Rayleigh-Taylor Instabilities of a Collapsing Cylindrical Shell in a Magnetic Field

The instability of a radially accelerated cylindrical shell in a magnetic field has been investigated. It was assumed that the shell was of infinitesimal thickness. For perturbations which do not bend the lines of the magnetic field, the growth rate was found to be w = (gk)½, where g is the acceleration of the shell and k is the wavenumber. This growth rate is independent of the shell thickness. Perturbations which do bend the lines of the field were also found to be unstable. From a supplementary calculation, it was concluded that these instabilities were effective only for wavelengths greater than 8πa where 2a is the shell thickness.