Ballooning modes in 3-D Stellarators with shear

Pressure-driven ballooning and interchange instabilities in three-dimensional (3-D) vacuum Stellarator equilibria similar to those of the Heliotron-E device are investigated. The toroidal curvature dominates the mode structure, which concentrates where the field line bending is weakest. The Mercier criterion yields a more stringent condition for stability than the incompressible ballooning mode equation. The growth rates vary significantly with the radial wave number only on those field lines located on high-shear flux surfaces close to the edge of the plasma. They remain almost constant from field line to field line of a flux surface. An outward shift of the plasma induced with a vertical magnetic field increases the vacuum magnetic well, which improves the conditions for ballooning stability. An inward shift decreases the vacuum magnetic well, which deteriorates the conditions for ballooning stability.