Compressible Bell–Plesset effects of Rayleigh–Taylor instability in a finite-thickness cylindrical shell

The double-shell target is an important pathway toward inertial confinement fusion ignition, and its implosion performance is sensitive to perturbation feedthrough from the outer surface of the inner shell. This feedthrough is governed by compressibility, Bell–Plesset (BP) effects, and double-interface interaction, yet the coupled dynamics remains incompletely described. In this work, the Equal Convergence Ratio Hypothesis (ECRH) is first proposed as a closure, providing an analytical description of the coupled dynamics for a vacuum-bound cylindrical shell. Then, an asymptotic solution is derived via Wentzel–Kramers–Brillouin analysis. The hypothesis and solution are validated against numerical solutions and hydrodynamic simulations, showing good agreement during the linear stage. Compared with the incompressible model, the ECRH-based model is simpler yet more accurate. Compared with that in the classical Rayleigh–Taylor instability, the inner perturbation growth is enhanced because BP convergence shortens the effective wavelength. The normalized outer-to-inner feedthrough strength is likewise enhanced. With an initial phase difference, the outer perturbation phase varies monotonically with mode number m and the radius ratio α, whereas the inner phase first approaches and then recedes from the outer phase as m increases. Finally, the competing dependence of the growth rate and of the feedthrough on m determines the most unstable mode for a given shell thickness, which follows the approximate scaling law mαm+1=const: for thicknesses of 10–30 μm, the most unstable mode number is 40–100. This work provides a new theoretical description of the compressible BP effect in cylindrical double-interface instabilities.