Maximum beta for a small-aspect-ratio tokamak

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Abstract
Ideal linear magnetohydrodynamic (MHD) stability calculations demonstrate reasonable adherence at low aspect ratio (ARAR=5/3), a wide range of stable equilibria having volume‐averaged beta, 〈β〉, in excess of 20% is found. A systematic approach for estimating the maximum beta is used. First, the aspect ratio is reduced, for fixed shape and profiles, starting from the Troyon optimized case at AR=2.5; the plasma cross‐section shape is then varied for fixed profiles at fixed AR=5/3; and finally, pressure and safety factor profiles are varied for fixed shape and aspect ratio. The calculations are carried out for low n (n=1–3), usually with a conducting wall at a radius of 1.5 times the plasma minor radius, for n=∞ ballooning modes, and for Mercier stability. Several additional ‘‘spot checks’’ on the effects of moving the conducting wall to infinity and of the stability of n=0 and n=4 and 5 modes indicate good stability properties for these, also. The calculations presented here demonstrate a straightforward extrapolation of the Troyon scaling formula to low aspect ratio, in spite of qualitative differences previously noted in low‐aspect‐ratio equilibria.