Kink instabilities of a sharp boundary plasma with small aspect ratio are studied. The results of numerical calculations show that a conductive shell has a stabilizing effect to some extent and critical beta of toroidal mode number n=1 is the minimum whether there is a conductive shell or not, i.e. the perturbation with n=1 is the most dangerous one. With decrease of aspect ratio, the critical beta increases initially, when a/R = 0.7, it appears as a maximum, when a/R≥0.6, the critical beta values of high beta limit and low beta limit are nearly equal.
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