Ferromagnetic and resistive wall effects on the beta limit in a tokamak

The ferromagnetic and resistive wall effects on the beta limit in a high aspect ratio tokamak are investigated. It is shown that the beta limit is reduced to 90% of that without ferromagnetic effect for a high aspect ratio tokamak, when the relative permeability of the ferromagnetic wall is 2. In these analyses, parabolic profiles for both plasma current and pressure are employed and the radius and thickness of the resistive wall are r(w) = 1.43a and d = 0.07a (a is plasma minor radius), respectively. The stability window with respect to the external kink modes is shown to be reduced by a high permeability effect in the case of a uniform current tokamak plasma, which is different from the case where only the finite resistivity effect is considered. The effect of toroidal plasma flow is also investigated, and it is shown that the toroidal background flow velocity of 0.3nu(pa), nu(pa) is poloidal Alfven velocity, is sufficient for the resistive wall to have the stability effect of an ideal wall. The ferromagnetic effect of the wall destabilizes both resistive wall and ideal kink modes.