Fluid dynamical instabilities in a partially ionized flow

In this paper, we reveal that there are two fluid dynamical instabilities f or a partially ionized flow with quasi-static contraction: the instability of the Alfven wave and the two-fluid instability. We find them by means of linear perturbation analysis, adopting the following unperturbed state; the magnetic field has a gradient against the terminal flow of neutrals, which are accelerated because of gravity. The terminal velocity is determined by the balance between the gravity and the friction force, which originates f rom the ion-neutral collisions. The instability of the Alfven wave occurs b ecause of the imbalance of the restoring force, which is generated by the u nperturbed background magnetic field if a wavelength is longer than a criti cal wavelength. Indeed, this critical wavelength is obtained from the compa rison between the local restoring efficiency and that of the background unp erturbed field. It is estimated as of the order of similar to 0.01 pc when the grains are the dominant charged particles. Thus, we speculate that this instability is responsible for the formation of the observed small-scale s tructure in the molecular clouds. If the relative speed between the ions an d the neutrals is larger than the thermal speed of the neutrals, there is a nother instability, i.e., the so-called two-fluid instability. Fortunately, although the two-fluid instability coexists with the instability of the Al fven wave, structure formation via the instability of the Alfven wave is po ssible since its growth rate is larger than that of the two-fluid instabili ty.