Analysis of ideal MHD equilibrium and axisymmetric stability for finite aspect ratio tokamaks with elliptic cross-section and flat current profile

To calculate the equilibrium and stability of finite aspect ratio tokamaks, even for circular and elliptical plasma cross-sections, intricate numerical methods must usually be employed, which require a fast and large computer. So far, these calculations have been carried out analytically only for infinite aspect ratio. In fact certain analytical equilibrium solutions at finite aspect ratio are known, but these do not include such important cases as elliptical cross-sections. In this paper, finite aspect ratio equilibrium solutions are derived for circular, prolate and oblate elliptical cross-sections and for a flat current profile. In addition, the problem of axisymmetric stability is studied for prolate elliptical cross-sections, the approach being almost entirely analytical.