Key Laboratory of Analytical Chemistry for Living Biosystems, Institute of Chemistry, Chinese Academy of Sciences, Beijing, China.
J Am Soc Mass Spectrom. 2013 May;24(5):794-800. doi: 10.1007/s13361-013-0589-x. Epub 2013 Mar 16.
In this article, we investigated the nonlinear resonance effect in the Paul trap with a superimposed hexapole field, which was assumed as a perturbation to the quadrupole field. On the basis of the Poincare-Lighthill-Kuo (PLK) perturbation method, ion motional equation, known as nonlinear Mathieu equation (NME) was expressed as the addition of approximation equations in terms of perturbation order. We discussed the frequency characteristics of ion axial-radial (z-r) coupled motion in the nonlinear field, derived the expressions of ion trajectories and nonlinear resonance conditions, and found that the mechanism of nonlinear resonance is similar to the normal resonance. The frequency spectrum of ion motion in nonlinear field includes not only the natural frequency series but also nonlinear introduced frequency series, which provide the driving force for the nonlinear resonance. The nonlinear field and the nonlinear effects are inevitable in practical ion trap experiments. Our method provides better understanding of these nonlinear effects and would be helpful for the instrumentation for ion trap mass spectrometers.
本文研究了外加六极场作用下 Paul 阱中的非线性共振效应，将外加六极场视为对四极场的微扰。基于 Poincaré-Lighthill-Kuo（PLK）微扰方法，离子运动方程可表示为按微扰阶数展开的近似方程，即非线性 Mathieu 方程（NME）。本文讨论了非线性场中离子轴向-径向（z-r）耦合运动的频率特性，推导出离子轨迹和非线性共振条件的表达式，发现非线性共振的机制与正常共振相似。非线性场中离子运动的频谱不仅包括自然频率系列，还包括非线性引入的频率系列，这些系列为非线性共振提供了驱动力。在实际的离子阱实验中，非线性场和非线性效应是不可避免的。本文的方法为更好地理解这些非线性效应提供了帮助，有助于离子阱质谱仪的仪器设计。
