LABORATORY-FRAME AND ROTATING-FRAME ION TRAJECTORIES IN ION-CYCLOTRON RESONANCE MASS-SPECTROMETRY

The magnitude of the ion cyclotron resonance (ICR) time-domain signal detected from the oscillating differential charge induced on opposed detector electrodes depends on the number, ICR orbital and magnetron radii, and phase coherence of the trapped ions. In this paper, we present analytical solutions for the motion of magnetically confined ions of arbitrary initial position, velocity and phase during and after excitation by a spatially uniform oscillatory electric field. Resonant and non-resonant single-frequency and frequency-sweep (chirp) excitation are treated. Spatial coherence may then be incorporated by analyzing the ion ensemble into ion packets, such that ions in each packet share a common ICR orbit center. We find that resonant (single-frequency or frequency-sweep) electric field excitation not only increases the ICR orbital radius, but also induces an oscillating (for linearly polarized excitation) or rotating (for circularly polarized excitation) shift in the center of the ion cyclotron orbit of the ion packet (i.e. the magnetron radius). The amplitude of the r.f.-induced oscillating or rotating magnetron radius increases directly with ion mass-to-charge ratio and r.f. electric field amplitude. Optimal excitation for high mass ions should therefore be conducted with low magnitude long-duration excitation rather than a short high magnitude "rectangular" (or "burst" or "impulse") waveform. None of the above excitation waveforms changes the initial spatial distribution of the ion packet: in particular, off-resonance single-frequency excitation results in oscillatory variation in ICR orbital radius, but does not induce any net spatial synchronization in the ion packet. Finally, ion trajectories during on- and off-resonance single-frequency excitation are displayed in the usual fixed laboratory coordinate frame as well as in a coordinate frame rotating about the z-axis at the ICR orbital frequency of that ion. Phase coherence and shifts in the center of the ICR orbit are much more easily visualized in the new rotating-frame representation. © 1990.