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Maxim Dvornikov uses classical electrodynamics to study electrons oscillating in spherically symmetric patterns inside a plasma. Such radial pulsations carry no magnetic field, so they lose no energy to radiation, which can explain why spherical plasmoids formed in nature are relatively stable. He works out the electromagnetic potentials of radially oscillating charges, then treats both free and forced oscillations of the electrons. Electrons oscillating this way interact by exchanging ion acoustic waves, and the effective potential can be attractive and exceed the Debye-Hückel potential. He proposes that oscillating electrons form bound states early in the life of a spherical plasma structure, with applications to the theory of natural plasmoids.

Formation of bound states of electrons in spherically symmetric oscillations of plasma