Axisymmetric stability of vertically asymmetric tokamaks at large beta poloidal

The stability of high-..beta.. vertically asymmetric tokamak equilibria to rigid displacements is investigated analytically. It is found that vertical stability at large beta poloidal is mainly determined by a coupling between the shape of the plasma surface and the Shafranov shift of the magnetic axis. To the lowest order, symmetric components of the plasma surface shape are found to be the critical destabilizing elements. Asymmetric components have little effect. The inclusion of higher order terms in the high ..beta.. tokamak expansion leads to further destabilization. Qualitative agreement between these analytic results and numerical stability calculations using the PEST code is demonstrated.