New construction of the magnetohydrodynamic spectrum of stationary plasma flows. II. Rayleigh-Taylor and Kelvin-Helmholtz instability

In a preceding paper [J. P. Goedbloed, Phys. Plasmas 16, 122110 (2009)] a new method was developed to compute the magnetohydrodynamic spectrum of waves and instabilities of stationary plasma flows by means of the construction of the solution paths, P-s and P-u, of stable waves and instabilities in the complex omega plane of an extended boundary value problem and the monotonicity of the alternator R equivalent to xi/Pi (ratio of displacement and total pressure perturbation) along those paths to find the eigenvalues. This method is applied in this paper to explicitly construct the solution paths, and the eigenvalues on it, for a plane gravitating plasma slab with shear flow. The topology of the solution paths for Rayleigh-Taylor and Kelvin-Helmholtz instabilities that are constructed here for the first time exhibits a surprising complexity. This is not a mathematical artifact, but characteristic for the structure of the magnetohydrodynamic spectrum of plasmas with background flow. Hence, its construction is crucial for the success of magnetohydrodynamic spectroscopy, aimed at determining the internal equilibrium characteristics of astrophysical and laboratory fusion plasmas.