We employ a numerical technique to optimize the shape of tokamak plasmas to achieve maximum stable volume-averaged β with respect to ballooning modes. We have examined dee shapes with moderately peaked current profile, poloidal β=1, and R/a=2.76. 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 b/a=3.
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Miller et al. (1979) studied this question.
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