Axisymmetric MHD Equilibria from Kruskal-Kulsrud to Grad

1993 ◽  
pp. 111-134 ◽  
Author(s):  
Peter Lawrence ◽  
Edward Stredulinsky
Keyword(s):  
Mhd Equilibria

Global coronal and heliospheric magnetic field modelling for Solar Orbiter

2021 ◽  
Author(s):  
Thomas Wiegelmann ◽  
Thomas Neukirch ◽  
Iulia Chifu ◽  
Bernd Inhester
Keyword(s):  
Magnetic Field ◽  
Solar Rotation ◽  
Coronal Magnetic Field ◽  
Important Research ◽  
Parker Spiral ◽  
Important Research Topic ◽  
Mhd Equilibria ◽  
Solar Wind Flow ◽  
Nonlinear Force

<p>Computing the solar coronal magnetic field and plasma<br>environment is an important research topic on it's own right<br>and also important for space missions like Solar Orbiter to<br>guide the analysis of remote sensing and in-situ instruments.<br>In the inner solar corona plasma forces can be neglected and<br>the field is modelled under the assumption of a vanishing<br>Lorentz-force. Further outwards (above about two solar radii)<br>plasma forces and the solar wind flow has to be considered.<br>Finally in the heliosphere one has to consider that the Sun<br>is rotating and the well known Parker-spiral forms.<br>We have developed codes based on optimization principles<br>to solve nonlinear force-free, magneto-hydro-static and<br>stationary MHD-equilibria. In the present work we want to<br>extend these methods by taking the solar rotation into account.</p>

Localized Ideal and Resistive Instabilities in 3-dimensional MHD Equilibria with Closed Field Lines

1990 ◽  
Vol 45 (9-10) ◽  
pp. 1074-1076
Author(s):  
Dario Correa-Restrepo
Keyword(s):  
Radial Direction ◽  
Mhd Equations ◽  
Closed Field ◽  
Stability Criteria ◽  
Energy Principle ◽  
3 Dimensional ◽  
Pressure Surface ◽  
Mhd Equilibria ◽  
Field Lines ◽  
Low Shear

Abstract A class of stability criteria is derived for MHD equilibria with closed field lines. The destabilizing perturbations have finite gradients along the field and are localized around a field line, the localiza-tion being stronger on the pressure surface than in the radial direction. By contrast, in sheared configurations the localization is comparable in both directions. The derived stability criteria are less stringent than those obtained for MHD equilibria with shear for similarly localized perturbations in the limit of low shear. These results, obtained from the energy principle, are a particular case of those obtained by solving the linearized resistive MHD equations with an appropriate ansatz and subsequently taking the limit of vanishing shear and resistivity.

scholarly journals An optimization principle for the computation of MHD equilibria in the solar corona

2006 ◽  
Vol 457 (3) ◽  
pp. 1053-1058 ◽  
Author(s):  
T. Wiegelmann ◽  
T. Neukirch
Keyword(s):  
Solar Corona ◽  
Optimization Principle ◽  
Mhd Equilibria

scholarly journals Finite beta effects on MHD equilibria and energetic ion losses in a rippled tokamak

2012 ◽  
Vol 52 (8) ◽  
pp. 083009 ◽  
Author(s):  
M. Bunno ◽  
Y. Nakamura ◽  
Y. Suzuki ◽  
K. Shinohara ◽  
G. Matsunaga
Keyword(s):  
Mhd Equilibria

Magnetohydrodynamic Equilibria

2020 ◽  
Author(s):  
Thomas Wiegelmann
Keyword(s):  
Magnetic Field ◽  
Boundary Conditions ◽  
Lorentz Force ◽  
Plasma Flow ◽  
Plasma Pressure ◽  
Mhd Equations ◽  
The Sun ◽  
Planetary Magnetospheres ◽  
Mhd Equilibria ◽  
The Magnetic Field

Magnetohydrodynamic equilibria are time-independent solutions of the full magnetohydrodynamic (MHD) equations. An important class are static equilibria without plasma flow. They are described by the magnetohydrostatic equations j×B=∇p+ρ∇Ψ,∇×B=μ0j,∇·B=0. B is the magnetic field, j the electric current density, p the plasma pressure, ρ the mass density, Ψ the gravitational potential, and µ0 the permeability of free space. Under equilibrium conditions, the Lorentz force j×B is compensated by the plasma pressure gradient force and the gravity force. Despite the apparent simplicity of these equations, it is extremely difficult to find exact solutions due to their intrinsic nonlinearity. The problem is greatly simplified for effectively two-dimensional configurations with a translational or axial symmetry. The magnetohydrostatic (MHS) equations can then be transformed into a single nonlinear partial differential equation, the Grad–Shafranov equation. This approach is popular as a first approximation to model, for example, planetary magnetospheres, solar and stellar coronae, and astrophysical and fusion plasmas. For systems without symmetry, one has to solve the full equations in three dimensions, which requires numerically expensive computer programs. Boundary conditions for these systems can often be deduced from measurements. In several astrophysical plasmas (e.g., the solar corona), the magnetic pressure is orders of magnitudes higher than the plasma pressure, which allows a neglect of the plasma pressure in lowest order. If gravity is also negligible, Equation 1 then implies a force-free equilibrium in which the Lorentz force vanishes. Generalizations of MHS equilibria are stationary equilibria including a stationary plasma flow (e.g., stellar winds in astrophysics). It is also possible to compute MHD equilibria in rotating systems (e.g., rotating magnetospheres, rotating stellar coronae) by incorporating the centrifugal force. MHD equilibrium theory is useful for studying physical systems that slowly evolve in time. In this case, while one has an equilibrium at each time step, the configuration changes, often in response to temporal changes of the measured boundary conditions (e.g., the magnetic field of the Sun for modeling the corona) or of external sources (e.g., mass loading in planetary magnetospheres). Finally, MHD equilibria can be used as initial conditions for time-dependent MHD simulations. This article reviews the various analytical solutions and numerical techniques to compute MHD equilibria, as well as applications to the Sun, planetary magnetospheres, space, and laboratory plasmas.

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