Kinetic Simulation Study of Electron Holes Dynamics During Collisions of Ion-Acoustic Solitons

Abstract

Abstract-Ion acoustic (IA) solitons are accompanied by vortex-shaped nonlinear structures (e.g. hollows, plateaus or humps) in the electron distribution function, called electron holes, portraying trapped electrons. These structures appear as charged flexible clouds (shielded by the background plasma) in the phase space with their own inertia, depending on the number of trapped electrons. According to simulation studies, electron holes tend to merge in pairs until one accumulative hole remains in the simulation box. This tendency has been analytically and qualitatively explained in the frame of the energy conservation principle. However, electron holes accompanying IA solitons should not merge due to stability of IA solitons against mutual collisions. In this report based on a fully kinetic simulation approach, detailed study of the collisions of IA solitons reveals the behavior of electron holes under these two conflicting predictions, i.e. stability against mutual collisions and merging tendency. Four main results are reported here. Firstly, we find that among the three different types of collisions possible for electron holes, just two of them happen for electron holes accompanying IA solitons. We present different collisions, e.g. two large/small and large versus small holes, to cover all the these three different types of collisions. Secondly, we show that although electron holes merge during collisions of IA solitons, the stability of IA solitons forces the merged hole to split and form new electron holes. Thirdly, we reveal that holes share their trapped population during collisions. Post-collision holes incorporate some parts of the oppositely propagating before-collision holes. Finally, it is shown that the newly added population of trapped electrons goes through a spiral path inside the after-collision holes hole because of dissipative effects. This spiral is shown to exist in the early stage of the formation of the holes in the context of the IA soliton dynamics.

Expansion of a mildly relativistic hot pair cloud into an electron-proton plasma

“…The one-dimensional PIC simulation in Ref. [12] showed that for plasma conditions similar to the ones we use here electron phase space holes form, which are connected to ion solitary waves [17]. Here we have shown that such solitary waves grow to a large amplitude also in a 2D simulation.…”

“…6(a) and also for an electron phase space hole, which corresponds to a localized positive excess charge around which the electrons oscillate. Both non-linear plasma structures often coexist and the ion acoustic wave lends the electron phase space hole additional stability [17]. Protons at the wave crest at y ≈ 1.98 in Fig.…”

“…Onedimensional PIC simulations [12] have examined the interaction of a hot pair cloud that expands into an ambient plasma. The simulations have shown that electron phase space holes [13][14][15][16], which form and evolve on electron time scales, and the ion acoustic solitary waves that are tied to them [17] could be an efficient means to accelerate ions to high energies especially when the ion acoustic solitary waves break [18]. Our aim is to study these processes in more detail with a two-dimensional particlein-cell (PIC) simulation that resolves competing multidimensional instabilities such as those that destroy phase space holes in more than one dimension [13].…”

“…The observed bipolar electric field pulses suggest the involvement of electron phase space holes in the proton acceleration to MeV energies also in the twodimensional simulation. Indeed an ion acoustic solitary wave is tied to an electron phase space hole and stabilizes it [17]. A second instability emerges at late times.…”

Impact of the electron to ion mass ratio on unstable systems in particle-in-cell simulations

“…Ion acoustic waves are linearly undamped if the ratio between the electron temperature and ion temperature is large [4], which is the case in our simulation after the Buneman instability has saturated. We note, however, that the presence of the electron phase space holes means that the ion velocity oscillations may not be linear since electron phase space holes and large ion acoustic waves can couple [31].…”