Resistive ferromagnetic wall modes in theory and experiment

摘要

Effects of the ferromagnetic resistive wall on the plasma stability are analyzed. The analysis is basedon the equations describing the perturbation dynamics outside the plasma, assuming a linear plasmaresponse. A single-mode cylindrical model is used with two features that differ from the standardcase: the wall magnetic permeability is incorporated and the thin-wall approximation is waived. Thederivations are performed so that the results can be applied to both tokamaks and line-tied pinches.This is done to allow conclusions for tokamaks from comparison of the developed theory with theexperimental data on the resistive and ferromagnetic wall modes in the Wisconsin rotating wallmachine with and without a ferritic wall [W. F. Bergerson, D. A. Hannum, C. C. Hegna, R. D.Kendrick, J. S. Sarff, and C. B. Forest, Phys. Rev. Lett. 101, 235005 (2008)]. The model shows thatthe ferromagnetic wall effect is always destabilizing. However, it must be small under standardconditions in tokamaks. The effect can be much stronger in the pinch with lower magnetic field andlarger wall permeability. The dispersion relation obtained here makes possible an explanation of theexperimental results available so far, including those from the Wisconsin machine reported recentlyas strongly contradictory to expectations based on earlier models. Also, an easy practical solution forcompensating the destabilizing ferromagnetic effect in tokamaks is proposed.