The shaping effect of cross section on ballooning modes in tokamak plasmas

The ideal magnetohydrodynamic (MHD) ballooning instability is investigated using an up-down symmetric local equilibrium model [W Yu et al 2012 Phys . Plasmas 19 072520 ] in a tokamak plasma with a shaped cross section. The influence of the shaping factors on the transition to the second stability region is stressed. Since the local equilibrium solution is expressed using eight independent parameters, and the derivative of the Shafranov shift is self-consistently determined in the model, the effect of the single shaping factor can be studied separately without equilibrium construction repeatedly. We found that the increasing elongation provides some improvement for the transition to the second stability region when holding other parameters fixed. In addition, positive plasma triangularity is more favorable for access to the second stable region than negative triangularity for moderate elongation.