Magnetohydrodynamic stability and the effects of shaping: a near-axis view for tokamaks and quasisymmetric stellarators

How much does the cross-section of a toroidal magnetic field configuration tell us about its MHD stability? It is generally believed that positive triangularity (typically leading to bean-shaped cross-sections with their indentation on inboard side in stellarators) contributes positively stability. In this paper, we explore basis statement within near-axis description for axisymmetric and quasisymmetric configurations. agreement existing literature, show stabilises vertically elongated tokamaks. stellarators, asymmetry flux surfaces modifies relation. The behaviour stellarator-symmetric, stellarators can still be described terms shape one up-down symmetric cross-sections. However, sample configurations, positive-bean-shaped do not contribute Unlike case, also learn finite $\beta$ improve stability even without shear.