Magneto-Rayleigh-Taylor, Sausage And Kink Mode In Cylindrical Liners*

This paper analyzes the coupling of magneto-Rayleigh-Taylor (MRT), sausage (azimuthal mode number m$=$0) and kink mode (m$=$1) in an imploding cylindrical liner, using ideal MHD. A uniform axial magnetic field of arbitrary value is included in each region: liner, its interior, and its exterior. The dispersion relation, the feedthrough factor, and the temporal evolution of perturbations were solved exactly, for arbitrary values of g ($=$ gravity), k ($=$ axial wavenumber), m, aspect ratio, and equilibrium quantities in each region. For small k, a positive g (inward radial acceleration in the lab frame) tends to stabilize the sausage mode, but destabilize the kink mode. For large k, a positive g destabilizes both the kink and sausage mode. This analysis might shed lights into some puzzling features in Harris' classic paper [1], and in the recent cylindrical liner experiments [2] on MRT. \\[4pt] [1] E. G. Harris, Phys. Fluids 5, 1057 (1962).\\[0pt] [2] T. J. Awe, et al., PRL 111, 235005 (2013); PoP 21, 056303 (2014).