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研究生： 許翔傑
Hsu, Hsiang-Chieh
論文名稱： 使用於重力波探測器的低溫系統與主動阻尼減震系統的研究
Study of the cryogenic system and active vibration isolation system for gravitational wave detection
指導教授： 楊毅
Yang, Yi
共同指導教授: 王子敬
Wong, Henry Tsz-King
學位類別： 碩士
Master
系所名稱： 理學院 - 物理學系
Department of Physics
論文出版年： 2023
畢業學年度： 111
語文別： 英文
論文頁數： 222
中文關鍵詞： 重力波探測 、低溫系統 、主動阻尼減震系統 、即時回饋控制
外文關鍵詞： Gravitational wave detection, Cryogenics system, Active vibration isolation system, Real-time feedback control
相關次數： 點閱：134  下載：23 
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    • 地面干涉探測器，如LIGO、VIRGO和KAGRA，主要關注頻率大於10赫茲的重力波源，而太空探測器，如LISA，目標是頻率小於0.01赫茲的重力波。中央研究院物理研究所成立了一個名稱為ASGRAF的實驗室，它配備了基於低溫的雙扭桿重力探測器並運用Sagnac效應去測量訊號，並試圖填補LIGO和LISA之間的觀測空白。重力波探測器所配備的鏡子表面的熱擾動對干涉式重力波探測器的靈敏度造成一個本質上的限制。不僅如此，由於核心光學器件的表面和基底對光功率的吸收，將存在著熱梯度和扭曲的不利影響。這個問題可以通過選擇適當的測試質量的材料和環境溫度來緩解。故我們開發了一個由兩級脈衝管低溫冷卻器（PTC）組成的低溫系統，其中一級可維持溫度在50 K的溫度，而另一級可以達到4 K。除了減少探測器的熱雜訊外，該系統還可以對塗層在低溫環境中的光學和機械損耗測量做出貢獻。然而，引進低溫系統會造成另外一種振動，進而產生新的雜訊。來自PTC和驅動壓縮機的振動會造成一種周期性訊號。這將會影響到我們的重力波量測。對此我們有辦法做得更多，而不是勉強讓儀器在充滿噪音的環境中工作，而使之成為可能的一套技術被稱為即時回饋控制。一組探測器（光學探測器和加速規）和壓電執行器可以主動地隔離振動。六個光學探測器和六個加速規被安裝在與低溫致冷器相連的平台上，此平台有六個壓電執行器作為支撐腳。藉由這些探測器與執行器，我們發展一套即時回饋系統來主動降低來自於低溫致冷頭的振動。本研究介紹了ASGRAF實驗室以及團隊，並詳細闡述低溫系統的性能和安裝在上面的儀器實現的主動減震系統，以及我們系統如何即時回饋並控制整個系統的細節。目前為止，對於兩級的溫度記錄如下，我們4 K 以及 50 K平台達到了 3.87 K和34.16 K（此時低溫致冷頭頭在4 K 以及50 K端分別為2.80 K 和27.95 K）。而對於即時回饋的主動減震系統，我們現在可以在六個自由度中同時實現回饋控制，範圍是由0 Hz到大約1Hz之間，且在控制系統的同時，我們成功降低了該頻段間中的雜訊。

    The ground-based interferometric detectors, such as LIGO, VIRGO, and KAGRA, focus on the gravitational wave source with a frequency larger than 10 Hz, and the target of the space-borne detectors, such as LISA, is the gravitational waves with frequencies less than 0.01 Hz. A laboratory in Academia Sinica called ASGRAF, equipped with cryogenic-based dual-torsion bars gravitational detector and the sagnac interferometry, tries to fill the observation gaps between LIGO and LISA. The thermal fluctuation of mirror surfaces is the fundamental limitation of interferometric gravitation wave detectors. Furthermore, there are detrimental effects of thermal gradients and distortion due to the absorption of optical power in the surface and substrates of the core optics. The issue can be mitigated by well choosing the test mass material and the environment temperature. We developed a cryogenics system consisting of a two-stage pulse tube cryocooler (PTC); one stage is 50 K, while the other is 4 K. In addition to reducing the thermal noise of detectors, the system could also contribute to the coating's optical and mechanical loss measurements in the cryogenics environment. However, the unwanted measurable levels of equipment vibration from PTC and the electrically driven compressor are one of the problems for periodic noise. We have at our disposal the means to do more than barely make the instrument work in a noisy environment, and the set of techniques that makes this possible is called feedback control. A set of sensors (photosensors and accelerometers) and the piezoelectric actuators can actively isolate the cryogenics vibration. Six photosensors and six accelerometers are mounted on the stage, which is connected to the cryocooler and with six piezoelectric actuators as legs. This study presents the performance of the cryogenic system and active vibration isolation system achieved by the instruments mounted on it and the detail of real-time feedback control in our system. Recently, the temperature record of the lower and higher stage is 3.87 K and 34.16 K, respectively (cooling lower head 2.80 K and higher head 27.95 K). Also, we can achieve feedback control in the six degrees of freedom simultaneously with unity gain frequency below ~ 1Hz and suppress the noise in the frequency band under our control.

