SELF-CONSISTENT STABILITY ANALYSIS OF ABLATION FRONTS WITH SMALL FROUDE NUMBERS

The linear growth rate of the Rayleigh-Taylor instability is calculate d for accelerated ablation fronts with small Froude numbers (Fr much l ess than 1). The derivation is carried out self-consistently by includ ing the effects of finite thermal conductivity (kappa similar to T-v) and density gradient scale length (L). It is shown that long-wavelengt h 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 - be ta 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 stabi lized by ablative convection, finite density gradient, and thermal smo othing. 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 num bers near the cutoff k(c). The parameters alpha and c(0-2) mainly depe nd 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. Furthermor e, an asymptotic formula reproducing the growth rate at small and larg e Froude numbers is derived and compared with numerical results. (C) 1 996 American Institute of Physics.