Abstract
The traditional theory of the resistive wall modes (RWMs) in the toroidal fusion systems was developed assuming the magnetic permeability μ of the wall the same as the vacuum one μ0. Here, we analyze the dynamics of unstable RWMs at the presence of a ferromagnetic wall with μ≡μ/μ0≤4. This choice with μ=const corresponds to the saturated state of ferritic materials in a strong magnetic field, as it should be in a tokamak reactor. The study is based on the cylindrical dispersion relation valid for arbitrary s/dw, where s is the skin depth and dw is the wall thickness. This equation is solved numerically, and the solutions are compared with analytical asymptotes obtained for slow (s≫dw) and fast (s≪dw) RWMs. Within the model, only very slow RWMs are found insensitive to variations of μ, while slightly above the no-wall stability limit the growth rate of the modes increases with larger μ. It is shown that at s<dw this increase is roughly given by a factor of μ compared to a similar case with μ=1. The de...
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