Statistical Properties of Fluctuation of Charged Fine Particles in an AC Trap

We have investigated the behavior of a small number of charged fine particles under Coulomb interactions in an AC trap. There is a transition from ballistic to diffusive motion in the mean square displacement of the angle, θ, for a single charged fine particle described by a nonlinear dissipative Mathieu equation. Stable forced oscillations with an angular frequency Ω exist for the displacement vector of two charged fine particles described by a coupled Mathieu-Coulomb equation. Displacement vector motion becomes chaotic, depending on the control parameters in a coupled Mathieu-Coulomb equation. Stable solutions with a triangular configuration, and which oscillate with an angular frequency Ω, exist for three particles. An irregular replacement of particles in the triangle configuration occurs, depending on the control parameters in a coupled Mathieu-Coulomb equation.