Topics on MHD Equilibrium and Stability in Heliotron / Torsatron

Recent topics on the MHD properties with and without bootstrap current in Heliotron / Torsatron configurations are presented. In a currentless equilibrium with a large Shafranov shift, a high-n ballooning mode can be unstable even in the region with positive gradient of the rotational transform. This is because the local shear in the field line bending term can be reduced by the fact that the local enhancement of the poloidal field varies in the radial direction. Since the local curvature of the field lines depends on the label of the magnetic field line, alpha, in Heliotron/Torsatron, the eigenvalue omega^2 also depends on alpha. In the Mercier stable region, the level surfaces of omega^2 of unstable modes form spheroids in the (psi, theta_k, alpha) space, where psi and theta_k are the label of the flux surface and the radial wave number, while they form cylinders in tokamaks. Such high-n modes cannot be related to low-n modes in this case. In the LHD configuration, bootstrap current depends on the collisionality of the plasma. When the beta value is raised by increasing the temperature with the density fixed, the plasma becomes less collisional and the bootstrap current grows in the direction where the rotational transform is increased. On the contrary, when the beta value is raised by increasing the density with the temperature fixed, the plasma becomes more collisional. While a small amount of the current flows in the same direction as in the above sequence at low beta in this case, the direction of the current reverses at high beta equilibrium. This is because the geometrical factor in the expression of the bootstrap current in the plateau regime has opposite signature to that in the 1/nu regime. The latter equilibrium sequence is more stable in the Mercier criterion than the former one. Thus, the beta should be raised by increasing the density rather than the temperature to obtain stable high beta plasma