  We apply the hydrodynamic theory of electron liquid to demonstrate that a
circularly polarized radiation induces the diamagnetic, helicity-sensitive dc
current in a ballistic nanoring. This current is dramatically enhanced in the
vicinity of plasmonic resonances. The resulting magnetic moment of the nanoring
represents a giant increase of the inverse Faraday effect. With increasing
radiation intensity, linear plasmonic excitations evolve into the strongly
non-linear plasma shock waves. These excitations produce a series of the well
resolved peaks at the THz frequencies. We demonstrate that the plasmonic wave
dispersion transforms the shock waves into solitons. The predicted effects
should enable multiple applications in a wide frequency range (from the
microwave to terahertz band) using optically controlled ultra low loss
electric, photonic and magnetic devices.
