40th International Workshop on High Energy Density Physics with Intense Ion and Laser Beams

we derived the dispersion relation for the RTI problem at cylindrical fluid/fluid, solid/solid and fluid/solid interfaces by the decomposition method and also its planar counterpart, which is still easily expanded to study the behaviors of the interfaces by the impulsively accelerated model. Searching for the mathematical details of the dispersion relation, we developed a methodology to study the evolution of the growth rates in terms of the Atwood number (At), the viscosity ratio(m), the elastic ratio (T) and the elastic/viscous ratio (S), and the controlling parameter Br and deduced a mathematical representation to understand the behaviors of the growth rates . Our approaches yield the same growth rates of RTI at cylindrical interfaces for fluid/ fluid interface in comparison with the numerical simulation results. In the solid case, this method produces reasonable explanations for the cutoff azimuthal mode number in agreement with the experimental observations. Last, we expanded this theory to study the evolutions of the linear growth rate at solid/fluid interface. This theory is expected to provide an instructive way to investigate the intrinsic properties of the behaviors of the solid target and its transitions into more complicated plasma states on Z-pinch and the future experiments LAPLAS at GSI. Finally, by using the impulsively accelerated mode, the RMI at different cases of interfaces are discussed, in particular for the low mode perturbations, which behaves totally different than that in the planar geometry. Also this method may prove to be helpful to study the Bell-Plesset effect and the transition from elasticity to plasticity in cylindrical geometry.