Dust vortex flow analysis in weakly magnetized plasma

Analysis of driven dust vortex flow is presented in a weakly magnetized plasma. The 2D hydrodynamic model is applied to the confined dust cloud in a non-uniform magnetic field in order to recover the dust vortex flow driven in a conservative force field setup, in absence of any non-conservative fields or dust charge variation. Although the time independent electric and magnetic fields included in the analysis provide conservative forcing mechanisms, when the a drift based mechanism, recently observed in a dusty plasma experiment by [M. Puttscher and A. Melzer, Physics of Plasmas, 21,123704(2014)] is considered, the dust vortex flow solutions are shown to be recovered. We have examined the case where purely ambipolar electric field, generated by polarization produced by electron EB drift, drives the dust flow. A sheared EB drift flow is facilitated by the magnetic field gradient, driving the vortex flow in the absence of ion drag. The analytical stream-function solutions have been analyzed with varying magnetic field strength, its gradient and kinematic viscosity of the dust fluid. The effect of B field gradient is analyzed which contrasts that of E field gradient present in the plasma sheath.