Analytical model of the ablative Rayleigh–Taylor instability in the deceleration phase

A sharp boundary model for the deceleration phase of imploding capsules in inertial confinement fusion, in both direct and indirect drive, has been developed. The model includes heat conduction, local α-particle energy deposition, and shell compressibility effects. A differential equation for the temporal evolution of the modal amplitude interface is obtained. It is found that the α-particle energy has a strong influence on the evolution of the low l modes, via the compressibility of the shell. The modes are damped by vorticity convection, fire polishing, and α-particle energy deposition. The existence of a cutoff l number arises from the high blow of velocity into the hot region (rocket effect) if density gradient scale length effects are taken into account at the interface. The differential equation for the modal amplitude is used as a postprocessor to the results of 1D-SARA code [J. J. Honrubia, J. Quant. Spectrosc. Radiat. Transfer. 49, 491 (1993)] in a typical capsule for indirect-drive ignition designed on the National Ignition Facility. It is found that modes with l>180 are completely stabilized. The results are in agreement with two-dimensional simulations.