MHD beta limits: scaling laws and comparison with Doublet III data

Abstract

Simple scaling laws for the ideal-MHD β-limit (βc) as a function of plasma shape parameters (inverse aspect ratio ε, elongation κ, and triangularity δ) in the range covered by recent high-β (≤ 4.5%) experiments in Doublet III are derived. β-limits are obtained by optimizing the current profile. A large class of profiles is considered. β-limits are presented for a single Gaussian profile as they do not significantly improve with more elaborate profiles. Excluding the region dominated by sawtooth activity, experimental values do not exceed the n = ∞ ballooning mode β-limit, but do exceed the n = 1 kink mode limit if no wall stabilization is assumed, even in the presence of a cool mantle. If wall stabilization is assumed, the kink limit is above the ballooning limit when the safety factor at the plasma surface (qs) is greater than two. Even with a fairly close wall, the kink is still unstable when qs < 2. Kinetic effects are not found to significantly improve the ballooning limit in this work. A unified limit curve is postulated which combines the commonly observed hard qs = 2 kink limit with the n = ∞ ballooning limit for qs > 2: βc(%) = 27 ε1.3κ1.2 (1 + 1.5δ) for qs > 2 and βc = 0 for qs < 2. This expression shows that triangularity is almost as important as elongation to reach high β-values.