Excitation modes for fourier transform-ion cyclotron resonance mass spectrometry

Various geometric configurations for the excitation of coherent ion motion in Fourier transform-ion cyclotron resonance mass spectrometry (FT-ICR/MS) are analyzed (in some cases for the first time) with unified notation. The instantaneous power absorption, F v, in which v is ion velocity and F the force produced by the applied excitation electric field (harmonic, single frequency, on-resonance, in-phase), is time averaged and then set equal to the time rate of change of ion total (cyclotron + magnetron + trapping) energy, to yield a differential equation that is readily solved for the (time-dependent) amplitude of each of the various ion motions. The standard FT-ICR excitation (namely, radial dipolar) is reviewed. The effects of quadrature and radial quadrupolar excitation on ion radial (cyclotron and magnetron) motions are also reviewed. Frictional damping is shown to decrease the ion cyclotron orbital radius and trapping amplitude but increase the magnetron radius. Feedback excitation (i.e., excitation at the simultaneously detected ion cyclotron orbital frequency of the same ion packet) is introduced and analyzed as a means for exciting ions whose cyclotron frequency changes during excitation (as for relativistically shifted low-mass ions). In contrast to conventional radial dipolar excitation, axial dipolar excitation of the trapping motion leads to a mass-dependent ion motional amplitude. Parametric (i.e., axial quadrupolar) excitation is shown to produce an exponential increase in the ion motional amplitudes (hyperbolic sine and hyperbolic cosine amplitude for cyclotron and magnetron radii, respectively). More detailed consideration of parametric excitation leads to an optimal ion initial radial position in parametric-mode FT-ICRjMS.