Numerical Matching Scheme for Linear Magnetohydrodynamic Stability Analysis

A new matching scheme for linear magnetohydrodynamic (MHD) stability analysis is proposed in a form offering tractable numerical implementation. This scheme divides the plasma region into outer regions and inner layers, as in the conventional matching method. However, the outer regions do not contain any rational surface at their terminal points; an inner layer contains a rational surface as an interior point. The Newcomb equation is therefore regular in the outer regions. The MHD equation employed in the layers is solved as an evolution equation in time, and the full implicit scheme is used to yield an inhomogeneous differential equation for space coordinates. The matching conditions are derived from the condition that the radial component of the solution in the layer is smoothly connected to those in the outer regions at the terminal points. The proposed scheme is applied to the linear ideal MHD equation in a cylindrical configuration, and is proved to be effective from the viewpoint of a numerical scheme.