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A new theoretical framework for describing how magnetic fields are generated and amplified is provided by finding magnetogravitational modes that involve gravity, density gradients, and di erential rotation in an essential way. Other factors, such as the presence of a high temperature particle population or of a temperature gradient, can contribute to their excitation. These modes identified by a linearized analysis are shown to be important for the evolution of plasma disks surrounding black holes toward di erent configurations. Since the nonlinear development of these modes can lead to radially localized regions with a relatively small di erential rotation, new stationary structures have been identified, in the (fully) nonlinear limit, which are localized radially over regions with negligible gradients of the rotation frequency. These structures, characterized by solitary plasma rings, do not involve a pre-existing “seed” magnetic field, unlike other configurations found previously. The relevant magnetic energy density is comparable to the gravitationally confined plasma pressure. The “source” of these configurations is the combination of the gravitational force and of the plasma density gradient orthogonal to it that is an important factor in the theory of magneto-gravitational modes, another important factor being an anisotropy of the plasma pressure.

Solitary plasma rings and magnetic field generation involving gravity and differential rotation