A constant-pressure tokamak model with skin currents on the plasma surface is used to optimize the plasma shape for fixed values of the aspect ratio and poloidal beta so as to maximize the total beta. The constraint is imposed for the plasma to be stable with respect to axisymmetric MHD modes. Although the absolute value of the maximum attainable beta is strongly determined by non-axisymmetric instabilities, the omission of these is demonstrated to be of minor influence on the optimum shape for the plasma model considered. The energy principle is used to determine axisymmetric stability. For shape optimization a modified method of steepest descent is used which adjusts the Fourier coefficients representing the plasma boundary. Since for small aspect ratio there is a preference for doublet-type shapes, a theory of axisymmetric stability for surface current doublets is included in the paper.
Wall stabilization of high-beta anisotropic plasmas in an axisymmetric mirror trap