Chaos-Induced Diffusion in a Nonlinear Dissipative Mathieu Equation for a Charged Fine Particle in an AC Trap

Abstract

Charged fine particles confined in an AC trap exhibit either periodic motion or irregular motion, depending on the frequency and amplitude of the AC electric field. This motion was analyzed using an idealized electric field model with a nonlinear term in the radial direction ( r ) and an angular (θ-dependent) term. The potential U ( r ,θ, z , t ) generates a rotational diffusion of chaotic orbits, and a transition from ballistic motion to diffusive motion was observed in the mean square displacement (MSD) of θ. The distribution function f (τ) for the lifetime of angular unidirectional motion is exponential. This exponential distribution is produced by the chaotic switching between clockwise and anticlockwise rotations of orbits on the x y -plane. The time-correlation function C (τ) of v θ also has an exponential decay form as a result of the lifetime distribution function f (τ). The scaling function of the MSD of θ(τ) is derived using the correlation time τ c of C (τ).