Hydrodynamic instabilities in an imploding cylindrical plasma shell

Hydrodynamic instabilities of a cylindrical plasma shell which is imploded by the pressure of an external massless fluid are considered. The plasma shell is assumed to be a compressible, isentropic fluid which is describable as an ideal gas ($p=a{\rho }^{\gamma },\gamma \ne 1$). The unperturbed plasma shell is assumed to undergo a self-similar motion. This assumption together with mass conservation determines the time-dependent pressure profile of the plasma shell. Linear stability analyses for this prescribed self-similar motion are carried out analytically. Stability criteria are obtained in terms of the ratio of specific heats $\gamma$ and an azimuthal mode number of perturbations. It is shown that the imploding plasma shell is unstable to compressible perturbations when $\gamma <2\mathrm{}$. In the case of incompressible perturbations, similar calculations show that the Rayleigh-Taylor instability occurs at the outer surface and, in addition, the unstable mode develops at the inner surface. A plausible mechanism for the development of the unstable mode at the inner surface is given.