Modeling of the rotational stabilization of tokamak plasmas with account of skin effect in the resistive wall

Abstract

The influence of the Resistive Wall Mode (RWM) rotation on its stability in tokamaks is analyzed. Recently developed analytical theory [V. D. Pustovitov, Phys. Plasmas 19, 062503 (2012)] predicts that, when the skin depth s becomes much smaller than the wall thickness d _w , the resistive dissipation in the wall in combination with the mode rotation stabilizes the mode up to complete suppression of instability. Here this effect is studied without the restriction on the ratio s/d _w . Thereby the applicability of analytical predictions and accuracy of asymptotic expressions relating the growth rate to the rotation frequency of RWM is clarified. The dispersion relation for the rotating modes is derived in the single-mode cylindrical approximation and solved numerically. It is shown that the rotational stabilization of the plasma, the same as found earlier, is possible even at s/d _w of the order unity if the mode rotation frequency is above a critical level. The dependences of the growth rate on the mode frequency are calculated for different plasma parameters. It is shown that, at a given plasma state with a linear response to external perturbations, the growth rate of the mode is maximal at the mode locking (when the rotation is lost). The relation of the mode minimal rotation frequency at the stability boundary with the growth rate at the mode locking is found. The analysis demonstrates strong influence of dissipation in the wall on the dynamics of rotating and locked RWMs and confirms the necessity to incorporate the skin effect into their description. The obtained estimates allow one to compare these predictions with experimental results.