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系統識別號 U0026-2108201715544300
論文名稱(中文) 立方衛星用頂帽型電子探測儀之研發
論文名稱(英文) Development of Top-Hat Electrostatic Analyzers for Cube Satellites
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 105
學期 2
出版年 106
研究生(中文) 蔡宜良
研究生(英文) Yi-Liang Tsai
學號 LA6041111
學位類別 碩士
語文別 英文
論文頁數 87頁
口試委員 口試委員-陳秋榮
口試委員-談永頤
指導教授-張博宇
中文關鍵字 立方衛星  頂帽型帶電粒子探測儀 
英文關鍵字 Cube satellite  Top-Hat Electrostatic Analyzers 
學科別分類
中文摘要 本論文將設計一個可放在小型的衛星(3U立方衛星CubeSat)中的頂帽型帶電粒子探測儀Top-Hat Electrostatic Analyzer (THEA),來瞭解太空中帶電粒子的分布函數,其中每一個U是立方衛星的基本單元,大小為10x10x10立方公分。為了能夠更加了解外太空的科學現象,我們必須透過更多的衛星記錄在同一時間不同位置所發生的數據資料,才能夠對在外太空發生的科學現象有更完整、客觀的描述。因為立方衛星的成本較低,所以可以發射多顆搭載頂帽型電子探測儀的立方衛星至外太空,同時於不同地點量測太空當中的帶電粒子的分布函數。頂帽型帶電粒子探測儀是由兩個金屬球殼所構成,若在兩個球殼上施加不同的電壓,當帶電粒子進入時就會受到電場的影響,使其運動方向因受力而偏折,其偏折程度取決於帶電粒子的能量、荷質比、及兩球殼間電壓差,本論文將著重於量測電子的分布函數上。我們將開發模擬程式去計算探測儀內部電場分佈和電子軌跡。透過利用理想的頂帽型電子探測儀,即雙同心的金屬球殼,來估算能夠量測到的最大電子能量。當球殼內外半徑為44mm、 45mm且內外球殼的電壓分別為 1kV、 0V,可量測到的電子能量為22.2 keV。其中,頂帽型帶電粒子探測儀裡的電場,是透過高斯-賽代爾法(Gauss-Seidel method)解拉普拉斯方程式而得,並且為了要節省模擬的時間我們在高斯-賽代爾法中引入了〝旗幟法〞,只針對被選定的區域進行計算;另外,使用4階的龍格-庫塔法(Runge-Kutta method)計算相對論效應下電子在頂帽型電子探測儀中的運動軌跡。透過模擬統計,一個內外球殼半徑為 44 mm 和 45 mm,電壓分別為1kV 和 0V的頂帽型電子探測儀的幾何因子為2.64 * 〖10〗^(-4)(cm^2-sr-keV/keV)。

關鍵字:立方衛星、頂帽型帶電粒子探測儀
英文摘要 A top-hat electrostatic analyzer (THEA), well-developed charged particle analyzers for small satellites, will be adopted to cube satellites, which are made out of multiple 10x10x10 cm^3 cubic unit. Data from a single satellite can only be collected at single point at one time. However, to understand any events in the space thoroughly, it is essential to collect data at different locations in the space simultaneously to capture the whole picture. In other words, measurements from multiple satellites are required. Because of the much lower cost of building cube satellites, many cube satellites carrying THEAs can be launched and measure distribution functions of charged particles in different locations in space at the same time. It enables us to have a better understanding of distribution functions of charged particles in the whole space. An zeroth-order approximated using an ideal THEA consisting of two concentric spheres shows that a THEA for measuring electrons with energy up to 22.2 keV can be fit in a cube satellite. Different voltages will be given to two shells so that the trajectories of electrons entering the analyzer will be bent by the corresponding electric fields. Only electrons with the radii of their circular motions that match the average curvature of the shells reach the detector located at the bottom of the analyzer. In this thesis, the electric fields in THEA are calculated by solving the Laplace’s equation using Gauss–Seidel method. The Gauss-Seidel method is sped up using〝Flag technique〞where only points in THEA are calculated. Trajectories of electrons with relativistic effect will be simulated using 4^th order Runge-Kutta method. Results of calculated electric fields and electron trajectories are shown. Simulations show that electron with energy of 21.7 keV can pass through the THEA.
The key parameter g-factor which represents the sensitivity of the THEA will also be simulated. The g-factor of a THEA where the radius and the potential of the inner and outer sphere are 44 mm, 45 mm, 1kV, and 0V, respectively, equals to 2.64 * 〖10〗^(-4)(cm^2-sr-keV/keV).


Key words: Cube satellite, Top-Hat Electrostatic Analyzers
論文目次 摘要 I
ABSTRACT II
誌謝 III
LIST OF FIGURES VI
LIST OF TABLES IX
CHAPTER 1 INTRODUCTION AND MOTIVATION 1
CHAPTER 2 INTRODUCTION OF CUBESAT 5
CHAPTER 3 INTRODUCTION OF TOP HAT ELECTROSTATIC ANALYZERS (THEA) 8
3.1 Zeroth order estimation 9
3.2 Geometric factor 12
CHAPTER 4 DEVELOPMENT OF THE SIMULATION CODE 14
4.1 Introduction of numerical methods 14
4.1.1 Finite Difference method 15
4.1.1.1 Boundary conditions 20
4.1.2 Gauss Seidel method 21
4.1.3 Gauss Seidel method accelerated by using Flag method 23
4.1.4 Bilinear interpolation method 24
4.1.5 Runge-Kutta method 26
4.2 Laplace’s equation solver for an ideal THEA 30
4.2.1 Benchmarking the Laplace’s equation solver 35
4.3 Trajectories of electrons in ideal THEA 37
4.3.1 The electron trajectories without Relativistic 37
4.3.1.1 Benchmarking the bilinear interpolation of simulated electron fields 40
4.3.2 The electron trajectories with relativistic effect 42
4.3.2.1 Runge-Kutta method with relativistic effect 45
4.3.2.2 The speed of electron is much less than speed of light 47
4.3.2.3 The speed of electron is closed to the speed of light 48
4.3.3 Summary 50
CHAPTER 5 SIMULATION RESULTS OF THEA 51
5.1 The electric potential of an actual THEA 51
5.2 Electron trajectories 57
5.3 G-factor calculation 59
5.3.1 Initial conditions 60
5.3.2 G-factor calculations 62
CHAPTER 6 CONCLUSION AND SUMMARY 66
CHAPTER 7 FUTURE WORKS 67
REFERENCE 69
APPENDIX A 72
APPENDIX B 75
APPENDIX C 77
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