Nonlinear Alfvén Waves in Weakly Ionised Dusty Plasmas

The effects of charged dust on the steepening of the fields in nonlinear Alfvén waves in astro-physical weakly ionised plasmas are investigated. It is found that the formation of current singularities in the wave due to nonlinear ambipolar diffusion is strongly modified by the effects of the dust. The basic modes for propagation along the magnetic field in a dusty plasma are highly dispersive and split by the anisotropy of the magnetic field into two modes that are oppositely circularly polarised rather than linearly polarised. The right hand circularly polarised wave experiences a cutoff due to the presence of the dust. We derive nonlinear fluid equations describing the dusty plasma, and make approximations for strong coupling of the dust to the neutrals, and for stationary dust. Numerical solution of the equations shows that a nonlinear wave with sharp current features due to ambipolar diffusion involves a rotation of the wave magnetic field about the direction of propagation, and an oscillation of the field components, due to the mode splitting effects of the dust. This is in contrast to the dust-free case, where the sharp reversal of the transverse magnetic field component occurs in a single plane.