Self-Consistent Stability Analysis of Ablation Fronts with Large Froude Numbers

LLE Review, Volume 65 17 In inertial-confinement fusion (ICF), the ablation front of the imploding capsules is hydrodynamically unstable.1,2 The heavy material of the compressed pellet is accelerated by the low-density ablating plasma, thus making the pellet interface unstable to density perturbations (Rayleigh-Taylor instability).3 The classical treatment3 of this instability occurring at the interface of a heavy fluid with uniform density ρh, supported by a light fluid with uniform density ρl, yields the growth rate γ cl T A kg = , where g is the acceleration and AT h l h l = − ( ) + ( ) ρ ρ ρ ρ is the Atwood number. It is noteworthy that, in the classical case, the growth rate monotonically increases with the mode wave number k, and the Atwood number is constant. However, in ICF, the convection of ablated material through the interface leads to a reduction of the growth rate with respect to the classical value γ γ cl < ( ) 1 and, for sufficiently short wavelengths, the instability is suppressed.4–20 Thus, only those modes with wave number smaller than a critical value14–16 (k < kc, where kc is the cutoff wave number) are unstable. In addition, the density profile of ICF targets monotonically decreases in the ablation and blowoff regions, thus complicating the definition of a light-fluid density (ρl) to be used in the definition of the classical Atwood number. For a monotonic density profile and mode wavelength smaller than the density-gradient scale length,