This thesis describes experimental work performed on laser cooled magnesium ions, confined in a quadrupole ion trap operating in the Penning or the combined mode. Information is gained about the dynamical motion of the ions. This is done by analyzing the time delays between scattered fluorescence photons in the case of small ion clouds (generally less than ten ions). For larger clouds (upwards of 100 ions), a fraction of the ions is "tagged" and a subsequent study made of the time evolution of the fluorescence. We have developed an innovative, non-invasive method for measuring ion oscillation frequencies which is based on analyzing photon-photon correlations present in the emitted ion fluorescence. This technique has been used to measure all three Penning trap frequencies for a wide range of dc voltage. The data have been fitted to theory and we have obtained a global fit of these data to one set of trap parameters. We also demonstrate that our technique enables us to measure space-charge shifted values of the trap resonances. This method has also been applied to the combined trap and we report experimental verification of the predicted trap resonances for a wide range of trapping parameters. These data fit well to theory. This is for all three oscillation frequencies for one set of trap parameters consistent with the data for the Penning trap. Further experiments are reported concerned with the dynamics of larger ion clouds in a Penning trap. A pulsed laser is used to "tag" a small number of the ions in large ion clouds. This removes those ions from the cooling cycle by placing them in a metastable state. Subsequently, we have monitored the time evolution of the fluorescence. By analyzing these data we have been able to determine cloud rotation frequencies for large ensembles of ions.