MAGNETOHYDRODYNAMICS OF STATIC PLASMAS

As the basic equations of MHD spectral theory date back to 1958for static plasmas (Bernstein et al., 1958) and to I960 for stationary plasma flows (Frieman and Rotenberg, I960), progress on the latter subject has been slow since it suffers from lack of analytical insight concerning the structure of the spectrum. One of the reasons is the usual misnomer of \non-self adjointness' of the stationary flow problem. Actually, self-adjointness of the occurring operators, namely the generalized force operator and the Doppler-Coriolis gradient operator, was proved right away by Frieman and Rotenberg. Based on the reality of the two quadratic forms corresponding to these operators, it is constructed here (a) an effective method to compute the solution paths in the complex to plane on which the eigenvalues are situated, (b) the counterpart of the oscillation theorem for eigenvalues of static equilibria (Goedbloed andSakanaka, 1974) for the eigenvalues of stationary flows, based on the monotonicity of the alternating ratio of the boundary values of the displacement £ and the total pressure perturbation. This enables one to map out the complete spectrum of eigenvalues in the complex UJ-plane. The intricate topology of the solution paths is discussed for the fundamental examples of Rayleigh-Taylor, Kelvin-Helmholtz and combined instabilities.