The Rayleigh Taylor instability in partially ionized plasmas: ambipolar diffusion effects in the non linear phase

Abstract

Aims. We aim to determine how ion neutral coupling and ambipolar diffusion affect the linear and the nonlinear growth of the RTinstability under astrophysically relevant conditions, and to identify the coupling regimes in which departures from the classical single fluid picture become significant. Methods. We perform 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 is revisited using a physically consistent formulation with different ion neutral coupling strengths across the interface and validated against the simulations. We investigate the physics of the instability using morphology based diagnostics of the mixing layer to compare simulations at equivalent nonlinear stages, complemented by spectral, force, and energy budgets analyses. Results. 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 nonlinear regime, ambipolar diffusion modifies the classical quadratic growth and introduces a coupling dependent evolution. For multi wavelength perturbations, the nonlinear 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 thenonlinear evolution

Figures (11)

• Figure 1: Theoretical linear growth rate as a function of the horizontal wavenumber in the presence of a magnetic field ($\theta=10^\circ$). Black curves indicate the asymptotic limits corresponding to the fully uncoupled and fully coupled regimes. Colored curves show intermediate coupling cases for two different assumptions on the variation of the collision frequency across the interface. Dashed bands mark the ranges of wavelengths injected in the simulations, illustrating how the numerical experiments sample the different coupling regimes predicted by linear theory.
• Figure 2: Normalized finger--bubble height $h/h_0$ plotted as a function of the reduced time $\bar{t}=\omega_{\rm th} t$ for three injected wavelengths. curves correspond to the numerical results, while the solid green line show the corresponding theoretical linear growth rates. Top panel: no--coupling (NC) case. Bottom panel: bi--fluid simulation in the intermediate--coupling (IC) regime.
• Figure 3: Quadratic scaling of the mixing height in the single–fluid case ($\nu_{\rm nc}=0$). Each color represents a different value of the perturbation wavelength.
• Figure 4: Quadratic scaling of the mixing height for No , Low, Intermediate , High Coupling cases (NC, LC, IC, HC) for $\lambda=1/4 L_x$. Top Panel: simulation result, bottom panel : Theoretical evolution, predicted by the local two--fluid simplified model
• Figure 5: Snapshots of the charge density $\rho_c$ in hydrodynamic simulations with multi--wavelength initial perturbations, extracted at an equivalent nonlinear stage defined by a fixed normalized mixing layer thickness, $\Delta h/L_x \simeq 0.35$. From left to right: increasing coupling strength ($\alpha=0$, weak, intermediate, and strong coupling). All snapshots are shown using the same spatial window and color scale. (the density of the charge fluid $\rho_c$ is given in unit of the $\rho_{c1}$, the lighter fluid)