scholarly journals Local representation and construction of Beltrami fields II.solenoidal Beltrami fields and ideal MHD equilibria

2019 ◽  
Vol 400 ◽  
pp. 132142 ◽  
Author(s):  
N. Sato ◽  
M. Yamada
Keyword(s):  
Local Representation ◽  
Beltrami Fields ◽  
Ideal Mhd ◽  
Mhd Equilibria

Ballooning Modes in Three-dimensional MHD Equilibria with Shear

1978 ◽  
Vol 33 (7) ◽  
pp. 789-791 ◽  
Author(s):  
D. Correa-Restrepo
Keyword(s):  
Magnetic Field ◽  
Eigenvalue Problem ◽  
Field Line ◽  
Magnetic Field Line ◽  
Three Dimensional ◽  
One Dimensional ◽  
Ideal Mhd ◽  
Mhd Equilibria

Stability with respect to ballooning modes in arbitrary, three-dimensional, ideal MHD equilibria with shear is studied. The destabilizing perturbations considered here have finite gradients along the field and are localized around a closed magnetic field line, the localization being weaker on the surface than transversally to it. This kind of localization allows the problem of stability to be reduced to the solution of a one-dimensional eigenvalue problem.

The only three classes of symmetric MHD equilibria

1980 ◽  
Vol 24 (3) ◽  
pp. 515-518 ◽  
Author(s):  
J. W. Edenstrasser
Keyword(s):  
Space Variable ◽  
Magnetic Axis ◽  
Ideal Mhd ◽  
Mhd Equilibria

Ideal MHD equilibria with an ignorable space variable are investigated. It is shown that only three classes of these symmetric equilibria exist: the systems with a straight, a (cylindric) helical, and a circular magnetic axis.

Computation of Tokamak Equilibria With Steady Flow

1987 ◽  
Vol 42 (10) ◽  
pp. 1154-1166 ◽  
Author(s):  
W. Kerner ◽  
S. Tokuda
Keyword(s):  
Steady Flow ◽  
Stationary Flow ◽  
Plasma Boundary ◽  
Ideal Mhd ◽  
Mhd Equilibria ◽  
Free Plasma

The equations for ideal MHD equilibria with stationary flow are re-examined and addressed as numerically applied to tokamak configurations with a free plasma boundary. Both the isothermal (purely toroidal flow) and the poloidal flow cases are treated. Experiment-relevant states with steady flow (so far only in the toroidal direction) are computed by the modified SELENE40 code.

Computation of ideal MHD equilibria

1976 ◽  
Vol 12 (1) ◽  
pp. 33-44 ◽  
Author(s):  
K. Lackner
Keyword(s):  
Ideal Mhd ◽  
Mhd Equilibria

An energy criterion for the linear stability of conservative flows

2000 ◽  
Vol 402 ◽  
pp. 329-348 ◽  
Author(s):  
P. A. DAVIDSON
Keyword(s):  
Variational Principle ◽  
Linear Stability ◽  
Energy Criterion ◽  
Conservative System ◽  
Base Flow ◽  
Recirculating Flow ◽  
Ideal Mhd ◽  
Mhd Equilibria ◽  
Euler Flows ◽  
The Stability

We investigate the linear stability of inviscid flows which are subject to a conservative body force. This includes a broad range of familiar conservative systems, such as ideal MHD, natural convection, flows driven by electrostatic forces and axisymmetric, swirling, recirculating flow. We provide a simple, unified, linear stability criterion valid for any conservative system. In particular, we establish a principle of maximum action of the formformula herewhere η is the Lagrangian displacement,e is a measure of the disturbance energy, T and V are the kinetic and potential energies, and L is the Lagrangian. Here d represents a variation of the type normally associated with Hamilton's principle, in which the particle trajectories are perturbed in such a way that the time of flight for each particle remains the same. (In practice this may be achieved by advecting the streamlines of the base flow in a frozen-in manner.) A simple test for stability is that e is positive definite and this is achieved if L(η) is a maximum at equilibrium. This captures many familiar criteria, such as Rayleigh's circulation criterion, the Rayleigh–Taylor criterion for stratified fluids, Bernstein's principle for magnetostatics, Frieman & Rotenberg's stability test for ideal MHD equilibria, and Arnold's variational principle applied to Euler flows and to ideal MHD. There are three advantages to our test: (i) d2T(η) has a particularly simple quadratic form so the test is easy to apply; (ii) the test is universal and applies to any conservative system; and (iii) unlike other energy principles, such as the energy-Casimir method or the Kelvin–Arnold variational principle, there is no need to identify all of the integral invariants of the flow as a precursor to performing the stability analysis. We end by looking at the particular case of MHD equilibria. Here we note that when u and B are co-linear there exists a broad range of stable steady flows. Moreover, their stability may be assessed by examining the stability of an equivalent magnetostatic equilibrium. When u and B are non-parallel, however, the flow invariably violates the energy criterion and so could, but need not, be unstable. In such cases we identify one mode in which the Lagrangian displacement grows linearly in time. This is reminiscent of the short-wavelength instability of non-Beltrami Euler flows.

Nonlinear Evolution of Internal Ideal MHD Modes Near the Boundary of Marginal Stability

1982 ◽  
Vol 37 (8) ◽  
pp. 816-829
Author(s):  
E. Rebhan
Keyword(s):  
Equations Of Motion ◽  
Stability Limit ◽  
Mhd Equations ◽  
Marginal Stability ◽  
Unstable State ◽  
Stable Regime ◽  
Ideal Mhd ◽  
Mhd Equilibria ◽  
The Stability ◽  
Marginal Mode

A family of ideal MHD equilibria is considered introducing the concept of a driving parameter λ the increase of which beyond a certain threshold λ0 drives the plasma from a linearly stable to an unstable state. Using reductive perturbation theory, the nonlinear ideal MHD equations of motion are expanded in the neighbourhood of λ0 with respect to a small parameter ε. An appropriate scaling for the expansions is derived from the linear eigenmode problem. Integrability conditions for the reduced nonlinear equations yield nonlinear amplitude equations for the marginal mode. Nonlinearly, the instabilities are either oscillations about bifurcating equilibria, or they are explosive. In the latter case, the stability limit depends on the amplitude of the perturbation and is shifted into the linearly stable regime. Generally bifurcation of dynamically connected equilibria is observed at λ0

Stability of axisymmetric modes in plasma–vacuum equilibria

1997 ◽  
Vol 58 (4) ◽  
pp. 655-664
Author(s):  
D. LORTZ
Keyword(s):  
Perturbation Theory ◽  
Aspect Ratio ◽  
Cross Section ◽  
Stability Criterion ◽  
Axis Ratio ◽  
Elliptical Cross ◽  
Linear Profiles ◽  
Ideal Mhd ◽  
Mhd Equilibria ◽  
Half Axis

A stability criterion for axisymmetric modes of ideal MHD equilibria without wall stabilization is derived for linear profiles with vanishing current density at the edge. Using perturbation theory, the critical half-axis ratio of the elliptical cross-section is computed for finite aspect ratio.

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