Theory of Fourier transform ion cyclotron resonance mass spectroscopy. I. Fundamental equations and low-pressure line shape

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Abstract
The fundamental relationships for linewidth and resolution for all forms of ion cyclotron resonance spectroscopy are derived. Mass resolution and frequency resolution are shown to be numerically identical in all forms of ion cyclotron resonance spectroscopy. Theoretical Fourier transform ion cyclotron resonance (FT–ICR) spectral line shape has been calculated for the low‐pressure limit in which there are essentially no ion–molecule collisions during the observation period. Absorption, dispersion, and magnitude (absolute‐value) line shapes are illustrated and discussed. FT–ICR linewidth and resolution are calculated as a function of ionic mass and charge, applied magnetic field strength, and data acquisition time, for various linewidth criteria, and the results are tabulated. FT–ICR linewidth and resolution are then expressed in terms of ionic mass, computer data storage size, and minimum specified ionic mass in the FT–ICR mass range, for various linewidth criteria, and the results are tabulated. Next, FT–ICR upper mass limit is calculated as a function either of ionic charge, applied magnetic field strength, and data acquisition time, or computer data storage size and minimum specified ionic mass in the FT–ICR mass range, and the results are tabulated for several linewidth criteria. For the same observation time and linewidth criterion, FT–ICR zero‐pressure resolution is 47% better than with conventional ’’drift’’ cell or ’’trapped‐ion’’ cell ICR detection. Finally, the theoretical basis for the FT–ICR spectral segment extraction technique is described, for use in enhancing FT–ICR resolution by several orders of magnitude.