Regular structures in self-gravitating dusty plasmas

The formation of nonlinear structures in a self-gravitating dusty plasma is considered when the dust dynamics includes the electrostatic and gravitational forces on an equal footing. Here, we obtain a Helmholtz wave equation, which describes the propagation of stationary gravitational-electrostatic waves. The characteristic lengths of the space regularities, as found here, are much smaller than the wavelengths of the gravitational-electrostatic waves Furthermore, it is shown that consideration of a uniform dusty plasma rotation around a fixed axis, gives rise to a circular rotating filament structure. Finally, the problem of the Jeans instability for circular waves in a rotating dusty plasma is generalized, and it is found that the purely growing Jeans instability assumes the form of a periodic instability.