Nonlinear structure in a current-carrying collisional dusty plasma

A perpendicular ion drift is proposed as a possible mechanism for the generation of magnetic field structures in a highly collisional dusty plasma. The basic dissipation mechanism is assumed to be the dust-neutral 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 presented. Possible 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 of the present work to magnetic field structures in planetary rings, comets, and low-temperature dusty plasma experiments are discussed. A necessary condition for the validity of the model is a sufficiently slow time scale of the generated magnetic fields in dusty plasmas.