Dust molecules, strings, and crystals

Summary form only given. In discharges, dust normally resides at the edge of the sheath, where it is subject to ion streaming at velocity c/sub s/. The dust grains interact via a dynamically shielded potential O(r) that takes the form of a wake-field downstream. The dust grains may be strongly coupled to each other, but ions and electrons are only weakly coupled to the grains. However, this system differs from ordinary strongly coupled systems in that the potential O(r) is not symmetric upstream and downstream. Consequently, Newton\´s third law does not hold and neither energy nor momentum is conserved. We have used both analytic theory and simulation in a systematic exploration of this N-body system. Longer strings can exist only if there is a vertical confining force. As a model for this, we consider equally-spaced grains arranged in a vertical string in a periodic system . If there is also a horizontal confining potential, there are multiple 3-D equilibria occur which are connected by hysteretic processes that resemble phase transitions. In this non-conserving system, there is no general way to distinguish the ground state. However, the problem of two grains in a harmonic well can be reduced to a "quasi-Hamiltonian single-particle" form, permitting solution for ground and excited states. Crystals can be regarded as ordered collections of strings. Crystal structure is determined by the competition between the vertical forces that keep the strings aligned, the repulsive forces between strings, and the vertical and horizontal external confining forces. The phonon instabilities of dust crystals, which lead to melting below a critical pressure, are closely related to the hose instabilities of the strings. Thresholds and growth rates for these instabilities can be calculated using the analytically computed wakefield potentials.