(The) PIC simulation study of ion solitary wave structures by ion beam

Abstract

Ion holes are traditionally discussed in relation with double layers. These ion hole structures are re-lated with density depletion and thus called cavitons. They have been investigated theoretically in many years, but it has been difficult to detect them in observations and simulations. Some simulations show the formation of ion holes, but they have not considered electrons in the development of the instabilities. In this study, we investigated the generation of ion holes by ion-acoustic instability via electron-ion beam interaction using one-dimensional electrostatic particle simulations. The simulations show that firstly, electron holes are formed in early stage (until $250/\omega_{pe}t$) of the development of the beam driven instability, and then decelerated beams start to mix with background ions. After around $1000/\omega_{pe}t$, BGK ion holes propagated with drift speed in the order of ion-acoustic wave speed and showed density depletion around 30% from the initial density. However, these types of ion holes were rarely created as the ion to electron mass ratio is increased from the reduced value to the real value.

The ion-ion two-stream instability has been suggested as the main generation mechanism for the ion holes propagating with speed close to the drift speed of ion beams in observations. Thus, previous simulation studies have not much considered the role of electrons and used reduced ion-to-electron mass ratios to save computation time. It has been assumed that ion and electron dynamics are sufficiently separated because of largely different response time scales between ions and electrons. However, the effect of such reduced mass ratios has never been closely examined. In this study, we examined whether the system can be properly re-scaled according to the reduced mass ratios by comparing two different methods of rescaling the parameters and how the evolution of the ion beam driven instability is affected by the reduced ion mass. The reference simulation was performed with a mass ratio of 100, and the results were compared with those using the real mass ratio with parameters rescaled accordingly. We applied constant ambient electric field, which accelerates the electrons and excites an ion-acoustic type instability. The results show that ion holes were generated via merging of electron holes. Merging of the electron holes affected the ion dynamics significantly when the reduced mass ratio was used while the interplay between the electron and ion dynamics became different de-pending on the rescaling methods with respect to the mass ratios. Even though the parameters were rescaled by conserving the kinetic energy, the nonlinear evolutions for different mass ratios were not perfectly identi-cal. The development patterns were similar when the parameters were rescaled while maintaining the ion beam kinetic energy, but there were still significant distinctions that the similarity law cannot be applied, which might be due to the strong electron-ion coupling. In another simulation test with much enhanced exter-nal electric field, electron holes were seen with the reduced mass ratio while only the ion holes were seen, without large scale electron trappings, with the real mass ratio. These results imply that reduced mass ratios should be used cautiously in PIC simulations because the electron dynamics can significantly modify the ion instabilities by affecting the ion dynamics.

Additionally, we observed the electron flat-top phase space distribution at the saturation stage of the instabilities. The electron flat-top distributions have been observed in various regions in space, such as Earth’s bow shock, Earth’s magnetotail, and solar wind. It has been suggested that wave-particle interactions are the responsible mechanism for the formation of the electron flat-top distributions. In the present study we report the formation of electron flat-top distributions by ion beam driven instabilities using 1D PIC simulations. Simulation results show that in the early phase of the development electrostatic solitary waves were quasi-periodically formed, and later they were fully dissipated resulting in heated, flat-top distributions. Occasion-ally new electron beam components were also formed. We parametrically investigated the development of electron phase space distributions for various drift speeds of ion beams and temperature ratios between ions and electrons. These results were compared with the observations of the flat-top distributions in space. Also, we discuss the physical implication of the formation of the flat-top distributions for the equilibrium of a plasma system.