On middle panel snapshots of the electron distribution function in the phase space, exhibiting a “layered” Y-shape structure. On top and bottom panels, the selected particle population in the phase space, corresponding to “streams” located at (top) and (bottom) where is the thermal momentum along y. This simulation has been performed using the 1D2V full kinetic Vlasov-Maxwell solver phase space, exhibiting a “layered” Y-shape structure.
Phase space behaviour of a selected electron population of the stream initially located at , at different times during the evolution of the system. Results were obtained using the multistream model with seven streams. WI is here driven by a temperature anisotropy of and in the longitudinal and transverse directions, respectively. Just before the saturation of the instability, particles experience the beginning of a particle trapping mechanism dominated by the magnetic field. We observe here the formation of the magnetic trapping structure rotating in phase space.
Time evolution of the magnetic energy obtained, respectively, from the V-model on top panel and the mS-model on bottom panel. The physical parameters are identical in both numerical simulations. The perturbation is made on the magnetic field on the mode with a small amplitude of in dimensionless units. The density energy of Bz increases in an exponential way in both simulations until time . Thus, after the instability saturates, the amplitude of the magnetic energy density oscillates for a few cycles and the period of oscillation is found to be close to the bounce frequency of .
Temporal evolution of the magnetic energy (top panel) and of theelectrostatic part (bottom panel). The physical parameters are with a temperature anisotropy of using the Schlickeiser's distribution as indicated in Ref. 18 . The growth of the magnetic energy is accompanied by a strong increase of electrostatic activity. Furthermore, the energy density of the electrostatic energy rapidly decreases after saturation. Here, the estimated growth rate of this initial phase was found to be close to . Results were obtained using the V-model with full kinetic effects.
Phase space representation of the distribution function in the space for a given value of the py momentum component chosen at one half of momentum . The initial configuration evolves slowly but at time , the formation of the trapping structure starts. On middle panel, one sees the beginning of the coalescence process of the two first magnetic structures at left. When the fusion of the two vortices is achieved, the system exhibits a mode m = 5 on the bottom panel. Results were obtained using the V-model using a perpendicular temperature of and a temperature anisotropy of using the Schlickeiser's distribution, corresponding to Fig. 4 .
Phase space representation of the distribution function in the space for the second selected stream now chosen at . The observed behaviour corresponds to the combined action of the bounce frequency variation induced by stream velocity, compensated for the reorganization of the plasma in the form of an inverse-type cascade scenario. The physical parameters are with a temperature anisotropy of using the Schlickeiser's distribution. Results were obtained using the V-model.
The phase space dynamics of the latter stream defined by . The curve corresponds for plots shown in Fig. 6 obtained with the V-model. Results were obtained using the mS-model in the relativistic regime of WI.
The phase space dynamics of the central stream. As evident from a comparison between Figs. 5–7 , particles of the central stream exhibits ten trapping vortices at time , with a weak modulation on the magnetic mode m = 5, indicating that particles are now being trapped by the combined action of the electric potential and the magnetic fields. Ten vortices are clearly visible in phase space indicating that the dominant mode is here m = 10, i.e., . Results are obtained using the mS-model.
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