Self-consistent theory of the Darrieus–Landau and Rayleigh–Taylor instabilities with self-generated magnetic fields

The Rayleigh–Taylor (RT) and Darrieus–Landau (DL) instabilities are studied in an inertial confinement fusion context within the framework of small critical-to-shell density ratio $DR$ and weak acceleration regime, i.e., large Froude number Fr. The quasi-isobaric analysis in Sanz et al. [Phys. Plasmas 13, 102702 (2006)] is completed with the inclusion of non-isobaric and self-generated magnetic-field effects. The analysis is restricted to perturbation wavelengths $k−1$ larger than the conduction length scale at the ablation front, yet its validity ranges from wavelengths shorter and larger than the conduction layer width (distance between the ablation front and the critical surface). The use of a sharp boundary model leads to a single analytical expression of the dispersion relation encompassing both instabilities. The two new effects come into play by modifying the perturbed mass and momentum fluxes at the ablation front. The momentum flux (perturbed pressure at the spike) is the predominant stabilizing mechanism in the RT instability (overpressure) and the driving mechanism in the DL instability (underpressure). The non-isobaric effects notably modify the scaling laws in the DL limit, leading to an underpressure scaling as $∼k−11/15$ rather than $∼k−2/5$ obtained in the quasi-isobaric model. The magnetic fields are generated due to misalignment between pressure and density gradients (Biermann battery effect). They affect the hydrodynamics by bending the heat flux lines. Within the framework of this paper, they enhance ablation, resulting in a stabilizing effect that peaks for perturbation wavelengths comparable to the conduction layer width. The combination of parameters $DRFr2/3$ defines the region of predominance of each instability in the dispersion relation. It is proven that the DL region falls outside of the parameter range in inertial confinement fusion.