Key Laboratory of Analytical Chemistry for Living Biosystems, Institute of Chemistry Chinese Academy of Sciences, Beijing, China.
J Am Soc Mass Spectrom. 2011 Feb;22(2):386-98. doi: 10.1007/s13361-010-0045-0. Epub 2011 Jan 19.
The potential distribution in the curved quadrupole is exactly characterized by the Laplace equation, and an approximate solution to the Laplace equation is calculated. We represent the Laplace equation under the coordinates named minimal rotation frame (MRF) and derive an expression on the hexapole and octopole superposition. Our conclusion is in agreement with the results by the numerical (SIMION) method. Based on the Poincare-Lighthill-Kuo (PLK) method reported in our previous work, the nonlinear effects of ion motion are investigated in detail. The frequency shift of ion motion can be well eliminated by coupling the hexapole component with a positive octopole component, and the transmission efficiency of ions is found to decrease dramatically with the increase of the ionic kinetic energy in the z-direction. Furthermore, the transmission characteristics of ions are discussed with regards to the phase-space theory. The results show that the centrifugally introduced axis shift is mainly responsible for the ion losses. A modified direct current (dc) voltage supply pattern is hence proposed to compensate for this effect.
在弯曲的四极场中，电势的分布可以通过拉普拉斯方程来精确描述，并且可以计算出拉普拉斯方程的一个近似解。我们在称为最小旋转框架（MRF）的坐标下表示拉普拉斯方程，并推导出六极和八极叠加的表达式。我们的结论与数值（SIMION）方法的结果一致。基于我们之前工作中报道的庞加莱-李光涛-郭（PLK）方法，详细研究了离子运动的非线性效应。通过将六极分量与正八极分量耦合，可以很好地消除离子运动的频移，并且发现离子的传输效率随着 z 方向上离子动能的增加而急剧下降。此外，还根据相空间理论讨论了离子的传输特性。结果表明，离心引入的轴向偏移是离子损失的主要原因。因此，提出了一种改进的直流（dc）电压供电模式来补偿这种效应。
