Splitting instability of a high beta tokamak with noncircular cross section

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Abstract
The splitting of a tokamak with elliptical and bean‐shaped cross sections is studied for finite beta plasmas. When the plasma beta exceeds a critical value, an elliptical tokamak is subject to an ideal pressure‐driven instability, which deforms the ellipse in such a way that a thinned plasma current sheet is formed around the magnetic axis. As a result, magnetic reconnection is nonlinearly driven and the ellipse is split. The bean‐shaped tokamak, however, is stable against a splitting perturbation for limited equilibria that could be numerically constructed. An interesting similarity to the energy relaxation process in a force‐free plasma, namely, a two‐step evolution (initial occurrence of an ideal magnetohydrodynamic instability and subsequent occurrence of driven reconnection), is discussed.