  A problem of the instability of an inhomogeneous axisymmetric plasma jet in a
parallel magnetic field is solved. The jet boundary becomes, under certain
conditions, unstable relative to magnetosonic oscillations (Kelvin-Helmholtz
instability) in the presence of a shear flow at the jet boundary. Because of
its internal inhomogeneity the plasma jet has resonance surfaces, where
conversion takes place between various modes of plasma MHD oscillations.
Propagating in inhomogeneous plasma, fast magnetosonic waves drive the Alfven
and slow magnetosonic oscillations, tightly localized across the magnetic
shells, on the resonance surfaces. MHD oscillation energy is absorbed in the
neighbourhood of these resonance surfaces. The resonance surfaces disappear for
the eigen-modes of slow magnetosonic waves propagating in the jet waveguide.
The stability of the plasma MHD flow is determined by competition between the
mechanisms of shear flow instability on the boundary and wave energy
dissipation because of resonant MHD-mode coupling. The problem is solved
analytically, in the WKB approximation, for the plasma jet with a boundary in
the form of a tangential discontinuity over the radial coordinate. The
Kelvin-Helmholtz instability develops if plasma flow velocity in the jet
exceeds the maximum Alfven speed at the boundary. The stability of the plasma
jet with a smooth boundary layer is investigated numerically for the basic
modes of MHD oscillations, to which the WKB approximation is inapplicable. A
new "global" unstable mode of MHD oscillations has been discovered which,
unlike the Kelvin-Helmholtz instability, exists for any, however weak, plasma
flow velocities.
