Nonlinear solitary wave parallel propagation and particle dynamics in a cold, collision-free, magnetized plasma in the presence of dust

Dust plays a key role in solitary wave propagation in a plasma, giving rise to slow waves and a variety of interesting features dependent on dust mass and charge. To simplify the analysis, based on the Adlam-Allen method, two cases are studied here, those of heavy dust and ion-dust coupling, retaining the dynamics of both. The main result is that resonant conditions corresponding to well-localized circularly polarized solutions exist for any value of the relative dust density, in both cases. Scaled resonance conditions were derived in both cases, for varying dust mass and charge, as functions of the relative density. Characteristic fields, particle density, and particle velocity calculated at resonance were presented in both regimes of interest, for the representative case of a hydrogen plasma. Further solutions are obtained corresponding to unconventional particle oscillations, presenting equally unconventional electric field profiles or magnetic field polarization, to be studied and pursued in greater detail in dedicated work.