Simulated ion trajectory and induced signal in ion cyclotron resonance ion traps.

We present a numerical method for computation of electrostatic (trapping) and time-varying (excitation) electric fields and the resulting ion trajectory and detected time-domain-induced voltage signal in a rectangular (or cubic) ion cyclotron resonance (ICR) ion trap. The electric potential is calculated by use of the superposition principle and relaxation method with a large number of grid points (e.g., 100 × 100 × 100 for a cubic trap). Complex ICR experiments and spectra may now be simulated with high accuracy. Ion trajectories may be obtained for any combination of trapping and excitation modes, including quadrupolar or cubic trapping in static or dynamic mode; and dipolar, quadrupolar, or parametric excitation with single-frequency, frequency-sweep (chirp), or stored waveform inverse Fourier transform waveforms. The resulting ion trajectory may be represented either as its three dimensional spatial path or as two-dimensional plots of x-, y-, or z-position, velocity, or kinetic energy versus time in the absence or presence of excitation. Induced current is calculated by use of the reciprocity principle, and simulated ICR mass spectra are generated by Fourier transform of the corresponding time-domain voltage signal.