A model of a stable plasma formation, based on radial quantum oscillations of charged particles, is discussed. The given plasmoid is described with the help of the nonlinear Schrödinger equation. A new phenomenon of effective attraction between oscillating charged particles is considered within the framework of the proposed model. The possible existence of a composite plasma structure is also discussed. Hypotheses about using the obtained results to describe natural long-lived plasma formations which can serve as alternative energy sources are advanced.