The formation and propagation of ion phase-space vortices are observed
in a numerical particle-in-cell simulation in two spatial dimensions and with three
velocity components. The code allows for an externally applied magnetic field. The
electrons are assumed to be isothermally Boltzmann-distributed at all times, implying
that Poisson's 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 at the plasma boundary. We consider
the effect of a finite beam diameter and a magnetic field, in particular. A vortex instability
is observed, appearing as a transverse modulation, which slowly increases
with time and ultimately breaks up the vortex. When many vortices are present at
the same time, we find that it is their interaction that eventually leads to a gradual
filling-up of the phase-space structures. The ion phase-space vortices have a finite
lifetime, which is noticeably shorter than that found in one-dimensional simulations.
An externally imposed magnetic field can increase this lifetime considerably.
For high injected beam velocities in magnetized plasmas, we observe the excitation
of electrostatic ion-cyclotron instabilities, but see no associated formation of
ion phase-space vortices. The results are relevant, for instance, for the interpretation
of observations by instrumented spacecraft in the Earth's ionosphere and
magnetosphere.
Bragg localized structures in a passive cavity with transverse modulation of the refractive index and the pump