Dynamics and stability of a stagnating hot spot

Abstract

A simple model of a hot spot implosion is developed, where the key parameters are the areal density ρsRs, the central temperature Ts, and the implosion velocity v∞. The dynamics is dominated by the mechanical compressing work and the thermal conduction loss. A new type of self-similar solution is then found, describing the fluid motion in terms of ρsRs/T2s and v∞/√Ts. A scaling law for the minimum implosion velocity v∞* to reach the spark point (ρsRs,Ts) is derived: v∞*∝Ts5/2/ρsRs. The Rayleigh–Taylor (RT) instability in the stagnation phase is evaluated using the self-consistent spatial profile with density gradients, which is attributed to the thermal conduction. Substantial reduction of the RT growth is then found compared with the previous work without density gradients [Hattori et al., Phys. Fluids 29, 1719 (1986)].