Abstract.Oscillations with periods on the order of 5-10 min have been observed by instrumented spacecrafts in the Earth's magnetosphere. These oscillations often follow sudden impacts related to coronal mass ejections. It is demonstrated that a simple model is capable of explaining these oscillations and give a scaling law for their basic characteristics in terms of the basic parameters of the problem. The period of the oscillations and their anharmonic nature, in particular, are accounted for. The model has no free adjustable numerical parameters. The results agree well with observations. The analysis is supported by numerical simulations solving the Magneto-Hydro-Dynamic (MHD) equations in two spatial dimensions, where we let a solar wind interact with a magnetic dipole representing a magnetized Earth. We consider two tilt-angles of the magnetic dipole axis. We find the formation of a magnetosheath with the magnetopause at a distance corresponding well to the analytical results. Sudden pulses in the model solar wind sets the model magnetosphere into damped oscillatory motions and quantitatively good agreement with the analytical results is achieved.
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.
Abstract.Results on the formation and propagation of electron phase space vortices from laboratory experiments are summarized. The electron phase space vortices were excited in a strongly magnetized Q-machine plasma by applying a pulse to a segment of a waveguide surrounding the plasma. Depending on the temporal variation of the applied pulse, one or more phase space vortices can be excited, and their interaction can be followed in space and time. We were able to demonstrate, for instance, an irreversible coalescence of two such vortices. These results are extended by numerical simulations, showing how electron phase space vortices can also be formed by beam instabilities. Furthermore, a study of ion phase space vortices is performed by numerical simulations. Both codes allow for an externally applied magnetic field in three spatial dimensions. 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. By following the evolution of the ion distribution of the velocity perpendicular to the direction of propagation of the injected ion beam, we find a significant ion heating in the direction perpendicular to the magnetic field associated with the ion phase space vortices being formed. The results are relevant, for instance, for the interpretation of observations by instrumented spacecraft in the Earth's ionosphere and magnetosphere.
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 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 or short ion-bursts at the boundary. We consider the effects of finite beam diameters and the intensity of an externally imposed magnetic field.
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