A matching problem revisited for stability analysis of resistive wall modes in flowing plasmas

Abstract

The classical matching problem for magnetohydrodynamic stability analysis is revisited to study effects of the plasma flow on the resistive wall modes (RWMs). The Newcomb equation, which describes the marginal states and governs the regions except for the resonant surface, is generalized to analyze the stability of flowing plasmas. When there exists no flow, the singular point of the Newcomb equation and the resonant surface degenerate into the rational surface. The location of the rational surface is prescribed by the equilibrium, hence the inner layer, which must contain the resonant surface, can be set a priori. When the flow exists, the singular point of the Newcomb equation splits in two due to the Doppler shift. Additionally, the resonant surface deviates from the singular points and the rational surface if the resonant eigenmode has a real frequency. Since the location of the resonant surface depends on the unknown real frequency, it can be determined only a posteriori. Hence the classical asymptotic matching method cannot be applied. This paper shows that a new matching method that generalizes the asymptotic one to use the inner layer with finite width works well for the stability analysis of flowing plasmas. If the real frequency is limited in a certain range such as the RWM case, the resonance occurs somewhere in the finite region around the singular points, hence the inner layer with finite width can capture the resonant surface.