Nonlinear structure in a current-carrying collisional dusty plasma

A perpendicular ion drift is investigated as a mechanism for the generation of magnetic field structures in a highly collisional dusty plasma. The basic dissipation mechanism is assumed to be the dust-neutrals momentum exchange, so that plasmas with a small ionization fraction are natural candidates for experiments. The model reduces to a nonlinear partial differential equation for the vector potential. The conditions for linear instability are determined. The stationary states are periodic arrangements for the magnetic field, described by a Lienard equation. The fully depleted (ion-dust) case is also considered in detail. Applications to planetary rings, comets and dust acoustic instability experiments are analyzed. A necessary condition for the validity of the model is a sufficiently slow time-scale of the generated magnetic fields.