Ion phase-space vortices in 2.5-dimensional simulations

Abstract

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.

Phase space structures generated by absorbing obstacles in streaming plasmas

“…The conspicuous features of the potential structures seem to be associated with phase space vortices, where all the relevant dynamics seem to take place in {x, v x }-plane, as expected for potential structures elongated in the y-direction, as here. Such ion phase space vortices are well-known, and have been observed experimentally by Pécseli et al (1981Pécseli et al ( , 1984, as well as in a number of numerical simulations (Sakanaka, 1972;Børve et al, 2001;Daldorff et al, 2001;. In particular, the coalescence seen in Fig.…”

“…There are not the same particles which constitute a structure at all times. Studies of the lifetime of ion phase space vortices (Pécseli et al, 1984;Børve et al, 2001) refer to initial value problems, and do not apply for the present case. If ion phase space vortices were to be analyzed as initial value problems with these plasma parameters, the resulting structures would appear as transient phenomena.…”

Phase space vortices in collisionless plasmas

“…2.2, with the only complication here being a nonlinear Poisson equation Børve et al, 2001). This equation is solved by a nonlinear multigrid method, which consists of a full multigrid schedule with an adaptive strategy that allows one to skip the coarse-grid correction if the specified accuracy is already reached on that grid.…”

“…For very high ion beam velocities, the plasma will remain unstable, but in this case, for waves on the ion cyclotron branch . In this case, the linearly most unstable waves propagate with at an angle to the magnetic field (Michelsen, 1976), and no phase space vortices are formed (see also summary by Børve et al, 2001). The plasma is stable for small ion beam velocities below the sound speed, and it turns out that ion holes are being formed in a rather narrow "window" of ion beam velocities, and the variation of hole widths for varying ion beam velocities is rather modest .…”

The effect of boundaries on the ion acoustic beam-plasma instability in experiment and simulation

“…To investigate non-linear effects and to overcome diagnostic difficulties, simulations have been a useful tool [e.g. [17][18][19][20][21] to the point where comparisons with naturally observed structures can be made with remarkable accuracy [22,23].…”