Rayleigh–Taylor instability in multi-structured inertial confinement fusion targets

Abstract

A formalism for the analysis of the Rayleigh–Taylor instability in the multi-structured solid or shell targets is presented. The formulation covers both the plane and the curved geometry targets. A generalized eigenvalue equation for the exponential growth rate of the instability is derived along with the necessary boundary conditions. Analytical solutions for the growth rate are presented for some elementary density profiles and a comparative study is made between the plane, cylindrical and spherical targets. The solution for the step function density profile is generalized for any number Nof zones forming an arbitrary density profile. This general formulation is illustrated with the explicit calculations for N = 3 and 4. A qualitative treatment of the effects of the ablative flow is also presented. This study predicts a stabilizing effect of the ablative flow on the growth of the instability. Further, a dynamic analysis of the instability growth rate is presented for a representative inertial confinement fusion spherical solid target driven by the laser beams. This study demonstrates that an approximate analysis of the instability with the time independent initial density profile gives the conservative results for the instability growth rate.