field lines within a flux rope can suppress large-scale morphological changes of its axis, with magnetic energy reduced instead through reconnection and expansion. The structure of the background magnetic field can significantly affect the changing morphology of a flux rope.

show abstract

Evolution of field line helicity during magnetic reconnection

Cited by 51 publications

References 37 publications

Magnetic relaxation and the Taylor conjecture

Magnetic relaxation and the Taylor conjecture

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

Twisted versus braided magnetic flux ropes in coronal geometry

Contact Info

Product

Resources

About