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Force-Free Magnetic Fields: Solutions, Topology and Applications

01 Jan 1996-
TL;DR: The virial theorem solutions to the force-free field equations field topology magnetic energy in multiply connected domains applications force free fields and electromagnetic waves proof of the Jacobi polynomial identities separation of the wave equation, cyclides and boundary conditions as mentioned in this paper.
Abstract: The virial theorem solutions to the force-free field equations field topology magnetic energy in multiply connected domains applications force-free fields and electromagnetic waves proof of the Jacobi polynomial identities separation of the wave equation, cyclides and boundary conditions.
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Journal ArticleDOI
TL;DR: In this article, the magnetic field and electric currents are assumed to be proportional with one global constant, the so-called linear force-free field approximation, which is known as the force free field assumption, as the Lorentz force vanishes.
Abstract: The structure and dynamics of the solar corona is dominated by the magnetic field. In most areas in the corona magnetic forces are so dominant that all non-magnetic forces such as plasma pressure gradients and gravity can be neglected in the lowest order. This model assumption is called the force-free field assumption, as the Lorentz force vanishes. This can be obtained by either vanishing electric currents (leading to potential fields) or the currents are co-aligned with the magnetic field lines. First we discuss a mathematically simpler approach that the magnetic field and currents are proportional with one global constant, the so-called linear force-free field approximation. In the generic case, however, the relationship between magnetic fields and electric currents is nonlinear and analytic solutions have been only found for special cases, like 1D or 2D configurations. For constructing realistic nonlinear force-free coronal magnetic field models in 3D, sophisticated numerical computations are required and boundary conditions must be obtained from measurements of the magnetic field vector in the solar photosphere. This approach is currently a large area of research, as accurate measurements of the photospheric field are available from ground-based observatories such as the Synoptic Optical Long-term Investigations of the Sun and the Daniel K. Inouye Solar Telescope (DKIST) and space-born, e.g., from Hinode and the Solar Dynamics Observatory. If we can obtain accurate force-free coronal magnetic field models we can calculate the free magnetic energy in the corona, a quantity which is important for the prediction of flares and coronal mass ejections. Knowledge of the 3D structure of magnetic field lines also help us to interpret other coronal observations, e.g., EUV images of the radiating coronal plasma.

314 citations


Cites methods from "Force-Free Magnetic Fields: Solutio..."

  • ...For an overview on how the Grad–Shafranov equation can be derived for arbitrary curvilinear coordinates with axisymmetry we refer to (Marsh, 1996, section 3.2.)....

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Journal ArticleDOI
TL;DR: In this paper, the authors describe the construction of stepped-pressure equilibria as extrema of a multi-region, relaxed magnetohydrodynamic (MHD) energy functional that combines elements of ideal MHD and Taylor relaxation, and which they call MRXMHD.
Abstract: We describe the construction of stepped-pressure equilibria as extrema of a multi-region, relaxed magnetohydrodynamic (MHD) energy functional that combines elements of ideal MHD and Taylor relaxation, and which we call MRXMHD. The model is compatible with Hamiltonian chaos theory and allows the three-dimensional MHD equilibrium problem to be formulated in a well-posed manner suitable for computation. The energy-functional is discretized using a mixed finite-element, Fourier representation for the magnetic vector potential and the equilibrium geometry; and numerical solutions are constructed using the stepped-pressure equilibrium code, SPEC. Convergence studies with respect to radial and Fourier resolution are presented.

148 citations

Book
06 Sep 2018
TL;DR: In this article, the authors provide an introduction to integrable and non-integrable scalar field models with topological and nontopological soliton solutions focusing on both topologically and non topological solitons, bringing together debates around solitary waves and construction of soliton solution in various models and providing a discussion of soliton using simple model examples.
Abstract: Solitons emerge in various non-linear systems as stable localized configurations, behaving in many ways like particles, from non-linear optics and condensed matter to nuclear physics, cosmology and supersymmetric theories This book provides an introduction to integrable and non-integrable scalar field models with topological and non-topological soliton solutions Focusing on both topological and non-topological solitons, it brings together debates around solitary waves and construction of soliton solutions in various models and provides a discussion of solitons using simple model examples These include the Kortenweg-de-Vries system, sine-Gordon model, kinks and oscillons, and skyrmions and hopfions The classical field theory of scalar field in various spatial dimensions is used throughout the book in presentation of related concepts, both at the technical and conceptual level Providing a comprehensive introduction to the description and construction of solitons, this book is ideal for researchers and graduate students in mathematics and theoretical physics

119 citations

Journal ArticleDOI
TL;DR: In this paper, a connection between the field of contact topology (the study of totally non-integrable plane distributions) and the study of Beltrami fields in hydrodynamics on Riemannian manifolds in dimension three was made.
Abstract: We draw connections between the field of contact topology (the study of totally non-integrable plane distributions) and the study of Beltrami fields in hydrodynamics on Riemannian manifolds in dimension three. We demonstrate an equivalence between Reeb fields (vector fields which preserve a transverse nowhere-integrable plane field) up to scaling and rotational Beltrami fields (non-zero fields parallel to their non-zero curl). This immediately yields existence proofs for smooth, steady, fixed-point free solutions to the Euler equations on all 3-manifolds and all subdomains of 3 with torus boundaries. This correspondence yields a hydrodynamical reformulation of the Weinstein conjecture from symplectic topology, whose recent solution by Hofer (in several cases) implies the existence of closed orbits for all rotational Beltrami flows on S 3 . This is the key step for a positive solution to a `hydrodynamical' Seifert conjecture: all steady flows of a perfect incompressible fluid on S 3 possess closed flowlines. In the case of spatially periodic Euler flows on 3 , we give general conditions for closed flowlines derived from the algebraic topology of the vector field.

115 citations

Journal ArticleDOI
TL;DR: In this article, the topology of domains in 3-space has been studied in the context of vector calculus, and the authors propose a topology for 3-Space vector calculus.
Abstract: (2002). Vector Calculus and the Topology of Domains in 3-Space. The American Mathematical Monthly: Vol. 109, No. 5, pp. 409-442.

113 citations