New approach to magnetohydrodynamic stability: I. A practical stability concept

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Abstract
An equilibrium is called σ stable if growth faster than exp (σt) does not occur. On the basis of this definition a modified energy principle is obtained by means of which the stability of plasma confinement systems can be tested for times of thermonuclear interest, instead of the infinitely long times which are pertinent to the usual stability analysis. The theory is applied to the diffuse linear pinch, a theorem for σ stability is derived, and the connection with the normal-mode analysis is shown to be given with the Sturmian property, which holds for the unstable side of the spectrum, whereas the stable side consists of Sturmian and anti-Sturmian point spectra separated by continuous spectra. Growth rates and eigen-functions of Suydam modes are numerically calculated, and it is shown that violation of Suydam's criterion in the high and intermediate shear case leads to nonlocalized rapidly growing m = 1 modes. Consequently, this criterion obtains new relevance in the σ-stability analysis for this regime.