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This monograph presents results of investigations on fields and multipole expansion coefficients in axially symmetric (referred to as 3D) and two dimensional (2D) ion trap mass analysers. 3D mass analysers have a three-electrode geometry with two (electrically shorted) endcap electrodes and one central ring electrode. rf-only or rf/dc potential applied across the electrodes creates a linear trapping field in the central cavity of the mass analyser. 2D mass analysers have four longitudinal electrodes in which the opposite pairs of electrodes are electrically shorted. Here, rf-only or rf/dc potential applied across the pair of electrodes creates a linear trapping field and fragment ions of the analyte gas are trapped along the central axis of the mass analyser. Both these mass analysers have apertures machined on the electrodes (holes in case of 3D traps and slits in case of 2D traps) to permit entry of electrons for ionising the analyte gas and for collection of destabilized fragment ions. This thesis is concerned with how these apertures influence the fields and multipole expansion coefficients within the traps. This thesis is divided into five chapters.