Mass spectrometry is a technique that analyzes the chemical compositions of compounds based on the mass-to-charge ratio of their ionized constituents. Miniaturized ion trap mass spectrometry finds application in a wide range of fields where portable, rugged, and reliable analytical instruments are required. Ion traps of various designs have been introduced over the past decades, each with their own unique advantages and capabilities. However, the process of developing a novel miniaturized ion trap mass spectrometer continues to be fraught with challenges. This dissertation discusses simulation studies pertaining to the development of a novel dual ion trap, the simplified coaxial ion trap, consisting of a simplified toroidal ion trap and a cylindrical ion trap. Ions are initially trapped in the toroidal region and the target ions are transferred to the cylindrical region where they are fragmented and mass analyzed, while the rest of the ion population remains securely trapped in the toroidal region. The compact design and extended trapping volume secure several advantages that are not available to conventional ion trap designs. The simulations were geared towards the determination of an optimized geometry and optimal operating conditions for the simplified coaxial ion trap. Four main criteria were used in the determination of the ideal geometric and operating conditions; namely, mass-selectivity of transfer from the toroidal to cylindrical traps, transfer and trapping efficiency in the cylindrical ion trap, mass resolution, and unidirectional ejection. The optimized geometry demonstrates successful trapping of ions in the toroidal region and selective transfer of target ions to the cylindrical region. Unidirectional inward ejection of ions could be achieved with a positive hexapole component in the electric field. The mass resolution under optimized conditions of the toroidal trap was 0.3 Da (FWHM), which agrees with the experimental value. The simplified coaxial ion trap yielded a total transfer and trapping efficiency of 25%. A number of suggestions to improve the efficiency are also discussed as part of this work.