Transonic magnetohydrodynamic flows.

Stationary flows of an ideal plasma with translational symmetry along the (vertical) a axis are considered, and it is demonstrated how they can be described in the intrinsic (natural) coordinates (xi, eta, theta) where xi is a label of flux and stream surfaces, eta is the total pressure and theta is the angle between the horizontal magnetic (and velocity) field and the x axis. Three scalar nonlinear equilibrium equations of mixed elliptic-hyperbolic type for theta(xi, eta), xi(eta, theta) and eta(theta, xi) respectively are derived. The equilibrium equation for theta(xi, eta) is especially useful, and has considerable advantages compared with the coupled system of algebraic-differential equations that are conventionally used for studying plasma flows. In particular, for this equation the location of the regions of ellipticity and hyperbolicity can be deter mined a priori. Relations between the equilibrium equation for theta(xi, eta) and the nonlinear hodograph equation for xi(eta, theta) are elucidated. Symmetry properties of the intrinsic equilibrium equations are discussed in detail and their self-similar solutions are described. In particular, magnetohydrodynamic counterparts of several classical flows of an ideal fluid (the Prandtl-Meyer flows around a corner, the spiral flows and the Ringleb flows around a plate, etc.) are found. Stationary flows described in this paler can be used for studying both astrophysical and thermonuclear plasmas

The spectrum of MHD flows about X-points.

A recently proposed method to calculate the spectrum of linear, incompressible, unbounded plasma flows is applied to magnetohydrodynamic flows about X points. The method transforms the two-dimensional spectral problem in physical space into a one-dimensional problem in Fourier space. The latter problem is far easier to solve. application of this method to X-point plasma flows results in two kinds of essential spectra. One kind corresponds to stable perturbations and the other one to perturbations that become overstable whenever the square of the poloidal Alfven Mach number becomes larger than 1. Apart from these two spectra, no other spectral values were found

Spectrum and stability of a rigidly rotating compressible plasma.

We consider the spectrum and stability of a compressible, rigidly rotating plasma column with constant magnetic pitch. It is found tl-lat when the pressure on axis is zero, a continuous spectrum arises, which may become unstable. When the pressure on axis is finite or a conducting core is included, the spectrum is discrete, but may still be unstable. The instability is due to the poloidal magnetic field and/or the rotation of the cylinder in combination with the density profile. It is found numerically that the pressure stabilizes both types of instabilities