Numerical analysis of the Rayleigh-Taylor instability at the ablation front

The stability of the ablative flow in a plasma is studied numerically in the linear approximation for both planar and spherical flow geometries. The instability growth rates are found as eigenvalues of the self-consistent boundary-value problem. The set of equations describing the perturbations is integrated numerically using the integration scheme with successive orthogonalization. It is found that the growth rates of the ablation instability can be accurately represented in the Takabe form Lambda = alpha root kg - beta kv(a), where alpha approximate to 0.8-0.9; beta approximate to 2 for a planar flow and beta approximate to 3-4 for a spherical ablation wave. The computed growth rates of the ablation instability of a planar flow are shown to agree well with the analytic growth rates obtained previously [4,5].