Beta limits for ETF

ETF (Engineering Test Facility) one-dimensional transport simulations indicate that a volume-average beta of 4% is required for ignition. It is therefore important that theoretical beta limits, determined by requiring equilibria to be stable to all ideal modes, exceed 4%. This paper documents an ideal MHD analysis wherein it is shown that, with appropriate plasma cross-sectional shape and current profile optimization, operation near 5% is possible. The critical beta value, however, depends on the functional form used for ff', which suggests that higher critical betas could be achieved by directly optimizing the safety factor profile.