A theory of MHD instability of an inhomogeneous plasma jet

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.

💡 Research Summary

The paper presents a comprehensive theoretical investigation of magnetohydrodynamic (MHD) instabilities in an axisymmetric plasma jet that is embedded in a uniform magnetic field parallel to the jet axis. The authors consider two distinct configurations of the jet boundary: an idealized tangential discontinuity with a sharp radial jump, and a realistic smooth transition layer. For the sharp‑boundary case, the analysis is carried out analytically using the Wentzel–Kramers–Brillouin (WKB) approximation. Linearising the ideal MHD equations and assuming perturbations of the form exp(i m φ − i ω t), the authors derive a radial wave‑number equation that contains the local Alfvén speed V_A(r) and the sound speed C_s(r). The presence of a shear flow V₀(r) at the jet edge introduces a Kelvin‑Helmholtz (KH) drive. The WKB dispersion relation shows that the jet becomes KH‑unstable whenever the flow speed at the boundary exceeds the maximum Alfvén speed there, i.e. V₀(a) > max