The various aspects of injecting ions into a three-dimensional radio-frequency quadrupole trap and their trapping for considerable periods of time are investigated by a numerical method. It is shown that for suitably chosen experimental parameters sufficiently long trapping times can be achieved to make this method attractive for on-line high-resolution spectroscopy of short-lived isotopes and of highly charged stable ions. The narrow range of the phase of the driving voltage during which trapping of injected ions occurs is determined. Injection through an end cap electrode is more favorable than ring electrode injection. It is also shown that in the absence of collisions injection through the gaps between the electrodes of the quadrupole ion trap is not feasible. The process of moderating high-energy ions by a thin foil before trapping and the various mechanisms of energy reduction after trapping are discussed.
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