The influence of a nonlinear ion wake field on the dust-lattice wave is investigated in complex dusty plasmas. The dispersion relation for the dust-lattice wave is derived from the equation of motion including the contribution due to the nearest-neighbour dust grain interaction. The results show that the nonlinear wake-field effect increases the wave frequency, especially at the maximum peak positions. It is found that the oscillatory behaviour of the dust-lattice wave enhances with an increase of the spacing of the dust grains. It is also found that the amplitude of the dust-lattice wave significantly decreases with an increase of the inter-dust grain distance. In addition, it is found that the amplitude of the dust-lattice wave increases with increasing Debye length. The variation of the dust-lattice wave due to the Mach number and plasma parameters is also discussed.

We examine with a particle-in-cell (PIC) simulation the collision of two equally dense clouds of cold pair plasma. The clouds interpenetrate until instabilities set in, which heat up the plasma and trigger the formation of a pair of shocks. The fastest-growing waves at the collision speed $c/5$, where $c$ is the speed of light in vacuum, and low temperature are the electrostatic two-stream mode and the quasi-electrostatic oblique mode. Both waves grow and saturate via the formation of phase space vortices. The strong electric fields of these nonlinear plasma structures provide an efficient means of heating up and compressing the inflowing upstream leptons. The interaction of the hot leptons, which leak back into the upstream region, with the inflowing cool upstream leptons continuously drives electrostatic waves that mediate the shock. These waves heat up the inflowing upstream leptons primarily along the shock normal, which results in an anisotropic velocity distribution in the post-shock region. This distribution gives rise to the Weibel instability. Our simulation shows that even if the shock is mediated by quasi-electrostatic waves, strong magnetowaves will still develop in its downstream region.

The Jeans instability is examined in quantum dusty magnetoplasmas due to low-frequency magnetosonic perturbations. The fluid model consisting of the momentum balance equation for quantum plasmas, Poisson’s equation for the gravitational potential and Maxwell’s equations for electromagnetic magnetosonic perturbations is solved. The numerical analysis elaborates the significant contribution of magnetic field, electron number density and variable dust mass to the Jeans instability.