Kink instabilities of a sharp boundary plasma column with elliptical cross-section are studied. A general form of dispersion relation expressed in terms of elliptical eigenfunctions and analytical results for single-mode and double-mode perturbation (to second order in ellipticity ε) are given. For an arbitrary ellipticity, numerical calculations are carried out.Numerical results show that the coupling among modes has a destabilizing effect. qΣ required for stability increases rapidly with e. Accordingly, the number of coupled modes to be taken into account will also increase. When the coupled modes for a given e increases to a certain number, qΣ approaches a limit. With a/b > 2 and in the absence of a conductive shell, we obtain approximately: qΣ-l∝(a/b)2. For a system of finite length, perturbations having wavelength equal to the system length are the most dangerous ones. In the case of small ellipticity, as the system length shortens (i.e. the aspect ratio decreases) the value of qΣ required for those perturbations increases only slightly. A conductive shell close to the plasma has a stabilizing effect to some extent. However, if a/b is large enough, either perturbation with finite wavelength or any conductive shell has hardly any effect on the value of qΣ. In addition, in the presence of a conductive shell, qΣ changes abruptly at certain values of a/b. The stability condition is more stringent in the high-β system than in low-β system.
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