Beta limit of crescent and bean shaped tokamaks

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Abstract
The maximum attainable beta values which can be expected in tokamaks with crescent (BEAN 1) and rounded (BEAN 2) bean shaped cross-sections are obtained numerically by using the linear ideal MHD stability analysis code ERATO. The current profiles are optimized with a fixed pressure profile for high values of beta, keeping Mercier, high-n ballooning and n = 1 kink modes stable. The poloidal plasma cross-sections are inscribed in a rectangle with an aspect ratio of three and an ellipticity of two. A confocal wall, the distance of which from the plasma surface is equal to the horizontal minor plasma radius, is present to stabilize against the kink mode. Depending on the shape and triangularity (indentation), a beta value of 10 to 17% is obtained. It is also shown that the coefficient of the Troyon-type beta scaling increases for an indented plasma. In the case of small indentation, the BEAN 1 type tokamaks show higher beta values than the BEAN 2 type. For strong indentation, the BEAN 2 type gives the highest beta value.