High-n ballooning modes in highly elongated tokamaks

Abstract

An analytic study of stability against high-n ballooning modes in highly elongated axi-symmetric plasmas is presented and compared with computational results. – From the equation for the marginal pressure gradient, it is found that local shear has an important effect on the stability of elongated plasmas, and that stability deteriorates through high elongation since the stabilizing effects of field line bending and local shear are reduced. The net contribution of the local shear to stability decreases with elongation for strong ballooning modes (eigenfunctions strongly localized near the outer edge of the toroidal flux surfaces) but increases for interchange modes (eigenfunctions more uniform along the flux surfaces). – The computational study of high-n ballooning modes in a highly elongated plasma reveals that lowering the aspect ratio and broadening the pressure profile enhance the marginal beta for βp less than unity but severely reduce the marginal beta for βp larger than unity.