Numerical models of the electrostatic shock waves

The self-consistent evolution of the ion-acoustic collisionless shock with shock-reflected ions is numerically studied with kinetic simulations. We want to compare different approaches to the shock simulation based on the PIC-method. The results of one-dimensional fully kinetic simulation for both plasma components with the real ion-to-electron mass ratio are compared with those obtained for two different forms of the electron density distribution in terms of the wave electrostatic potential. One distribution corresponds to the Boltzmann approach, the other - to the approach of the adiabatically trapped electrons.