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研究生: 張書豪
Chang, Shu-Hao
論文名稱: 以質點網格法探討產生孤子的機制 - 關於太空天氣探測
Particle-in-Cell Simulation of Langmuir Solitons’ Generation Mechanism - Towards Space Weather Forecast
指導教授: 西村泰太郎
Yasutaro Nishimura
學位類別: 碩士
Master
系所名稱: 理學院 - 太空與電漿科學研究所
Institute of Space and Plasma Sciences
論文出版年: 2015
畢業學年度: 104
語文別: 英文
論文頁數: 58
中文關鍵詞: Langmuir 孤立波Zakharov方程式非線性Schrödinger方程式震盪雙流不穩定質點網格法第三型噴射太空天氣觀測
外文關鍵詞: Langmuir soliton, Zakharov equation, nonlinear Schrödinger equation, oscillating two stream instability, Particle-in-Cell, Type-III emission, Space weather forecast
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  • 太空天氣預報是非常重要的,根據預報可以避免地球上的設施遭受損壞。在這裡我們專注在Langmuir孤立波的生成機制。Langmuir孤立波可以藉由太陽爆發所引起的第三型噴射而生成,而第三型噴射是與Langmuir擾動所給予的信號藉著無線電波傳遞至地球有關。而這些現象我們將用質點網格法來進行模擬研究。
    一開始我們先模擬線性與非線性的Landau阻尼,並與 C. Z. Cheng 1976年的論文進行對照。接下來使用具有高能量的非高斯分布來試著產生Langmuir孤立波。這個具有高能量的非高斯分布所產生的不穩定狀態能讓我們對於基本的震盪雙流不穩定有所了解。
    接下來我們對Langmuir孤立波所產生的頻譜(k-光譜)進行詳細的討論。為了得到孤立波的初始條件,我們使用Zakharov方程式和非線性Schrödinger方程式獲得離子密度和電場分布,至於電子密度可以藉由逆Gauss’s定律推得。此外,我們使用外部射頻電場來產生孤立波(參考Valeo 1974年的論文),並對孤立波崩潰後進行觀測後可以獲得震盪雙流不穩定的資訊。在論文的最後,我們對震盪雙流不穩定的飽和狀態進行探討,並藉由仔細觀察相空間分布可發現速度分布的平坦化。

    Space weather forecast is crucial to avoid the damage on the earth. In this work, the generation mechanism of Langmuir solitons is investigated. Langmuir solitons can be generated by solar bursts induced type III emission (Goldman, 1984) which is closely related to Langmuir turbulence giving precursor signals by radio wave reaching the earth. The behavior of Langmuir soliton generation mechanism is investigated by Particle-in-Cell simulation.
    As a preliminary study, linear and nonlinear Landau damping are benchmarked with a paper by C. Z. Cheng and G. Knorr (Cheng, 1976). The evolution of Non-Gaussian distributions with high-energy components as the generation mechanism of Langmuir soliton is studied. The bump-on-tail instability which provides us with the base of oscillating two stream instabilities (OTSI) is resumed.
    During the Langmuir solitons generation the spectrum of wave vectors (k-spectrum) is studied in detail. For the initial condition, Analytical solution of Zakharov equations and nonlinear Schrödinger (NLS) equation is employed, first. To employ the ion density and the electric field for soliton profiles, the electron density is obtained by inverting Gauss’s law. Furthermore, the solitons by external Radio-Frequency (RF) electric field (Valeo, 1974) are generated. Onset of oscillating two stream instability is observed after the collapse of solitons. The saturation mechanism of OTSI is discussed and understood as flattening of the distribution function by carefully looking into phase space dynamics.

    摘要 1 Abstracts 2 Contents 3 List of Figures 4 Chapter 1 Introduction 8 Chapter 2 Theoretical and Numerical model 11 2.1 Normalized Vlasov and Poisson Equations 11 2.2 Ponderomotive Force 12 2.3 Derivation of Zakharov Equations and Nonlinear Schrödinger Equation 14 Chapter 3 Particle-in-Cell simulation 20 3.1 Particle’s Initial Loading 21 3.2 Gathering Particles 23 3.3 Electric Field for Self-Consistent Simulation 25 3.4 Time Advancing Particles’ Equation of Motion 28 3.5 Benchmarking of Landau Damping 29 3.6 Benchmarking of Bump-on-tail Instability 34 Chapter 4 Numerical Simulation of Langmuir Solitons 36 4.1 Numerical Simulation by Taking Zakharov Solution as an Initial Condition 36 4.2 Soliton Generated by Radio-Frequency Electric Field 43 4.3 Observation of Oscillating Two Stream Instability 50 Chapter 5 Summary and Future work 54 Reference 56

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