靜電激震波之電漿動力數值模擬與理論研究

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姓名

蔡宗哲(Tsung-Che Tsai) 查詢紙本館藏

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太空科學研究所

論文名稱

靜電激震波之電漿動力數值模擬與理論研究
(A Simulation and Theoretical Study of ion Acoustic Shocks Based on a Vlasov Simulation Code)

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摘要(中)

在過去的研究中，科學家曾經在行星的艏震波、行星際激震波與太陽風終止激震波的電子 foreshock區域觀測到靜電波之存在。而這些靜電波可能為電子聲波、質子聲波以及double layer。然而，電子聲波為電子時間尺度之物理現象，質子聲波與double layer為質子時間尺度的物理現象，由於時間尺度之差異，使得我們必須使用跨時間尺度之模擬碼才能夠模擬此區域之物理現象。在本論文所研建的靜電Vlasov模擬碼中，使用四階implicit scheme之時間積分、三階空間微分，以及在差分加減運算時，消去小於相對誤差之溢位數值誤差(run-off error)等方式來大幅減低模擬結果之數值雜訊，如此才得以完成史上第一個能研究跨電子與質子時空尺度靜電波耦合現象之模擬碼—靜電Vlasov模擬碼。我們利用此低雜訊之靜電Vlasov模擬碼，模擬地球艏震波附近之靜電波，藉此了解那些觀測到的非線性靜電波的形成機制，以及電子靜電加熱過程。在我們的模擬結果中，我們發現當靜電激震波上游冷電漿與下游熱電漿於過渡區相遇時，將於過渡區產生一電位差，其電位差之大小與上下游電子溫度差成正比。在下游電子溫度較低的例子中，我們發現質子在過渡區邊緣產生正電荷累積，造成overshoot的現象。另一方面，當下游電子溫度夠高以致於熱電子得以穿越過渡區溢散到上游時，將先後造成電位之foot結構、電子聲波、質子聲波以及double layer等非線性靜電波。另外，我們發現電子聲波與質子聲波將快速增加電子的溫度，但無法有效的提升質子的溫度。我們認為要有效的加熱質子，需要透過大振幅之質子時空尺度的電磁波。而電子沿磁場方向被靜電波加熱所造成的溫度非均向性，將是造成中高頻電磁不穩定的原因之一。此一部分之後續研究將於論文中討論之。

摘要(英)

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.

關鍵字(中)

★ 正離子聲波
★ 電子聲波
★ 靜電波
★ 電漿模擬
★ 激震波

關鍵字(英)

★ electron acoustic wave
★ ion acoustic wave
★ double layer
★ ion acoustic shock
★ electrostatic shock
★ Vlasov simulation

論文目次

中文摘要 i
英文摘要 ii
致謝辭 iv
本文目錄 v
圖目錄 vii
表目錄 xiii
第一章導論 1
第二章模擬碼之基本架構 6
2.1 模擬碼之基本方程式 6
2.2 模擬碼所使用之歸一化常數 7
2.3 模擬碼之數值流程 9
2.3.1 預測—修正法 9
2.3.2 三次曲線擬合法 10
2.3.3 邊界條件 11
2.4 模擬碼之測試與線性分析之方法 11
2.4.1 雙流不穩定之初始條件 13
2.4.2 線性分析之方法 14
2.4.2.1 雙流不穩定之流體線性頻散關係 15
2.4.2.2 雙流不穩定之動力學線性頻散關係 19
2.4.3 隨機雜訊低通濾波之建構方式 23
2.4.4 Vlasov模擬碼與全粒子碼模擬結果之比較 28
2.5 Vlasov模擬碼與全粒子碼執行速度之比較較 33
第三章靜電激震波之模擬結果 35
3.1 靜電激震波之初始條件 35
3.1.1 靜電激震波的躍遷條件 35
3.1.2 模擬碼初始條件之設定 38
3.2 電位差 43
3.2.1 過渡區電位差之模擬結果 43
3.2.2 電位差之理論解與模擬結果之比較 50
3.3 電子時間尺度模擬結果之分析 55
3.3.1 下游電子聲波之理論分析 58
3.3.2 上游電子聲波之理論分析 69
3.4 正離子時間尺度模擬結果之分析 79
3.4.1 上游正離子聲波與foot結構之分析 79
3.4.2 Overshoot之分析 86
3.4.3 正離子聲波觸發電子聲波之過程 92
3.4.4 Double layer 98
第四章總結與討論 106
參考文獻 110
附錄A Predictor-Corrector method 116
附錄B Cubic spline method 118

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指導教授

呂凌霄(Ling-Hsiao Lyu)

審核日期

2010-1-27

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