A measure of control sensitivity and saturation effects for Tokamak equilibria

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.