scholarly journals Generalized Grad–Shafranov equation for non-axisymmetric MHD equilibria

2020 ◽  
Vol 27 (10) ◽  
pp. 102504
Author(s):  
J. W. Burby ◽  
N. Kallinikos ◽  
R. S. MacKay
Keyword(s):  
Mhd Equilibria ◽  
Shafranov Equation

Stability criterion for symmetric MHD equilibria by minimizing the potential energy

1978 ◽  
Vol 20 (3) ◽  
pp. 503-520 ◽  
Author(s):  
Johann W. Edenstrasser
Keyword(s):  
Potential Energy ◽  
Stability Criterion ◽  
Sufficient Criterion ◽  
First Variation ◽  
General Symmetry ◽  
Linear Eigenvalue Problem ◽  
Mhd Equilibria ◽  
Shafranov Equation ◽  
The First Variation ◽  
Invariants Of Motion

The potential energy of an ideal static MHD plasma is minimized using the invariants of motion as variational constraints and assuming a general symmetry (dependence on two space variables only). For simplicity only the plasma-on- the-wall case is considered. The first variation yields a generalized Shafranov equation, the second the desired stability criterion. It is found that equilibria with a longitudinal current increasing monotonicaily towards the boundary are always stable with respect to symmetric modes. For equilibria with an outwardly decreasing current a sufficient criterion (for symmetric modes) is derived, which only requires the solution of a linear eigenvalue problem. The theory is applied to the straight circular cylinder and to the axisymmetric torus.

scholarly journals Grad-Shafranov equation for non-axisymmetric MHD equilibria

2020 ◽  
Author(s):  
Joshua William Burby ◽  
Nikos Kallinikos ◽  
Robert MacKay
Keyword(s):  
Mhd Equilibria ◽  
Shafranov Equation

scholarly journals Generalized Grad-Shafranov Equation for Gravitational Hall-MHD Equilibria

2008 ◽  
Author(s):  
C. Cremaschini ◽  
A. Beklemishev ◽  
J. Miller ◽  
M. Tessarotto ◽  
Takashi Abe
Keyword(s):  
Mhd Equilibria ◽  
Shafranov Equation ◽  
Hall Mhd

Solving the Grad–Shafranov equation with spectral elements

2014 ◽  
Vol 185 (5) ◽  
pp. 1415-1421 ◽  
Author(s):  
E.C. Howell ◽  
C.R. Sovinec
Keyword(s):  
Spectral Elements ◽  
Shafranov Equation

scholarly journals A family of analytic equilibrium solutions for the Grad–Shafranov equation

2007 ◽  
Vol 14 (11) ◽  
pp. 112508 ◽  
Author(s):  
L. Guazzotto ◽  
J. P. Freidberg
Keyword(s):  
Equilibrium Solutions ◽  
Shafranov Equation

Three-dimensional nonlinear ideal MHD equilibria with field-aligned incompressible and compressible flows

2016 ◽  
Vol 23 (8) ◽  
pp. 082502 ◽  
Author(s):  
S. M. Moawad ◽  
D. A. Ibrahim
Keyword(s):  
Compressible Flows ◽  
Three Dimensional ◽  
Ideal Mhd ◽  
Mhd Equilibria

scholarly journals Criticality of the Grad–Shafranov equation: transport barriers and fragile equilibria

2004 ◽  
Vol 46 (3) ◽  
pp. L7-L13 ◽  
Author(s):  
Emilia R Solano
Keyword(s):  
Transport Barriers ◽  
Shafranov Equation

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>

Simple MHD Equilibria

2009 ◽  
pp. 91-98
Author(s):  
Dalton D. Schnack
Keyword(s):  
Mhd Equilibria
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