Rayleigh–Taylor instability in a spherically stagnating system

The Rayleigh–Taylor instability induced on the fuel–pusher interface in the deceleration phase of shell implosion is investigated in spherical geometry. A linearized equation for the perturbation from the background dynamics described by a self-similar motion is solved analytically and numerically. The effective growth rate of the Rayleigh–Taylor instability is not found to be sensitive to the compressibility. In a spherical system where the gravity and wavelength of the perturbation vary in time and space, the growth of the perturbation is found to be approximately expressed in the form ‖ξ‖∝ Rc exp[∫(αAkeffgeff)1/2dt], where keff and geff are the effective wavelength and gravity at the contact surface, with Rc the radius and αA the Atwood number.