| dc.description.abstract | Large amplitude electrostatic waves have been observed in the electron foreshock region of the planetary bow shocks, interplanetary shocks, and the solar wind termination shock. The observed electrostatic waves include electron acoustic waves, ion acoustic waves, and double layers. Based on the linear instability analysis, only the electron acoustic waves are expected to be found in the electron foreshock region. Since the electron acoustic waves are electron-time-scale phenomena, but the ion acoustic waves and the double layers are ion-time-scale phenomena, it is in need of a reliable cross-scale simulation code to simulate the cross-scale evolution of the nonlinear electrostatic waves in the electron foreshock region. A low-noise simulation scheme is developed in this study. This simulation scheme consists of a fourth-order implicit time integration scheme, a third-order derivative solver, and an elegant run-off error removing process. We apply this simulation scheme to the Vlasov equation and build a low-noise electrostatic Vlasov simulation code. The electrostatic shocks are studied by means of the new Vlasov simulation code. Our simulation results show a cross-scale nonlinear coupling between the ion acoustic waves and electron acoustic waves in the vicinity of the electrostatic shock. To our knowledge, this is the first simulation code that is able to simulate the nonlinear cross-scale coupling between the ion acoustic waves and electron acoustic waves. Our simulation results indicate that the cross shock potential jump is established when the hot downstream electrons meet the cold upstream electrons. The magnitude of the cross shock potential jump is found nearly proportional to the temperature difference between the downstream and the upstream electrons. It is found that, when the downstream electrons are not hot enough such that the potential jump is not high enough to slow down the upstream ions, the shock front will retreat and the incoming ions will pile up at the shock front to form a potential overshoot at the retreated shock ramp until the overshoot potential energy is comparable to the kinetic energy of the incoming ions. On the other hand, we also found that, when the downstream electrons are hot enough such that the hot downstream electrons can leak across the shock ramp, the leakage electrons can lead to formations of potential foot structure, electron acoustic waves, ion acoustic waves, and double layers in the upstream shock transition regions. Both ion acoustic waves and electron acoustic waves can lead to electron heating in the electrostatic shocks. Since little ion heating can be found in our electrostatic shock simulation, we believe that ion heating in the shock should be done primarily by the ion-time-scale electromagnetic waves. Possible electromagnetic instability induced by the field-aligned electron heating process is discussed in this thesis.
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