Axisymmetric Stability in Ferromagnetic Tokamaks

In the first generation of fusion power plants, ferritic steels are attractive candidate materials for structural elements of first wall and breeding regions. These materials, however, are ferromagnetic and uncertainties remain as to the magnitude of the negative effects this may have on plasma confinement, particularly with the significant quantities of steel required. Vertical stability and control in tokamaks is an important design concern, particularly so at high plasma elongation. We present an analytical model of vertical displacement events in tokamaks with resistive walls, which assesses the modification to their passively stabilising influence when ferromagnetic effects are included. A dichotomy is found in the dependence of the instability growth rate upon the material’s magnetic permeability. For rapid instabilities, the induced currents penetrate only part way through the wall and its passive stabilising force is depleted. For slower instabilities, the wall is magnetically thin and the ferromagnetic field evolves in a quasi-steady manner, providing an additional destabilising influence. In either case, the growth rate is increased by a factor on the order of the effective relative magnetic permeability ($\sim2$).