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系統識別號 U0026-0808201911414800
論文名稱(中文) 太空與實驗室環境中太陽風與非磁化星球的交互作用之理論研究
論文名稱(英文) Theoretical study of the solar wind interacting with an unmagnetized planet in space and in laboratory
校院名稱 成功大學
系所名稱(中) 太空與電漿科學研究所
系所名稱(英) Institute of Space and Plasma Sciences
學年度 107
學期 2
出版年 108
研究生(中文) 葉宜霖
研究生(英文) I-Lin Yeh
電子信箱 yih125guy@gmail.com
學號 LA6074017
學位類別 碩士
語文別 英文
論文頁數 73頁
口試委員 指導教授-張博宇
口試委員-談永頤
口試委員-呂凌霄
中文關鍵字 未磁化行星的弓形震波  對峙距離  氣體動力學理論  電離層  實驗室太空科學  脈衝功率系統 
英文關鍵字 bow shock of the unmagnetized planet  standoff distance  ionosphere  gasdynamics theory  laboratory space sciences  pulsed-power system 
學科別分類
中文摘要 我們正在研究由太陽風與未磁化行星相互作用產生的火星弓形震波 (Martian bow shock)。透過理論研究太陽風的參數,例如太陽風動態壓力和太陽極紫外線通量,如何影響弓形震波的位置,這個課題目前尚未被完全了解。這項理論研究將用於設計我們的實驗室太空科學的實驗,透過國立成功大學太空與電漿科學研究所的6000焦耳的脈衝功率系統來驅動錐形線陣列產生馬赫數高達20的超音速電漿噴流流過障礙物來實現。雖然震波的形成機制在太空和實驗室上有所不同,不過我們透過歐拉相似性的分析證明了在我們未來的實驗中研究火星弓形震波位置是可行的。

我們提出了一個適用於太陽風和非磁化行星之間的相互作用的公式來表達弓形震波鼻子(ionopause nose)的位置,這個公式將用於設計我們未來的實驗。我們用氣體動力學方法計算了弓形震波位置,也就是電離層邊界位置和間隙距離的總和。其中電離層邊界的位置是由壓力平衡公式計算而得的。而弓形震波的間隔距離是由半經驗模型所計算到得到的,其正比於電離層邊界鼻子的曲率半徑。我們最後算出了弓形震波鼻子位置的公式,它取決於電離層的高度尺度,太陽風的動態壓力和電離層的峰值壓力。此外,我們推導出電離層邊界鼻子附近的輪廓方程 (profile equation)。最後我們將我們的理論與氣體動力學模擬和太空儀器量測結果做初步比較,我們的理論結果與模擬和太空儀器量測結果是一致的。
英文摘要 Martian bow shock, the solar wind interacting with the unmagnetized planet, will be studied. We theoretically investigated how the solar parameters, such as solar wind dynamic pressure and solar EUV flux, influences the bow shock location, which is still currently not well understood. This theoretical study will be used to design the laboratory space science experiments. The experiment will be implemented by producing a supersonic plasma jet with Mach number up to 20, which will be generated using a conical wire array, flowing through an obstacle. The conical wire array will be driven by a 6 kJ pulsed-power system in the Institute of Space and Plasma Sciences, National Cheng Kung University, Taiwan. Although the shock formation mechanism is different in space and laboratory condition, we have shown that, through the analysis of the Euler similarity, studying the Martian bow shock location in our potential experiment is feasible.

We present the formula for the location of the bow shock nose for the interaction between the solar wind and unmagnetized planet. This formula will be used to design future experiments. We calculate the bow shock location, the sum of the ionopause location and standoff distance, in the gasdynamics approach. We determine the ionopause nose location using pressure balance formula. The standoff distance of the bow shock is determined by a semiempirical model proportional to the radius of curvature at the ionopause nose. We derived the formula of the shock nose position, which depends upon the scale height in ionosphere, dynamic pressure of the solar wind, and the peak pressure of the ionosphere. Furthermore, we derived the equation of the ionopause profile around the nose. The preliminary comparison of our theory with the results of the gasdynamics simulation and the spacecraft measurement will be presented. Our derived formula is consistent with the simulation and the spacecraft measurement results.
論文目次 1 Introduction 1
1.1 The interaction between solar wind and unmagnetized planet . . . . . . . . 1
1.1.1 Martian Bow Shock . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.2 Previous research on the Martian bow shock location . . . . . . . . 3
1.1.3 Hydrodynamics boundary condition . . . . . . . . . . . . . . . . . . 5
1.2 The goal of the project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 Laboratory Space Sciences 10
2.1 Scaling relation and similarity criteria . . . . . . . . . . . . . . . . . . . . . 10
2.2 Introduction to our experiment system . . . . . . . . . . . . . . . . . . . . 13
2.2.1 Pulsed-power system . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.2 Conical-wire arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3 Our potential experiment and scaling relation . . . . . . . . . . . . . . . . 16
3 Determination of the location of the bow shock nose 19
3.1 Overview of the theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.2 Ionopause (obstacle boundary) . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2.1 Thermal pressure at the ionopause . . . . . . . . . . . . . . . . . . 23
3.2.2 Nose position of the ionopause ro . . . . . . . . . . . . . . . . . . . 24
3.2.3 Radius of curvature at ionopause nose Ro . . . . . . . . . . . . . . . 25
3.3 Bow shock standoff distance ∆ . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.4 The formula of the bow shock nose location . . . . . . . . . . . . . . . . . 34
3.5 Comparison with the simulation and spacecraft measurement results . . . . 35
3.5.1 Verification of the analytical form of the radius of curvature by simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.5.2 Comparison with hydrodynamics simulation . . . . . . . . . . . . . 37
3.5.3 Comparison with spacecraft measurements . . . . . . . . . . . . . . 39
4 Experiment designs 42
5 Future works 44
6 Conclusion 46
References 47
A Hydrostatic equilibrium 51
B Rayleigh pitot tube formula 52
C 1D electrostatic particle-in-cell simulation 57
C.1 Fundamental of particle-in-cell simulations . . . . . . . . . . . . . . . . . . 57
C.2 My 1D electrostatic particle-in-cell program - two-stream instability . . . . 58
C.2.1 Dimensionless equations . . . . . . . . . . . . . . . . . . . . . . . . 58
C.2.2 Input parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
C.2.3 Program overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
C.2.4 Leapfrog method for solving equations of motion . . . . . . . . . . . 62
C.2.5 Gauss-Seidel method for solving Poisson equation . . . . . . . . . . 63
C.2.6 Linear weighting method for connecting particles and grids . . . . . 64
C.3 Two-stream instability: selected results and analysis . . . . . . . . . . . . . 66
C.4 Comparison withe the linear theory . . . . . . . . . . . . . . . . . . . . . . 71
D Setup of the code "PIConGPU" on our cluster 73
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