In this paper, the practical existence of ideal MHD equilibria is investigated for various Tokamak designs. It is known from past experiment that, with increasing poloidal field-shaping coil distance, with increasing plasma elongation and with more strongly shaped plasma cross-section, obtaining the desired plasma cross-section becomes more difficult. It is also known from experiments that maintaining the desired cross-section in these parameter regimes of enhanced sensitivity becomes more difficult. A mathematical means of quantifying some of these designs and control problems is proposed, and it is hoped that these techniques can be used to improve the design of next-generation Tokamaks.
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