Space Charge Induced Nonlinear Effects in Quadrupole Ion Traps

  • Dan Guo
  • Yuzhuo Wang
  • Xingchuang Xiong
  • Hua Zhang
  • Xiaohua Zhang
  • Tao Yuan
  • Xiang Fang
  • Wei Xu
Research Article


A theoretical method was proposed in this work to study space charge effects in quadrupole ion traps, including ion trapping, ion motion frequency shift, and nonlinear effects on ion trajectories. The spatial distributions of ion clouds within quadrupole ion traps were first modeled for both 3D and linear ion traps. It is found that the electric field generated by space charge can be expressed as a summation of even-order fields, such as quadrupole field, octopole field, etc. Ion trajectories were then solved using the harmonic balance method. Similar to high-order field effects, space charge will result in an “ocean wave” shape nonlinear resonance curve for an ion under a dipolar excitation. However, the nonlinear resonance curve will be totally shifted to lower frequencies and bend towards ion secular frequency as ion motion amplitude increases, which is just the opposite effect of any even-order field. Based on theoretical derivations, methods to reduce space charge effects were proposed.

Key words

Space charge Quadrupole ion trap Nonlinear resonance curve Harmonic balance method 



This work was supported by National Natural Sciences Foundation of China (21205005) and National Scientific Instrumentation Grant Program of China (2011YQ09000502, 2011YQ09000501 and 2012YQ040140-07).

Supplementary material

13361_2013_784_MOESM1_ESM.docx (135 kb)
ESM 1 (DOCX 134 kb)


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Copyright information

© American Society for Mass Spectrometry 2013

Authors and Affiliations

  • Dan Guo
    • 1
  • Yuzhuo Wang
    • 1
  • Xingchuang Xiong
    • 2
  • Hua Zhang
    • 3
  • Xiaohua Zhang
    • 3
  • Tao Yuan
    • 4
  • Xiang Fang
    • 2
  • Wei Xu
    • 1
    • 5
  1. 1.Department of Biomedical EngineeringBeijing Institute of TechnologyBeijingChina
  2. 2.National Institute of MetrologyBeijingChina
  3. 3.Beijing Purkinje General Instrument Co., LtdBeijingChina
  4. 4.KunShan Innowave Communication Technology Co., LtdJiangshuChina
  5. 5.School of Life Science, Beijing Institute of Technology, HaidianBeijing, 100081China

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