Hydrodynamic Instabilities in Ion-Beam Accelerated Shells

The role of Rayleigh-Taylor instabilities (RTI) in layers accelerated by heating with heavy-ion beams is of obvious importance but has received little attention. Owing to the lack of ablative stabilization, it is of special interest to what extent the density gradient can play a stabilizing role. We regard the situation shown in Fig. 1: an absorber region is heated by a beam in order to accelerate a payload. Both initial regions may have different densities. Later on, however, part of the heated material leaves the deposition region as pushed-out absorber material. For this general investigation, the ideal gas equation of state was used throughout and the ion beam was coupled into the absorber as a space and time-varying specific power added to the energy balance equation. An analytic solution was constructed for the unperturbed onedimensional motion in the case of ideal translational invariance in the x-direction of both the initial configuration and the beam deposition. This was then used as a basis for studying the development of the RTI generated by a small initial perturbation. The analytical solution described a constant acceleration of the payload with spatially homogeneous density in both absorber and payload, linked by exponential increase in the transition region. To produce this idealized solution required a highly specific (but not completely unrealistic) beam profile: a parabolic deposition distribution in space combined with a strong exponential time dependence. For the case of a continuous exponential density variation, the growth rates were analyzed by Mikaelian [2], although with a fixed width s of the transition layer. Nevertheless, this formula turned out to be even quantitatively useful. For the case of s>>h the growth rate for the fastest-growing mode is given by