Using chaos theory to analyze particle dynamics in asymmetry-induced transport

Abstract

Despite a large body of experimental work on asymmetry-induced transport in non-neutral plasmas, the correct theory remains elusive. Previous work using single particle computer simulations has shown that the particle dynamics in such systems can be quite complex. In this paper, the techniques of chaos theory are employed in an effort to better understand these dynamics. The dynamical equations are re-conceptualized as describing time-independent trajectories in a four-dimensional space consisting of the radius r, rotating frame angle ψ, axial position z, and axial velocity v. Initial work includes identification of an integral of the motion, fixed-point analysis of the dynamical equations, the construction and interpretation of Poincaré sections to visualize the dynamics, and, for the case of chaotic motion, numerical calculation of the largest Lyapunov exponent using the technique of Benettin et. al.