Nonlinear electromagnetic modes in astrophysical plasmas with dust distributions

A derivative nonlinear Schrodinger equation is obtained for parallel electromagnetic modes in plasmas containing polydisperse charged dust. The coefficient of the dispersive term in that equation is dominated by the dust rather than the (plasma) ions, and polydisperse dust yields a larger coefficient in absolute value than an equivalent monodisperse description. This leads to a significant broadening of the nonlinear structure due to the presence of polydisperse rather than monodisperse dust, the latter contributing in itself already to a substantial increase in the width of envelope solitons compared to dust-free plasmas. When modelling the charged dust by a power-law distribution occurring in planetary ring and other astrophysical systems, it depends very much on the power-law index whether the smaller or the larger grains are more important. For certain indices the more numerous smaller grains determine the charge and mass densities, but the larger dust dominates the linear and nonlinear dispersive effects.