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

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 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

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

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 Global well-posedness of the full compressible Hall-MHD equations

2021 ◽  
Vol 10 (1) ◽  
pp. 1235-1254
Author(s):  
Qiang Tao ◽  
Canze Zhu
Keyword(s):  
Global Solution ◽  
Large Time ◽  
Initial Temperature ◽  
Large Time Behavior ◽  
Initial Energy ◽  
Mhd Equations ◽  
Well Posedness ◽  
Time Behavior ◽  
Magnetohydrodynamic Flows ◽  
Hall Mhd

Abstract This paper deals with a Cauchy problem of the full compressible Hall-magnetohydrodynamic flows. We establish the existence and uniqueness of global solution, provided that the initial energy is suitably small but the initial temperature allows large oscillations. In addition, the large time behavior of the global solution is obtained.

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
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