Resonance Curves and Jump Frequencies in a Dual-Frequency Paul Trap on Account of Octopole Field Imperfection

Nonlinear phenomena inside a dual-frequency Paul trap are investigated. The dynamics inside the trap under the influence of an external sinusoidal driving force, collisional damping, and even-order octopole field imperfection can be encapsulated by a damped driven Duffing-type equation. Harmonic balance technique is applied to analyze the dynamics around the primary resonance. The amplitude of the resonance curves, the inflection frequency at which the jump phenomena occurs, and transitional frequencies often termed as jump-up and jump-down frequencies are found to depend on the voltage and frequency ratios of the dual-frequency Paul trap.