Localized vortices in inhomogeneous electron beams

In this paper the authors analyze the possibility of the appearance and the characteristics of localized vortices in non-neutral inhomogeneous by density and velocity electron beams propagating in vacuum along the external magnetic field. These vortices are analogous, in a certain sense, to the Rossby waves in rotating fluids or solitary vortices in plasma. They are the result of external disturbances or the appearance and development of instabilities like for instance a diocotron instability in hollow beams and a slipping-instability in solid beams