Solitary waves propagating across the magnetic field in cold, collision-free plasmas in the presence of positively or negatively charged dust

Self-consistent nonlinear wave solutions propagating across the magnetic field are obtained for a three-element, cold, collision-free plasma. Various cases are presented to assess the effect of a “third element,” such as dust, heavy ions, and positrons, in hydrogen plasma. The model and solution scheme are generic, take into account all particle dynamics, with no assumptions on the wave amplitude, and can be readily adapted to any background plasma and dust particle/secondary ion. The model permits to study particle dynamics and field characteristics as they critically depend on dust charge, mass, and relative abundance. In particular, selective acceleration is obtained in specific cases, leading to the possibility of designing experiments to test the model presented here. The amplitude of the wave solutions depends on the Mach number, defined with respect to the plasma Alfvén speed. The resulting magnetic field is capped, while the electrostatic field due to the local density separation is typically bipolar and may increase significantly.