Theoretical study on singularity and matching problem for stability analysis of flowing plasma

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The matching method can extract the most important effect in the stability analysis. But for flowing plasmas, it is shown that the conventional matching method falls short of stability analysis since positions of singular points are not known a priori. We generalize the matching method by invoking inner layers with finite width, and show that the generalized method can be applied to flowing plasmas. By numerical studies based on the generalized matching theory, we clarified the location where the plasma flow plays a significant role. Additionally, based on the generalized matching theory, we derive an analytic dispersion relation, and clarified the most important physical effect affecting the stability of flowing plasmas.