arXiv subjects

G. Hornig

Publications and source records attributed to G. Hornig.

24 records · Page 2Linked to original sources

arXiv2008

Dynamic non-null magnetic reconnection in three dimensions - II. Composite solutions

In this series of papers we examine magnetic reconnection in a domain where the magnetic field does not vanish and the non-ideal region is localised in space. In a previous paper we presented a technique for obtaining analytical solutions to the stationary resistive MHD equations in such a situation and examined specific examples of non-ideal reconnective solutions. Here we further develop the model, noting that certain ideal solutions may be superimposed onto the fundamental non-ideal solutions and examining the effect of imposing various such flows. Significant implications are found for the evolution of magnetic flux in the reconnection process. It is shown that, in contrast to the two-dimensional case, in three-dimensions there is a very wide variety of physically different steady reconnection solutions.

astro-ph↗

arXiv2008

Magnetic Braiding and Parallel Electric Fields

The braiding of the solar coronal magnetic field via photospheric motions - with subsequent relaxation and magnetic reconnection -- is one of the most widely debated ideas of solar physics. We readdress the theory in the light of developments in three-dimensional magnetic reconnection theory. It is known that the integrated parallel electric field along field lines is the key quantity determining the rate of reconnection, in contrast with the two-dimensional case where the electric field itself is the important quantity. We demonstrate that this difference becomes crucial for sufficiently complex magnetic field structures. A numerical method is used to relax a braided magnetic field to an ideal force-free equilibrium; that equilibrium is found to be smooth, with only large- scale current structures. However, the equilibrium is shown to have a highly filamentary integrated parallel current structure with extremely short length- scales. An analytical model is developed to show that, in a coronal situation, the length scales associated with the integrated parallel current structures will rapidly decrease with increasing complexity, or degree of braiding, of the magnetic field. Analysis shows the decrease in these length scales will, for any finite resistivity, eventually become inconsistent with the stability of a force- free field. Thus the inevitable consequence of the magnetic braiding process is shown to be a loss of equilibrium of the coronal field, probably via magnetic reconnection events.

astro-ph↗

arXiv2003

New classes of exact solutions for magnetic reconnective annihilation

Analytical solutions for reconnective annihilation in curvilinear geometry are presented. These solutions are characterized by current density distributions varying both along the radial and azimuthal coordinates. They represent an extension of previously proposed models, based on purely radially dependent current densities. Possible applications of these solutions to the modeling of solar flares are also discussed.

physics.plasm-ph↗

arXiv2002

Exact solutions for magnetic annihilation in curvilinear geometry

New exact solutions of the steady and incompressible 2D MHD equations in polar coordinates are presented. The solutions describe the process of reconnective magnetic annihilation in a curved current layer. They are particularly interesting for modeling magnetic reconnection in solar flares caused by the interaction of three photospheric magnetic sources.

physics.plasm-ph↗

arXiv2002

Exact solutions for reconnective annihilation in magnetic configurations with three sources

Exact solutions of the steady resistive three dimensional (3D) magnetohydrodynamics (MHD) equations in cylindrical coordinates for an incompressible plasma are presented. The solutions are translationally invariant along one direction and in general they describe a process of reconnective annihilation in a curved current layer with non vanishing magnetic field. In the derivation of the solutions the ideal case with vanishing resistivity and electric field is considered first and then generalized to include the effects of finite electric field and resistivity. Particular attention is devoted to the analysis how the latter ones influence the presence of singularities in the solutions. In this respect comparisons with the purely two-dimensional case are made and the resulting important differences are highlighted. Finally, applications of the solutions for modeling an important class of solar flares are discussed.

physics.plasm-ph↗

arXiv1999

Quasi-Separatrix Layers: Refined Theory and its Application to Solar Flares

Although the analysis of observational data indicates that quasi-separatrix layers (QSLs) have to play an important role in magnetic configurations of solar flares, the corresponding theory is only at an initial stage so far. In particular, there is still a need in a proper definition of QSL. This problem is analyzed here on the basis of geometrical properties of the mapping produced by the field lines which connect photospheric areas of positive and negative magnetic polarities of active regions. In general, one can find on the photosphere a unique pair of locally perpendicular line elements at one footpoint of a given field line, so that this pair is mapped into a similar pair of elements at the other footpoint. Along the directions of these elements the field line mapping only stretches and compresses the corresponding displacements of the neighboring field-line footpoints. This fact enables us to get a remarkably clear and concise definition of QSL as a volume filled by coronal field lines for which the ratio of the corresponding stretching and compressing coefficients is anomalously large. The new definition is also compared with the ones previously introduced by other authors. The theory is applied to flare events of the so-called sigmoid-type, using an analytical model of a twisted force-free configuration. It is shown that such a configuration may contain a QSL even if genuine separatrix surfaces are absent. Identifying QSLs is an essential prerequisite for understanding the mechanism of magnetic energy release in this type of flares. It is also demonstrated that the magnetic field under study has a Hamiltonian structure, which makes it possible to reveal a geometrical reason for the appearance of QSL in this case.

astro-ph↗