Theory of trapped ion motion in the non-quadrupolar electrostatic potential of a cubic ion cyclotron resonance cell

• Published in: International journal of mass spectrometry and ion processes Vol. 142; no. 1; pp. 1 - 22
• Main Author: Mitchell, Dale W.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 31-03-1995
• Subjects: Fourier transform ion cyclotron resonance mass spectrometry; Frequency shifts; Penning trap; Perturbation theory; Perturbation theory; Frequency shifts; Penning trap; Fourier transform ion cyclotron resonance mass spectrometry
• ISSN: 0168-1176; 1873-2801
• DOI: 10.1016/0168-1176(94)04090-T

Perturbation theory is employed to analytically investigate the dynamics of a single ion trapped in a cubic ion cyclotron resonance cell. The trapping potential is expanded in a Taylor series with terms which are quadratic, powers of four and powers of six in coordinates treated as zero-, first-, and second-order perturbations, respectively. Frequencies are calculated to second order while the mode amplitudes and coordinates are solved to first order. The frequency shifts derived by this method agree very well with numerically evaluated frequency shifts obtained using the exact cubic cell trapping potential. For low
m/z, the cyclotron frequency shift is shown to be due to just the cylindrically symmetric part of the cubic cell potential. An internal resonance involving energy exchange between the mode amplitudes is predicted to occur for an ion in a cubic cell when
m ≈
m
c/3, where
m
c is the high mass limit.