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On the multistream approach of relativistic Weibel instability. II. Bernstein-Greene-Kruskal-type waves in magnetic trapping
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10.1063/1.4817751
/content/aip/journal/pop/20/8/10.1063/1.4817751
http://aip.metastore.ingenta.com/content/aip/journal/pop/20/8/10.1063/1.4817751
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Time evolution of the magnetic energy for the dominant Fourier mode  = 3 in a logarithmic scale. WI proceeds through the linear stage for , in which the magnetic field strength grows exponentially in time, followed by the nonlinear saturation stage where magnetic trapping takes place.

Image of FIG. 2.
FIG. 2.

On top panel: Corresponding time evolution of the mode  = 3 of the inductive part of the electric field showing a strong decrease of the electric energy when the instability saturates. On bottom panel: corresponding electrostatic part showing that the field is non negligible at the saturation. Thus, the mode  = 3 results from the mixture of both magneticand electrostatic contributions. The perpendicular temperature is here and we have used .

Image of FIG. 3.
FIG. 3.

Phase space representation of a selected “stream” of the ring in the phase space. The distribution of the trapped particle population exhibits a three-vortex structure as the result of the magnetic trapping. The perpendicular temperature is here and we have used .

Image of FIG. 4.
FIG. 4.

Representation of the central stream in phase space for the same system shown in Fig. 3 . We can see clearly the formation and the growth of vortices induced by the presence of both modes  = 3 (i.e., the mode ) and  = 6 (the harmonic ). Notice that the plasma “heating” is weaker for the plasma bulk. Numerical results correspond to and to an anisotropy factor of .

Image of FIG. 5.
FIG. 5.

Time history of the mode  = 2 for the magnetic field component on top panel, and of the electric field on bottom panel. The evolution of the magnetic field is plotted in a logarithmic scale. The simulation was performed for a higher value of the perpendicular temperature of using an anisotropy factor of .

Image of FIG. 6.
FIG. 6.

Plots of the electron distribution function in the phase space for a selected stream of ring. We see clearly the formation of a three-vortex structure on the middle panel, emerging for the growth of the most unstable mode  = 3. The phase space structure is however unstable and the coalescence of two vortices takes place at time  = 75 on bottom panel. The perpendicular temperature is here and we have used .

Image of FIG. 7.
FIG. 7.

Phase space representation of the central stream. Particles of the central stream experiences a trapping mechanism induced by the electric potential. The simulation has been performed for and .

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/content/aip/journal/pop/20/8/10.1063/1.4817751
2013-08-09
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: On the multistream approach of relativistic Weibel instability. II. Bernstein-Greene-Kruskal-type waves in magnetic trapping
http://aip.metastore.ingenta.com/content/aip/journal/pop/20/8/10.1063/1.4817751
10.1063/1.4817751
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