The dust acoustic, or dust density, wave is a very low frequency collective mode in a dusty plasma that is associated with the motion of the charged and massive dust grains. An ion flow due to an electric field can excite these waves via an ion–dust streaming instability. Theories of this instability have often assumed a shifted-Maxwellian ion velocity distribution. Recently, the linear kinetic theory of this instability was considered using a non-Maxwellian ion velocity distribution (Kählert, Phys. Plasmas, vol. 22, 2015, 073703). In this paper, we present one-dimensional PIC simulations of the nonlinear development of the ion–dust streaming instability, comparing the results for these two types of ion velocity distributions, for several values of the ion drift speed and collision rate. Parameters are considered that reflect the ordering of plasma and dust quantities in laboratory dusty plasma experiments. It is found that, in general, the wave energy density is smaller in the simulations with a non-Maxwellian ion distribution.

Dust acoustic (or dust density) waves have been observed in many laboratory dusty plasmas. These low-frequency waves involve the dynamics of highly charged and massive dust grains, and can be excited by the flow of ions relative to dust. In this paper, we consider the nonlinear development of the dust acoustic instability, excited by thermal ion flow, in a collisional plasma containing dust with high kinetic temperature (warm dust). It is shown that under certain conditions there may be a long-wavelength secondary instability in the nonlinear stage as dust gets heated by the waves. The characteristics of the nonlinear development are considered as a function of the relative charge density of the dust. Application to possible experimental parameters is discussed.

The nonlinear development of a low frequency beam-cyclotron instability in a collisional plasma composed of magnetized ions and electrons and unmagnetized, negatively charged dust is investigated using one-dimensional particle-in-cell simulations. Collisions of charged particles with neutrals are taken into account via a Langevin operator. The instability, which is driven by an ion $\boldsymbol{E}\times \boldsymbol{B}$ drift, excites a quasi-discrete wavenumber spectrum of waves that propagate perpendicular to the magnetic field with frequency of the order of the dust plasma frequency. In the linear regime, the unstable wavelengths are of the order of the ion gyroradius. As the wave energy density increases, the dominant modes shift to longer wavelengths, suggesting a transition to a Hall-current-type instability. Parameters are considered that reflect the ordering of plasma and dust quantities in laboratory dusty plasmas with high magnetic field. Comparison with the nonlinear development of this beam cyclotron instability in a collisionless dusty plasma is also briefly discussed.