| Summary: | 碩士 === 國立中央大學 === 太空科學研究所 === 90 ===
The purpose of this thesis work is to develop a new type of one-dimensional electrostatic plasma simulation code. This simulation code is designed based on a general concept of numerical scheme proposed by Lyu et al. (2001) in their cross-scale simulation model. One of the objectives of this study is to perform a feasibility study of this proposed numerical scheme. For simplicity, we choose one-dimensional electrostatic simulation as a starting point. This simulation code is designed to study electron-scale plasma phenomena. Electron-scale plasma phenomena are used to be studied by means of full-particle code simulation. The new simulation code is carried out to study electrostatic shocks, which is characterized by non-periodic boundary conditions and was a very difficult subject to be studied by previous full-particle code simulation. Basic equations of this simulation code include Vlasov equation for relativistic electrons, Vlasov equation for non-relativistic ions, and Ampere's law with displacement current but without magnetic field. In this simulation code, we use cubic-spline method to evaluate differentiation and integration in phase space and use predictor-corrector method to advance simulation in time.
Based on our simulation results, an electrostatic shock can be characterized by a negative electric field (directed to the upstream) at shock ramp, which can decelerate upstream ions and accelerate upstream electrons. The magnitude of this negative ramp electric field depends on electrons' thermal pressure gradient at the shock ramp. Terminal speed of accelerated electrons depends on the magnitude of this ramp electric field. The accelerated beam electrons can result in ion-electron and electron-electron two-stream instabilities in the shock transition region downstream from the shock ramp. Nonlinear electrostatic waves result from these two-stream instabilities can lead to wave-particle interactions and result in phase mixing of electrons in the downstream shock transition region. An electron plasma solitary wave (or Langmuir solitary wave) can be formed in this phase-mixing region and propagates toward downstream. Our results indicate that thermalization and increasing of entropy in the collisionless electrostatic shock are mainly achieved by phase-mixing process in the shock transition region.
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