Kolmogorov Dissipation scales in Weakly Ionized Plasmas

In a weakly ionized plasma, the evolution of the magnetic field is described by a "generalized Ohm's law" that includes the Hall effect and the ambipolar diffusion terms. These terms introduce additional spatial and time scales which play a decisive role in the cascading and the dissipation mechanisms in magnetohydrodynamic turbulence. We determine the Kolmogorov dissipation scales for the viscous, the resistive and the ambipolar dissipation mechanisms. The plasma, depending on its properties and the energy injection rate, may preferentially select one of the these dissipation scales. thus determining the shortest spatial scale of the supposedly self-similar spectral distribution of the magnetic field. The results are illustrated taking the partially ionized part of the solar atmosphere as an example. Thus the shortest spatial scale of the supposedly self-similar spectral distribution of the solar magnetic field is determined by any of the four dissipation scales given by the viscosity, the Spizer resistivity (electron-ion collisions), the resistivity due to electron-neutral collisions and the ambipolar diffusivity. It is found that the ambipolar diffusion dominates for resonably large energy injection rate. The robustness of the magnetic helicity in the partially ionized solar atmosphere would facilitate the formation of self-organized vortical structures.