Self-consistent stability analysis of ablation fronts with small Froude numbers

The linear growth rate of the Rayleigh-Taylor instability is calculated for accelerated ablation fronts with small Froude numbers (Fr much less than 1). The derivation is carried out self-consistently by including the effects of finite thermal conductivity (kappa similar to T-v) and density gradient scale length (L). It is shown that long-wavelength modes with wave numbers kL(0) much less than 1 [L(0)=v(v)/(v+1)(v+1) min(L)] have a growth rate gamma similar or equal to root A(T)kg - beta kV(a), where V-a is the ablation velocity, g is the acceleration, A(T)=1+0[(kL(0))1/v], and 1<beta(v)<2. Short-wavelength modes are stabilized by ablative convection, finite density gradient, and thermal smoothing. The growth rate is gamma=root alpha g/L(0)+c(0)(2)k(4)L(0)(2)V(a)(2) - c(0)k(2)L(0)V(a) for Oa 1 much less than kL(0) much less than Fr--1/3, and gamma=c(1)g/(V(a)k(2)L(0)(2))-c(2)kV(a) for the wave numbers near the cutoff k(c). The parameters alpha and c(0-2) mainly depend on the power index v, and the cutoff k(c) of the unstable spectrum occurs for k(c)L(0) similar to Fr(-1/3)much greater than 1. Furthermore, an asymptotic formula reproducing the growth rate at small and large Froude numbers is derived and compared with numerical results. (C) 1996 American Institute of Physics.