Probing radial and axial secular frequencies in a quadrupole ion trap

We simulate an operating mode in which the ions are introduced inside a quadrupole trap and slowed down to be confined; after a given confinement time, they are ejected out of the trap towards the detector through the upper end-cap. This elementary experiment is repeated for a set of increasing confinement times. The temporal ion signal obtained is an image of the confined ions' motion. This signal, which is periodical, contains the radial and/or axial secular frequencies of all the confined ionic species depending on the mode of detection. In previous papers, we have shown that with a large circular exit hole centred on the z axis of the trap and with a numerical treatment of the ion time-of-flight (TOF) histogram recorded for each confinement time, we obtain only the z secular frequency. In this paper, we show that the exit position of an ion in the radial plane depends principally on its radial position at the end of the confinement. For this, simply by reducing the dimension of the centred exit hole or by decentring it and counting only the number of ions passing through the hole, we can obtain evidence on the radial secular frequencies. Also, this simulation work allows one to clarify the best operating conditions to measure the x-secular frequencies, that is a decentred exit hole tangential to the oz axis and an ion cloud the excursion of which along the ox axis is limited to the radial position of the exterior edge of the hole and with an ox dimension about three times lower than the hole diameter. In this case, the amplitude calibration is possible as the frequency peak amplitude is proportional to the square value of the mean number of created ions. Moreover, we give the signal over noise ratio under usual values of the operating parameters. This operating mode and its two associated modes of detection could be an useful tool to measure ion motion secular frequencies along the oz axis and along any radial directions. Besides mass spectrometry, the determination of the frequencies shifts and couplings related to the ion motion can lead to other important applications.