A sufficient condition in resistive MHD

doi:10.1016/0375-9601(90)90008-C

Physics Letters A

Volume 147, Issue 1, 25 June 1990, Pages 28-30

https://doi.org/10.1016/0375-9601(90)90008-C Get rights and content

Abstract

A sufficient stability condition with respect to purely growing modes is derived for resistive MHD. Though it may be, in general, violated, its ability to reduce in the appropriate limits to known necessary and sufficient stability conditions makes it instructive and conceptually useful.

References (4)

H. Tasso
Phys. Lett. A
(1983)
H. Tasso
Plasma Phys.
(1975)

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Cited by (8)

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A sufficient stability condition with respect to purely growing modes is derived for resistive magnetohydrodynamics. Its "nearness" to necessity is analysed. lt is found that for physically reasonable approximations the condition is in some sense necessary and sufficient for stability against all modes. This, together with hermiticity makes its analytical and numerical evaluation worthwhile for the optimization of magnetic configurations. Physically motivated test functions are introduced. This leads to simplified versions of the stability functional, which makes its evaluation and minimization more tractable. In the case of special force-free fields the simplified functional reduces to a good approximation of the exact stability functional derived by other means. It turns out that in this case the condition is also sufficient for nonlinear stability. Nonlinear stability in hydrodynamics and magnetohydrodynamics is discussed especially in connection with "unconditional" stability and with severe limitations on the Reynolds number. Two examples in magnetohydrodynamics show that the limitations on the Reynolds numbers Can be removed but unconditional stability is preserved. Practical stability needs to be treated for limited levels of perturbations or for conditional stability. This implies some knowledge of the basin of attraction of the unperturbed solution, which is a very difficult problem. Finally, a special inertia-caused Hopf bifurcation is identified and the nature of the resulting attractors is discussed.
A manifest Hopf bifurcation in resistive magnetohydrodynamics
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In a general stability condition obtained by the author in a previous work physically motivated test functions are introduced. This leads to simplified versions of the stability functional, which makes its evaluation and minimization more tractable. In the case of special force-free fields the simplified functional reduces to a good approximation of the exact stability functional derived by other means. It turns out that in this case the condition is sufficient for nonlinear stability also.
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The general sufficient condition obtained by the author in a previous work is analysed with respect to its “nearness” to necessity. It is found that for physically reasonable approximations the condition is in some sense necessary and sufficient for stability against all modes. This together with Hermiticity makes its analytical and numerical evaluation worth doing for the optimization of magnetic configurations.
Magnetogravitational instability of a rotating anisotropic plasma with finite-ion-Larmor-radius corrections and generalized polytropic laws
1998, Journal of Plasma Physics

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A sufficient condition in resistive MHD

Abstract

Phys. Lett. A

Plasma Phys.