Shape Optimization of Tokamak Plasmas to Localized Magnetohydrodynamic Modes

We employ a numerical technique to optimize the shape of tokamak plasmas to achieve maximum stable volume-averaged $\beta$ with respect to ballooning modes. We have examined dee shapes with moderately peaked current profile, poloidal $\beta =1\mathrm{}$, and $\frac{R}{a}=2.76\mathrm{}$. The optimal shape is a strongly modified dee with a large indentation on the inside edge of the plasma. Maximum beta increases with elongation and exceeds 14% when $\frac{b}{a}=3\mathrm{}$.