Motional coherence during resonance ejection of ions from Paul traps

Abstract

We present a study of constraints on pre-ejection dynamical states which cause differential resolution in resonance ejection experiments using Paul traps with stretched geometry. Both analytical and numerical computations are carried out to elucidate the role of damping and scan rate in influencing coherence in ion motion associated with the forward and reverse scan. Adopting the Dehmelt approximation, our analytical study is carried out on a damped, driven Duffing oscillator with positive octopole nonlinearity. Using the method of multiple scales, we derive approximate slow flow equations which describe the ion motion. The phase portraits generated from the slow flow equations, in the vicinity of the jump, display two stable equilibria (centers) and an unstable fixed point (saddle). Numerical studies on the original equation are used to understand the influence of damping and scan rate in causing coherent ion ejection in these experiments. In the forward scan experiments, for a given damping, low scan rates result in coherent motion of ions of a given mass at the jump point. At this point, the amplitude and phase of ions of a given mass, starting at different initial conditions, become effectively identical. As the scan rate is increased, coherence is destroyed. For a given scan rate, increasing damping introduces coherence in ion motion, while decreasing damping destroys this coherence. In reverse scan experiments, for a given damping, very low scan rates will cause coherent ion motion. Increasing the scan rate destroys this coherence. The effect of damping in reverse scan experiments is qualitatively similar to that in the forward scan experiments, but settling times in the forward scan are shorter, leading to improved coherence and resolution. For mass spectrometrically relevant scan rates and damping values, significantly greater coherence is obtained in the forward scan.