Abstract
Solenoidal (i.e. axially symmetric) magnetic field inhomogeneities, which in addition have symmetry under the operation z → − z are the most important to Fourier transform-ion cyclotron resonance (FT-ICR) mass spectrometry since they introduce frequency shifts at first-order in perturbation theory. Frequency shifts for all three fundamental modes are derived for the leading second-order and fourth-order solenoidal inhomogeneities without any restrictions on the initial conditions. The analytical frequency shifts agree very well with frequency shifts obtained from numerical trajectory calculations using the exact classical equations of motion. The effect of the inhomogeneity on the ion trajectory is solved analytically. For a strong magnetic bottle field, the cyclotron motion is frequency modulated at twice the z-oscillation frequency resulting in sidebands. However, the amplitude of these sidebands is negligibly small for typical inhomogeneity strengths. The effect of a magnetized ICR trap on the homogeneity of the magnetic field is studied by analytical methods. We find that the leading magnetic bottle field decreases as d −3, where d is the cylindrical ion trap diameter.
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