此模擬碼之基本架構是從Lyu et al.（2001）之跨尺度電漿模擬中簡化而來的，其目的是測試此跨尺度電漿模擬碼基本架構之可行性。我們先從最基本的也是最簡單的一維靜電電漿物理現象著手，以減低模擬碼之複雜度。此模擬碼所相對應之尺度為電子的時空尺度，其尺度與全粒子碼（full particle code）相同。在本論文中，將以此模擬碼來模擬傳統全粒子碼最棘手的問題之一：非週期性邊界之物理現象，靜電激震波（electrostatic shock）。本模擬碼所解之基本方程式為電子與離子之Vlasov equation以及有位移電流、無磁場的安培定律（Ampère’s law）三個方程式，並且在電子的Vlasov equation中，加入了相對論的效應，以防止電子之速度超過光速。在模擬碼中，我們使用cubic spline來計算相空間中的微分與積分，時間積分則是採用predictor-corrector method來處理。 由模擬的結果中顯示，電子穿過靜電激震波後，會先加速，形成一個低溫的電子束。此電子束會與下游電漿發生two-stream instability，產生非線性大振幅的靜電波，進而造成波與粒子的交互作用，在下游產生phase mixing的現象，同時出現一個類似electron plasma solitary wave（或稱Langmuir solitary wave）往下游傳播。由我們的結果中顯示，在非碰撞之靜電激震波中，電子主要是藉由phase mixing來增加其溫度與亂度。 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.
