Second ballooning stability in high-β, compact stellarators

Abstract

Second ballooning stability is examined in quasipoloidally symmetric, compact stellarator configurations. These high-β (volume-average β>4%) free-boundary equilibria are calculated using a reference Quasi-Poloidal Stellarator (QPS) configuration. QPS plasmas have low-shear, stellarator-like rotational transform profile with |B| that is approximately poloidally symmetric. The high-β QPS equilibria are similar in their magnetic configuration to previously studied tokamak-stellarator hybrids which have a high-shear, tokamak-like rotational transform profile. Both types of configurations have strong magnetic wells and consequently high interchange stability β limits. Free-boundary QPS equilibria have regions of second stability at high β. For infinite-n ballooning modes in QPS plasmas, the boundary for first instability is 〈β〉∼2% and the boundary for second stability is 〈β〉∼6%. Finite-n ballooning mode calculations show higher β limits, 〈β〉>5%. Increasing plasma current (for fixed plasma pressure) can lower the finite-n ballooning mode β limit to 〈β〉=3% by reducing magnetic shear. QPS plasmas with Ohmic current profiles (peaked on-axis) have both a lower infinite-n ballooning β-limit for the onset of first instability and a higher β-limit for the onset of second stability relative to QPS plasma with bootstrap current profiles (peaked off-axis). QPS plasmas are stable to low-n ideal magnetohydrodynamic kink modes and vertical modes for values of β in this range (〈β〉∼6%) due to the low level of plasma current in QPS relative to an equivalent tokamak.