The paper deals with particle dynamics in a Penning trap with a rotating electric dipole field and a buffer gas. Electromagnetic traps are widely used for the accumulation and storage of charged particles of matter and antimatter for further use in various experiments. In this paper, a general analytical criterion is established, which must satisfy the parameters of the type of trap under investigation in order to provide compression or expansion modes of the trajectory beam. These modes correspond to the cases of asymptotic stability or instability of the system under study. The most effective combinations of parameters were determined, providing the maximum possible degree of stability (or, accordingly, instability) of the system with the minimum possible amplitudes of the rotating electric field. Analytical solutions are constructed for the rapid calculation and analysis of the behavior of individual particles or envelopes of an ellipsoidal beam of trajectories and an estimate of the radius of the accumulated cloud. The proposed approach is applicable to the analysis of the system for any values of the parameters of the studied model of particle dynamics in a trap.