Brownian motion of a parametric oscillator: A model for ion confinement in radio frequency traps

Abstract

The distribution function for Brownian motion of a parametric oscillator is calculated exactly with the help of continued fraction expansions in the long time limit. We derive expressions for the energy and the widths of the spatial and velocity distribution. Our results are relevant to understand confinement of particles in radio frequency ion traps. © 1986 Springer-Verlag.