Dynamical Inference of Forces Using Three-dimensional Tomographic Imaging of Dusty Plasmas*

Charged, micron-sized particles can be suspended in a in a low-pressure plasma through a balance of gravitational and electrostatic forces. Known as a dusty plasma, the particles are also subject to a screened, Coulomb repulsion, in addition to a number of kinetic and hydrodynamic drag forces from the ambient environment, leading to a rich array of nonequilibrium collective behavior. Using a new, high-speed, three-dimensional imaging technique based on laser-sheet tomography, we are able to track the dynamics of up to 50 individual particles over tens of seconds. In small systems with 2-3 particles, normal-mode decomposition provides a quantitative estimate of the equilibrium charge of the particles, the Debye length in the plasma, and the local electric field. For larger systems with many particles, the data also allows us compute the average pairwise forces between particles as a function of separation. The method is robust to noise in the data, and can be applied to other many-body systems with complex interactions.