Wigner crystallization in macroscopic systems provides a simple avenue for studying classical many-body physics. The Coulomb repulsion of millimeter-sized conducting spheres rolling on a high potential surface enables the self-assembly of ordered structures. Prior attempts at formulating pairwise force models for Wigner islands have resulted in different functional forms with no apparent consensus. In this study, we explore fundamental particle interactions using the finite element method to solve the electrostatic problem for one-, two-, and many-sphere configurations. Analysis of charge and force shows three interaction regimes parametrized by the packing fraction, which includes many-body force behavior for compact geometries. We find that the force relationship between spheres is accurately represented by an aligned dipole model over all configurations. Both the finite element method and aligned dipole models were validated in absolute terms using an experimental setup featuring a gravity potential. Future dynamic studies, which rely on accurate force relationships, can now be treated.

Close

PrevNext

View figure in article

• Dusty or complex plasma
• Plasma crystals
• Strongly correlated systems
• Strongly-coupled plasmas
• Wigner crystal