EXCITATION ELECTRIC-FIELD INHOMOGENEITIES IN A CUBIC ION-CYCLOTRON RESONANCE CELL - ION MOTION FAR AWAY FROM THE CYCLOTRON FREQUENCY

A theory of ion motion in a cubic ICR cell is presented for differential sinusoidal excitation that explains the observed stability, orders of magnitude, and resonance positions for excitation frequencies away from the cyclotron frequency. This is accomplished by transforming the equations of motion to an amplitude-phase representation where resonance is identified as terms with slowly varying phase. The assumption of isolated resonance reduces the analysis to a case-by-case study of individual resonances. Two classes of nonlinear resonances are identified: those dependent only on the excitation field inhomogeneities and those dependent also on the linear excitation. The latter resonances are negligible compared to the first class. For the strong resonances in the first class, resonance frequencies are predicted at 2omega(z) +/- omega-, omega+ +/- 2omega(z), omega+ +/- 2omega-, 2omega+ +/- omega-, 3omega+, and 3omega-, where omega+, omega(z), and omega- are the cyclotron, z-axis, and magnetron frequencies characteristic of the unperturbed motion, respectively. The amplitude-phase equations show that the z-mode coupling coefficients are proportional to (mass)-1/2 while the radial modes are mass-independent in the low mass limit. Therefore, if the initial mode amplitudes are mass independent, mass discriminatory effects related to excitation inhomogeneities in quadrupolar traps are attributable to the z-mode. The coupling coefficient for the z-mode equation of motion has a relative order of magnitude approximately (omega+ - omega-)/omega(z) greater than the corresponding radial mode coefficients, hence the resonances at 2omega(z) +/- omega- and omega+ +/- 2omega(z) have the strongest effect on ion motion. The stability of ion motion in the isolated resonance approximation is governed by a constant of motion relating the mode-amplitudes for the mode coupling resonances. The observed stability at omega+ - 2omega(z) and instability at omega+ + 2omega(z) are explained by this invariant. Finally, FT-ICR double resonance experiments are used to show changes in the ICR signal for excitation near omega+ +/- 2omega(z), 2omega(z), 2omega+, and 3omega+. Experimental results agree qualitatively with theoretical predictions. Excitation at omega+ - 2omega(z) shows a small increase in the FT-ICR signal due to reduction in the z-mode amplitudes. The resonances at omega+ + 2omega(z) and near 2omega(z) show a decrease in the signal due to z-axis ejection. Excitation at 3omega+ and near 2omega+ gave changes in the FT-ICR signal consistent with radial mode excitation.