The filamentary structure of the molecular interstellar medium and the potential link of this morphology to star formation have been brought into focus recently by high resolution observational surveys. An especially puzzling matter is that local interstellar filaments appear to have the same thickness, independent of their column density. This requires a theoretical understanding of their formation process and the physics that governs their evolution. In this work we explore a scenario in which filaments are dissipative structures of the large-scale interstellar turbulence cascade and ion-neutral friction (also called ambipolar diffusion) is affecting their sizes by preventing small-scale compressions. We employ high-resolution, 3D MHD simulations, performed with the grid code RAMSES, to investigate non-ideal MHD turbulence as a filament formation mechanism. We focus the analysis on the mass and thickness distributions of the resulting filamentary structures. Simulations of both driven and decaying MHD turbulence show that the morphologies of the density and the magnetic field are different when ambipolar diffusion is included in the models. In particular, the densest structures are broader and more massive as an effect of ion-neutral friction and the power spectra of both the velocity and the density steepen at a smaller wavenumber. The comparison between ideal and non-ideal MHD simulations shows that ambipolar diffusion causes a shift of the filament thickness distribution towards higher values. However, none of the distributions exhibit the pronounced peak found in the observed local filaments. Limitations in dynamical range and the absence of self-gravity in these numerical experiments do not allow us to conclude at this time whether this is due to the different filament selection or due to the physics inherent of the filament formation.
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