Properties of Ballooning Modes in the Planar Axis Heliotron Configurations with a Large Shafranov Shift

In the three-dimensional magnetic confinement configurations, the results of local mode analyses of the ballooning modes in the covering space (quasi modes) cannot be directly connected by superposition to the global mode analyses of the ballooning modes in the configuration space (physical modes) because of the lack of symmetry. However, a qualitative relation has been established to connect the quasi modes to physical modes in planar axis heliotron configurations with a large Shafranov shift. This relation is based on the topological structure of the level surfaces of the eigenvalues of the quasi modes. High-beta magnetohydrodynamic equilibria in the inward-shifted Large Helical Device configuration are examined. It is shown that the core plasma stays in the second stability, and the peripheral plasma stays near the marginally stable state against ballooning modes.