Numerical study of the ideal-MHD stability limits in oblate spheromaks

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Abstract
The ideal-MHD stability properties of a class of hollow oblate spheromaks are studied numerically with a spectral code. An internal kink instability is found whenever the safety factor on axis, qo, rises above one. Its growth rate is only a weak function of the pressure. By shaping the current profile such that, simultaneously, q0 = 1 and the Mercier criterion is satisfied, full stability against internal perturbations is obtained up to a maximum value of β, this value increasing with the aspect ratio. For a configuration without a central hole, the maximum β is 1.5% and for an aspect ratio of 2.34, which is the largest that has been studied, it reaches 40%. Without a conducting shell, all equilibria are unstable to free-boundary modes, the fastest-growing mode being that associated with a global tilting motion. These modes, in contrast to the internal modes, are stabilized as the aspect ratio decreases. In the limiting case of no hole, the force-free equilibrium is only unstable with respect to n = 1 displacement which can be stabilized by a conducting shell located at a distance from the plasma boundary of 30% of the plasma minor radius.