The Rayleigh–Taylor instability in partially ionised plasmas: Ambipolar diffusion effects in the non-linear phase

The Rayleigh--Taylor (RT) instability is a key mechanism that drives mixing and structure formation in stratified astrophysical media. In partially ionised environments such as the molecular interstellar medium, including irradiated H_2 regions associated with stellar clusters (e.g. the Pleiades), ion--neutral coupling, and ambipolar diffusion are expected to play a major role in shaping the instability evolution in the presence of gravity and magnetic fields. Our aim was to determine how ion--neutral coupling and ambipolar diffusion affect the linear and the non-linear growth of the RT instability under astrophysically relevant conditions, and to identify the coupling regimes in which departures from the classical single-fluid picture become significant. We performed high-resolution two-fluid numerical simulations using the MPI--AMRVAC code, spanning a wide range of perturbation wavelengths, coupling strengths, from uncoupled to strongly coupled, passing by intermediate or ambipolar diffusion-dominated regimes, and magnetic field configurations. The linear theory was revisited using a physically consistent formulation with different ion--neutral coupling strengths across the interface and validated against the simulations. We investigated the physics of the instability using morphology-based diagnostics of the mixing layer to compare simulations at equivalent non-linear stages, complemented by spectral, force, and energy budget analyses. In the linear regime, theoretical growth rates are recovered over a wide range of wavelengths, from the single-fluid limit to intermediate bi-fluid coupling. In the non-linear regime, ambipolar diffusion modifies the classical quadratic growth and introduces a coupling-dependent evolution. For multi-wavelength perturbations, the non-linear dynamics becomes strongly scale-dependent: intermediate coupling enhances fragmentation in hydrodynamic configurations, while magnetised cases exhibit a non-monotonic reorganisation of the interface, with the smoothest morphologies occurring at intermediate coupling. Spectral and energetic diagnostics indicate that these behaviours correlate with changes in the relative contributions of ion--neutral drift and magnetic stresses during the non-linear evolution. Our results demonstrate that ambipolar diffusion does not merely rescale RT growth rates, but reshapes the non-linear, multi-scale dynamics by altering how gravity-driven kinetic energy is redistributed through magnetic tension and ion--neutral drift. In magnetised configurations, the magnetic field suppresses small-scale corrugations, while ambipolar diffusion weakens this constraint by allowing partial decoupling between ions and neutrals.