Lattice waves in dust plasma crystals

Abstract

Techniques previously known from solid state physics are used to look at linear and weak non-linear wave propagation in dust lattices. These expansion techniques include only electrostatic interactions between neighbor particles in addition to assuming small vibrations in the dust lattice. As a simple model for the dust lattice, a one-dimensional Bravais lattice is considered. For this particular lattice, expressions for the linear phase velocity are compared to a quasi-particle simulation. The word quasi here means that only the dust particles are represented as diffuse objects, while the plasma is treated as a fluid. The simulation is also used to study the breakdown of the analytical theory and to investigate non-linear dust lattice waves. A very good agreement is found between the analytical expressions and the particle simulations, for cases where the average dust separation a is of the order of or larger than the plasma Debye length λD. This is a condition which very often applies to dust crystal in laboratory experiments. Application of this wave theory is therefore discussed with respect to recent laboratory experiments where dust lattice waves are excited.