Method of symmetry transforms for ideal MHD equilibrium equations

2002 ◽  
pp. 195-218 ◽  
Author(s):  
Oleg I. Bogoyavlenskij
Keyword(s):  
Equilibrium Equations ◽  
Mhd Equilibrium ◽  
Ideal Mhd

scholarly journals CMEs ‘en rafale’ observations and simulations

2008 ◽  
Vol 4 (S257) ◽  
pp. 251-255
Author(s):  
Cristiana Dumitrache
Keyword(s):  
Magnetic Field ◽  
Magnetic Reconnection ◽  
Solar Disk ◽  
Large Scale ◽  
Stable Equilibrium ◽  
Time Dependent ◽  
Kink Mode ◽  
Mhd Equilibrium ◽  
Ideal Mhd ◽  
Slow Evolution

AbstractA CME is triggered by the disappearance of a stable equilibrium as a result of the slow evolution of the photospheric magnetic field. This disappearance may be due to a loss of ideal-MHD equilibrium or stability as in the kink mode, or to a loss of resistive-MHD equilibrium as a result of magnetic reconnection. We have obtained CMEs in sequence by a time dependent magnetohydrodynamic computation performed on three solar radii. These successive CMEs resulted from a prominence eruption. Velocities of these CMEs decrease in time, from a CME to another. We present observational evidences for large-scale magnetic reconnections that caused the destabilization of a sigmoid filament. These reconnections covered half of the solar disk and produced CMEs in squall (sequential CMEs).

Linear and nonlinear stability criteria for compressible MHD flows in a gravitational field

2013 ◽  
Vol 79 (5) ◽  
pp. 873-883 ◽  
Author(s):  
S. M. MOAWAD
Keyword(s):  
Gravitational Field ◽  
Variational Principles ◽  
Flow Speed ◽  
Equilibrium States ◽  
Order Partial Differential Equation ◽  
Equilibrium Equations ◽  
State Equations ◽  
Mhd Equilibrium ◽  
Linear And Nonlinear ◽  
Field Lines

AbstractThe equilibrium and stability properties of ideal magnetohydrodynamics (MHD) of compressible flow in a gravitational field with a translational symmetry are investigated. Variational principles for the steady-state equations are formulated. The MHD equilibrium equations are obtained as critical points of a conserved Lyapunov functional. This functional consists of the sum of the total energy, the mass, the circulation along field lines (cross helicity), the momentum, and the magnetic helicity. In the unperturbed case, the equilibrium states satisfy a nonlinear second-order partial differential equation (PDE) associated with hydrodynamic Bernoulli law. The PDE can be an elliptic or a parabolic equation depending on increasing the poloidal flow speed. Linear and nonlinear Lyapunov stability conditions under translational symmetric perturbations are established for the equilibrium states.

scholarly journals Free boundary 3D ideal MHD equilibrium calculations for non-linearly saturated current driven external kink modes in tokamaks

2018 ◽  
Vol 58 (7) ◽  
pp. 074001 ◽  
Author(s):  
A. Kleiner ◽  
J.P. Graves ◽  
W.A. Cooper ◽  
T. Nicolas ◽  
C. Wahlberg
Keyword(s):  
Free Boundary ◽  
Mhd Equilibrium ◽  
Ideal Mhd ◽  
External Kink ◽  
Equilibrium Calculations

scholarly journals On resistive magnetohydrodynamic equilibria of an axisymmetric toroidal plasma with flow

2000 ◽  
Vol 64 (5) ◽  
pp. 601-612 ◽  
Author(s):  
G. N. THROUMOULOPOULOS ◽  
H. TASSO
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Incompressible Flows ◽  
Type Equation ◽  
Magnetic Axis ◽  
Order Partial Differential Equation ◽  
Equilibrium Equations ◽  
Partial Differential ◽  
Toroidal Plasma ◽  
Mhd Equilibrium

It is shown that the magnetohydrodynamic (MHD) equilibrium states of an axisymmetric toroidal plasma with finite resistivity and flows parallel to the magnetic field are governed by a second-order partial differential equation for the poloidal magnetic flux function ψ coupled with a Bernoulli-type equation for the plasma density (which are identical in form to the corresponding ideal MHD equilibrium equations) along with the relation Δ*ψ = Vcσ (here Δ* is the Grad–Schlüter–Shafranov operator, σ is the conductivity and Vc is the constant toroidal-loop voltage divided by 2π). In particular, for incompressible flows, the above-mentioned partial differential equation becomes elliptic and decouples from the Bernoulli equation [H. Tasso and G. N. Throumoulopoulos, Phys. Plasma5, 2378 (1998)]. For a conductivity of the form σ = σ(R, ψ) (where R is the distance from the axis of symmetry), several classes of analytic equilibria with incompressible flows can be constructed having qualitatively plausible σ profiles, i.e. profiles with σ taking a maximum value close to the magnetic axis and a minimum value on the plasma surface. For σ = σ(ψ), consideration of the relation Δ*ψ = Vc σ(ψ) in the vicinity of the magnetic axis leads then to a proof of the non-existence of either compressible or incompressible equilibria. This result can be extended to the more general case of non-parallel flows lying within the magnetic surfaces.

Some uniqueness theorems for the ideal MHD equilibrium of a cylindrical tokamak

1979 ◽  
Vol 21 (1) ◽  
pp. 177-182 ◽  
Author(s):  
C.LL. Thomas
Keyword(s):  
Free Boundary ◽  
Uniqueness Theorem ◽  
Current Density ◽  
Equilibrium Equation ◽  
Uniqueness Theorems ◽  
Total Current ◽  
Mhd Equilibrium ◽  
Ideal Mhd ◽  
Boundary Equilibrium ◽  
The Ideal

The cylindrical MHD equilibrium equation is formulated in a manner suitable for numerical computations which require the application of a constraint. In this formulation a uniqueness theorem is proved for a free boundary equilibrium with a specified total current. Uniqueness is independent of the details of the current density and merely requires that the total current is compatible with the current density. Two uniqueness theorems for diffuse plasmas are also presented. Four free boundary examples are studied with a variety of constraints applied.

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