The operation of an omegatron is discussed with polyphase electric excitation. Use is then made of this analysis to investigate the ionic trajectories in an omegatron in which the natural frequency of the ion is a function of the orbital radius. This circumstance comes about from either the influence of space charge or from the use of a magnetic field which decreases with increasing radius.The nonuniform magnetic field and the radial electric field can enhance the resolving power. It also influences the peak shape, causing the sides to be nearly vertical.Trapping of the ions is essential for satisfactory operation of the omegatron. Two experimentally proven means of accomplishing trapping are presented.