Field topologies in ideal and near ideal magnetohydrodynamics and vortex dynamics

Abstract

Magnetic field topology frozen in ideal magnetohydrodynamics (MHD) and its breakage in near ideal MHD are reviewed in two parts. The first part gives a physically complete description of the frozen in field topology, taking magnetic flux conservation as fundamental and treating four topics, Eulerian and Lagrangian descriptions of MHD, Chandrasekhar-Kendall and Euler-potential field representations, magnetic helicity, and inviscid vortex dynamics in comparison to ideal MHD. A corollary clarifies the challenge of achieving a high degree of the frozen in condition in numerical MHD. The second part treats field topology breakage centered on the Parker Magnetostatic Theorem on a general incompatibility of a continuous magnetic field with the dual demand of force free equilibrium and an arbitrarily prescribed, 3D field topology. Preserving field topology as a global constraint readily results in formation of tangential magnetic discontinuities, i.e., electric current sheets of zero thickness. A similar incompatibility is present in the steady, force and thermal balance of a heated radiating fluid subject to an anisotropic thermal flux conducted strictly along the frozen in magnetic field in the low beta limit. In a weakly resistive fluid the thinning of current sheets by these incompatibilities inevitably results in sheet dissipation, resistive heating and topological changes in the field despite the small resistivity. Faraday induction drives but also macroscopically limits this mode of energy dissipation, storing free energy in self organized, ideal MHD structures. This property of MHD turbulence captured by the Taylor hypothesis is reviewed in relation to the Sun's corona, calling for a basic quantitative description of the breakdown of flux conservation in the low resistivity limit. A cylindrical, initial boundary value problem provides specificity in the review.

arXiv commentReview article, 20 pages, 2 figures, 158 references. see http://download.hao.ucar.edu/pub/low/Low_Sci_China-Phys_Mech_Astron_2015_58-015201.pdf

References in corpus (26)

• Physics of Solar Prominences: II - Magnetic Structure and Dynamics
• Physics of Solar Prominences: I - Spectral Diagnostics and Non-LTE Modelling
• The Emergence of a Twisted Flux Tube into the Solar Atmosphere: Sunspot Rotations and the Formation of a Coronal Flux Rope
• Fine strand-like structure in the solar corona from MHD transverse oscillations
• Three-Dimensional Simulations of Parker, Magneto-Jeans, and Swing Instabilities in Shearing Galactic Gas Disks
• Simulations of Prominence Formation in the Magnetized Solar Corona by Chromospheric Heating
• Magnetic Field Confinement in the Corona: The Role of Magnetic Helicity Accumulation
• Formation of Solar Filaments by Steady and Nonsteady Chromospheric Heating
• Deciphering Solar Magnetic Activity I: On The Relationship Between The Sunspot Cycle And The Evolution Of Small Magnetic Features
• On the Relationship Between a Hot-channel-like Solar Magnetic Flux Rope and its embedded Prominence
• Current Sheets Formation in Tangled Coronal Magnetic Fields
• The Relation between EIT Waves and Coronal Mass Ejections
• Numerical simulations of possible finite time singularities in the incompressible Euler equations: comparison of numerical methods
• The Dynamics of Funnel Prominences
• Thermal fine structure and magnetic fields in the solar atmosphere: spicules and fibrils
• The dependence of the helicity bound of force-free magnetic fields on boundary conditions
• Evidence for a singularity in ideal magnetohydrodynamics: implications for fast reconnection
• The Hydromagnetic Interior of a Solar Quiescent Prominence. I. Coupling between Force-balance and Steady Energy-transport
• The solar chromosphere observed at 1 Hz and 0."2 resolution
• Formation of Interstellar Clouds: Parker Instability with Phase Transitions
• Direct Measurements of Magnetic Twist in the Solar Corona
• The Parker Magnetostatic Theorem
• Magnetic Helicity of Self-Similar Axisymmetric Force-free Fields
• Do Potential Fields Develop Current Sheets Under Simple Compression or Expansion?
• Additive Self Helicity as a Kink Mode Threshold
• Polarimetric Diagnostics of Unresolved Chromospheric Magnetic Fields

Cited by in corpus (9)

• Some interesting topics provoked by the solar filament research in the past decade
• Statistical Analysis of Filament Features Based on the Hα Solar Images from 1988 to 2013 by Computer Automated Detection Method
• Global Coronal Waves
• Disintegration of an Eruptive Filament via Interactions with Quasi-Separatrix Layers
• Equilibria, Dynamics and Current Sheets Formation in Magnetically Confined Coronae
• Fast magnetic reconnection and the ideal evolution of a magnetic field
• A Model of Plasma Heating by Large-Scale Flow
• Deriving Potential Coronal Magnetic Fields from Vector Magnetograms
• Reconstruction of Coronal Magnetic Fields Using a Poloidal-Toroidal Representation