    Approval Letter i Abstract in Chinese ii Abstract in English iii Acknowledgements iv Contents viii List of Tables xv List of Figures xviii 1 Introduction 1 2 Gravitational Wave Science 4 2.1 Gravitational waves in general relativity 4 2.1.1 Descriptions of gravitational waves 7 2.1.2 Gravitational wave emission 8 2.2 Source of gravitational waves on Sub-Hz range 9 2.2.1 Motivation of improving low frequency sensitivity 9 2.2.2 Intermediate mass black holes 9 2.2.3 Stochastic gravitational wave background 12 3 Gravitational wave observation 13 3.1 Basic detection scheme 13 3.1.1 Angular dependence of the sensitivity of the interferometer 17 3.1.2 Folded interferometer arms 17 3.1.3 Recycling cavities 19 3.2 Laser interferometer gravitational-wave observatory (LIGO) 20 3.2.1 Advanced LIGO (aLIGO) 21 3.2.2 Cryogenic operation and LIGO Voyager 23 3.3 Other GW Detectors 25 4 Requirement of Cryogenic System in Academia Sinica Gravitational Physics Research Facility (ASGRAF) 26 4.1 The features of ASGRAF 27 4.1 The features of ASGRAF 27 4.1.1 Concept 27 4.1.2 Response to the gravitational waves 27 4.1.3 The Sagnac interferometer 30 4.2 Noises source 32 4.2.1 Seismic noise 32 4.2.2 Quantum noise .35 4.2.3 Thermal noise 37 4.2.4 Vacuum noise 40 4.2.5 Intensity noise 40 4.2.6 Parameters 41 4.3 The requirement for ASGRAF 41 4.3.1 The quantum limit detection 46 4.3.2 Intermediate mass black holes detection 47 4.3.3 The required temperature of ASGRAF 49 5 The Cryogenic System in ASGRAF 50 5.1 Test system of the cryogenics 50 5.1.1 The development of the cryogenic chamber 51 5.1.2 Cryogenic temperature sensors (Thermometers) 52 5.1.3 Multi-layer insulation (MLI) 59 5.1.4 Thermal loading map 62 5.1.5 Sidepod chamber 65 5.2 Overview of the whole system 69 6 Development of active vibration isolation system (AVIS) for the cryogenic system 71 6.1 The detail in the installation of the cryogenic system 71 6.2 Feedback control loop 73 6.2.1 The principle of the feedback control loop 74 6.2.2 Stability of the system 79 6.3 The components in the active vibration isolation system 82 6.3.1 Vibration sensor: Accelerometers 83 6.3.2 Vibration sensor: Photosensors 84 6.3.3 Piezoelectric Actuators 87 7 Characterization of Sensors and Actuators 90 7.1 Vibration Sensors: Photosensors 90 7.1.1 Model and assumption 90 7.1.2 Design of the photosensor 93 7.1.3 Readout and Electronics 98 7.1.4 Calibration 100 7.1.5 Installation 104 7.2 Vibration Sensors: Accelerometers 108 7.2.1 Introduction of the accelerometers 110 7.2.2 Readout and Electronics 112 7.2.3 Installation 114 7.3 Piezoelectric actuators 118 7.3.1 Introduction of the piezoelectric actuator 118 7.3.2 Readout and Electronics 119 8 Digital Control System 123 8.1 A brief introduction of the hardware in DGS 124 8.1.1 Optical timing distribution system 125 8.2 A brief introduction of the software in DGS 126 8.2.1 Motif Editor and Display Manager (MEDM) 127 8.2.2 Foton 127 8.2.3 Data Viewer (DV) 130 8.2.4 Diagnostic GUI (Diaggui) 130 9 Integration Test 132 9.1 Cooling procedure with two stages 132 9.2 Installation 134 9.3 Active vibration isolation with feedback control 134 9.3.1 First trial of feedback control 134 9.3.2 Problems in the first trial 141 9.3.3 Diagonalization 141 9.3.4 Control the system in six DoF simultaneously 150 10 Discussion 159 10.1 Cryogenic system 159 10.1.1 The thermal loading map 159 10.2 Sensors and actuators 160 10.2.1 Photosensors 160 10.2.2 Multiple reflections of the photosensors 160 10.2.3 The issue about the current of the LED 161 10.2.4 The temperature of the working environment 162 10.2.5 Accelerometers 62 10.2.6 Actuators 164 10.3 Vibration from the cryogenic system 164 10.3.1 The noise spectrum of the cryogenic system 164 10.3.2 Temperature-dependent of the cryocooler’s vibration 167 10.4 Active vibration isolation for the cryogenic system 169 11 Summary 170 Appendix A Transfer function of the suspension system 172 A.1 A suspension system 172 A.2 Transfer function (torque to angular velocity) 173 A.2.1 Lagrangian 174 A.2.2 Derivation 175 A.3 Transfer function (angle to angle) 178 A.4 Input parameters 180 Appendix B The derivation of the actuator matrix 183 B.1 The motions from the actuators 183 B.2 Numerical results 187 Appendix C Calibration of the Resistance thermometers (CX-1050-CU) 188 C.1 Jig for the sensors 188 C.2 Setup of the sensors 190 C.3 Data taking 190 C.4 Result 190 C.4.1 Curve fit 191 Appendix D The finite element calculation of the gravity field calibrators (GCal) 196 D.1 Gravity field calibrators 196 D.2 Point model of GCal 197 D.2.1 Configuration of GCal 197 D.2.2 Model 199 D.3 The results of different cases 201 D.3.1 Parameters 201 D.3.2 Point masses case 201 D.3.3 Finite element case 204 D.4 Summary 215 References 216

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