The Orbitrap is a mass analyzer that employs an electrostatic field to confine ions. The mass of an ion is determined from the frequency of its axial oscillations in the Orbitrap. The Orbitrap has high resolving power and accuracy. However, the electrodes of the Orbitrap have complicated curved shapes. As a consequence the Orbitrap is not easy to miniaturize. In this thesis we have proposed a class of easily machinable cylindrical-electrode structures to mimic the behavior of an Orbitrap. The proposed structure consists of a single cylinder and many coaxial equally spaced thick rings. A detailed numerical simulation of the cylindrical-electrode structure reveals that axial ion oscillations in it have many spurious frequency components in addition to the dominant frequency component. We have carried out a systematic shape optimization that adjusts the dimensions of the structure to minimize the amplitudes of the spurious frequency components of ion motion in the axial direction. The performance of the optimized structure was found to rival that of a practical Orbitrap.