Finite Coulomb Crystal Formation
Dust particles immersed within a plasma environment, such as those found in planetary rings or comets, will acquire an electric charge. If the ratio of the inter-particle potential energy to average kinetic energy is large enough the particles will form either a "liquid" structure with short-range ordering or a crystalline structure with long-range ordering. Since their discovery in laboratory environments in 1994, such crystals have been the subject of a variety of experimental, theoretical and numerical investigations. Most numerical and theoretical investigations have examined infinite systems assuming periodic boundary conditions. Since experimentally observed crystals can be comprised of a few hundred particles, this often leads to discrepancies between predicted theoretical results and experimental data. In addition, recent studies have concentrated on the importance of random charge variations between individual dust particles, but very little on the importance of size variations between the grains. Such size variations naturally lead to inter-grain charge variations which can easily become more important than those due to random charge fluctuations (which are typically less than one percent). Although such size variations can be largely eliminated experimentally by introducing mono-dispersive particles, many laboratory systems and all astrophysical environments contain significant size distributions. This study utilizes a program to find the equilibrium positions of a dusty plasma system as well as a modified Barnes-Hut code to model the dynamic behavior of such systems. It is shown that in terms of inter-particle spacing and ordering, finite systems are significantly different than infinite ones, particularly for the most-highly ordered states.