Stability formalism of a flowing two-fluid plasma

An improved formalism for a stability analysis of flowing two-fluid equilibria with constant density is developed. The two-fluid formalism, in which the generalized vorticity of each species is introduced as characteristic quantity, extends the usual single-fluid formalism. A new relation between the perturbed generalized vorticity and the displacement is found for each species. The spectral formalism is developed for stability of axisymmetric equilibrium. The missing elements in the single-fluid analysis of Frieman and Rotenberg [Rev. Mod. Phys. 32, 898 (1960)] are identified.