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We investigate the nature of the Alfv\'enic turbulence cascade in two fluidMHD simulations in order to determine if turbulence is damped once the ion andneutral species become decoupled at a critical scale called the ambipolardiffusion scale (L$_{AD}$). Using mode decomposition to separate the threeclassical MHD modes, we study the second order structure functions of theAlfv\'en mode velocity field of both neutrals and ions in the reference frameof the local magnetic field. On scales greater than L$_{AD}$ we confirm thattwo fluid turbulence strongly resembles single fluid MHD turbulence. Oursimulations show that the behavior of two fluid turbulence becomes more complexon scales less than L$_{AD}$. We find that Alfvenic turbulence can exist pastL$_{AD}$ when the turbulence is globally super-Alfv\'enic, with the ions andneutrals forming separate cascades once decoupling has taken place. Whenturbulence is globally sub-Alfvenic and hence strongly anisotropic with a largeseparation between the parallel and perpendicular decoupling scales, turbulenceis damped at L$_{AD}$. We also find that the power spectrum of the kineticenergy in the damped regime is consistent with a $k^{-4}$ scaling (in agreementwith the predictions of Lazarian, Vishniac & Cho 2004).

Alfvenic Turbulence Beyond the Ambipolar Diffusion Scale