Ion phase space vortices in 3 spatial dimensions

The formation and propagation of isolated ion phase space vortices are observed in a 3-dimensional numerical simulation. The code allows for an externally applied constant magnetic field. The electrons are assumed to be isothermal and Boltzmann distributed at all times, implying that Poissons equation becomes nonlinear for the present problem. Ion phase space vortices are formed by the nonlinear saturation of the ion-ion two-stream instability, excited by injecting an ion beam or short ion-bursts at the boundary. We consider the effects of finite beam diameters and the intensity for an externally imposed magnetic field.