Numerical simulation of dust-acoustic waves

We use molecular dynamics (MD) and particle-in-cell (PIC) simulation methods, in which dust grains are treated as discrete particles and the background plasma is included in the potential shielding (MD) or as a Boltzmann fluid (PIC), to investigate dust-acoustic waves in a one-dimensional, strongly coupled (with the Coulomb coupling parameter {Gamma} equal to the ratio of the Coulomb energy to the thermal energy, which is greater than 1) dusty plasma. We study cases both where the dust is represented by a small number of simulation particles that form into a regular array structure at large {Gamma} (crystal limit) and where the dust is represented by a much larger number of particles (fluid limit). We show that the measured frequency for dust acoustic waves satisfies either a fluidlike dispersion relation or a lattice wavelike dispersion relation, depending on {Gamma} and the number of simulation particles. Other PIC simulations, either with plasma ions represented as particles rather than as a Boltzmann fluid or with collisions between the dust and the background gas, have also been carried out and shown to agree with theoretical predictions. Numerical issues associated with smoothing of the accumulated charge density in PIC simulations have also been addressed; smoothing is shown to affect wave dispersion at high wave numbers in the fluid limit and low wave numbers in the crystal limit. {copyright} {ital 1999} {ital The American Physical Society}