Charged grains and Kelvin-Helmholtz instability in molecular clouds

The presence of dust grains profoundly affects the diffusion of the magnetic field in molecular clouds. When the electrons and ions are well coupled to the magnetic field and charged grains are only indirectly coupled, emergent Hall diffusion may dominate over all the other non-ideal magnetohydrodynamic (MHD) effects in a partially ionized dusty cloud. The low-frequency, long (∼0.01- pc) wavelength dispersive MHD waves will propagate in such a medium with the polarization of the waves determined by the dust charge density or the dust size distribution. In the presence of shear flows, these waves may become Kelvin-Helmholtz unstable with the dust charge density or the grain size distribution operating as a switch to the instability. When Hall diffusion time is long (compared to the time over which waves are sheared), the growth rate of the instability in the presence of sub-Alfvenic flow increases with the charge number |Z| on the grain, while it is quenched in the presence of Alfvnic or super-Alfvnic flows. However, when Hall diffusion is fast, the growth rate of the instability depends on the dust charge only indirectly.