A theory for two-dimensional Fourier-transform ion cyclotron resonance mass spectrometry

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Abstract
A theoretical model, based on the Lorentz equations for ion motion and the mass action law, is developed for two-dimensional Fourier-transform mass spectrometry known as 2D FT–ICR or 2D FTMS. The theory illustrates that the modulation of 2D FT–ICR ion signals in the additional time dimension comes from the modulation of the primary ion speed by the 2D excitation pulses. The modulation of the primary ion speed is found not to be sinusoidal and the modulation of the ion signals in 2D FT–ICR spectra is found to be complicated even in the simplest chemical system. The complex modulation creates higher harmonic components in the spectra. Based on the model, a data processing algorithm is proposed. The results show that the Fourier transformation should be performed stepwise in order to obtain complete information, and that the phase portion of the frequency domain generated by the second Fourier transformation should not be discarded since it contains useful information.

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