Alfvénic turbulence beyond the ambipolar diffusion scale

We investigate the nature of the Alfvénic turbulence cascade in two-fluid magnetohydrodynamic (MHD) simulations in order to determine if turbulence is damped once the ion and neutral species become decoupled at a critical scale called the ambipolar diffusion scale (L_AD). Using mode decomposition to separate the three classical MHD modes, we study the second-order structure functions of the Alfvén mode velocity field of both neutrals and ions in the reference frame of the local magnetic field. On scales greater than L_AD we confirm that two-fluid turbulence strongly resembles single-fluid MHD turbulence. Our simulations show that the behavior of two-fluid turbulence becomes more complex on scales less than L_AD. We find that Alfvénic turbulence can exist past L_AD when the turbulence is globally super-Alfvénic, with the ions and neutrals forming separate cascades once decoupling has taken place. When turbulence is globally sub-Alfvénic and hence strongly anisotropic, with a large separation between the parallel and perpendicular decoupling scales, turbulence is damped at L_AD. We also find that the power spectrum of the kinetic energy in the damped regime is consistent with a $k^{-4}$ scaling (in agreement with the predictions of Lazarian et al.).