臺灣博碩士論文加值系統

我們的 LC 電路探測器的目標是仔細研究質量約為 0.5μeV（對應於
120 MHz 頻率）的難以捉摸的軸子。在外加強磁場的存在下，軸子能夠
引發一種奇異電流，從而產生微弱但可察覺的振盪磁場。傳統的使用
腔體法的方式在這麼低頻率下檢測信號是不切實際的。為了克服這一
限制，我們提出了一種新穎的策略，即利用 LC 電路的諧振頻率來放大
我們對軸子引起的磁場的探測。這個 LC 電路的諧振頻率被設計為可調
諧，這一特性可以通過調整電容來實現。這不僅為我們提供了一個增
強信號的多功能工具，還開闢了探索軸子質量潛在變化的途徑。
通過精細調整 LC 電路的電容，我們可以精確控制並探索一系列共振
頻率。這種動態調諧能力對於適應不同的實驗條件和優化我們的探測
系統的靈敏度至關重要。此外，它使我們能夠在軸子質量上進行全面
的搜索，為這些難以捉摸的粒子的基本特性提供有價值的見解。本質
上，我們的創新方法利用了 LC 電路中的諧振頻率調諧的力量，提供了
一種複雜且可適應的手段來探索軸子物理的複雜性。這不僅增強了我
們檢測軸子引起的磁場的能力，還使我們處於尖端研究的前沿，推動
我們對基本粒子及其行為的理解邊界。

The objective of our LC circuit detector is to meticulously investigate the elusive axion with a specific mass hovering around 0.5 µ eV, corresponding to a frequency of 120 MHz.
In the presence of a strong static magnetic field, axions can instigate an exotic current, thereby inducing a subtle yet discernible oscillating magnetic field. The conventional
approach of employing the cavity method proves impractical for detecting signals at such low frequencies. To overcome this limitation, we propose a novel strategy that involves leveraging the resonant frequency of an LC circuit to amplify our pursuit of the axion-induced magnetic field. This LC circuit’s resonant frequency is designed to be tunable, a feature achievable by adjusting the capacitance. This not only provides us with a versatile tool for signal enhancement but also opens up avenues for probing potential variations in the axion’s mass.
By finely tuning the capacitance of the LC circuit, we can precisely control and explore a range of resonant frequencies. This dynamic tuning capability is instrumental
in adapting to different experimental conditions and optimizing the sensitivity of our detection system. Furthermore, it enables us to conduct a comprehensive search in the axion’s mass, offering valuable insights into the fundamental properties of these elusive particles. In essence, our innovative approach harnesses the power of resonant frequency tuning in an LC circuit, providing a sophisticated and adaptable means to explore the intricacies of axion physics. This not only enhances our ability to detect the axion-induced magnetic field but also positions us at the forefront of cutting-edge research, pushing the boundaries of our understanding of fundamental particles and
their behaviors

Contents
1 Motivation and Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2.1 The Dark Matter and the Axion . . . . . . . . . . . . . . . . . . . . 1
1.2.2 Current Results of the Axion Searches . . . . . . . . . . . . . . . . 2
2 Theoretical Derivation of the Axion Field 7
2.1 The B field solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 The E field solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 Theory of the Axion Searches with LC circuits . . . . . . . . . . . . . . . 11
3 The Design of the LC Lumped Elements 15
3.1 Inductor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2 Trimmer Capacitor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4 The External Setup of the TASEH-LC Experiment 21
4.1 The Cryogenic System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.1.1 Dilution Refrigerator . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.1.2 The Superconducting Magnet . . . . . . . . . . . . . . . . . . . . . 22
4.1.3 The Vector Network Analyzer and the Vector Signal Transceiver . 22
4.1.4 Motor tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.1.5 The Circulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
5 The Axion-searching Device Design with an LC Circuit 27
5.1 The First version design of LC circuit frame . . . . . . . . . . . . . . . . . 28
5.2 The Second version design of LC circuit frame . . . . . . . . . . . . . . . 33
5.3 The Third version design of LC circuit frame . . . . . . . . . . . . . . . . 38
6 Test for the Setups of the Coupling Wire and the LC Circuit 41
6.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
6.2 Test for the coupling wire at room temperature . . . . . . . . . . . . . . . 41
6.2.1 Optimization of the readout coupling wire . . . . . . . . . . . . . 41
6.2.2 Different coupling line position . . . . . . . . . . . . . . . . . . . 42
6.2.3 Different coupling wire-diameter . . . . . . . . . . . . . . . . . . 43
6.2.4 Different circumferences of coupling wire loops . . . . . . . . . . 44
6.3 Test for the LC circuit lump elements . . . . . . . . . . . . . . . . . . . . . 46
6.3.1 The wielding of copper readout wires to the LC circuit . . . . . . 46
6.3.2 The results of different wielding methods . . . . . . . . . . . . . . 47
6.3.3 The analysis of the data collected on 2023/06/29 . . . . . . . . . 49
6.4 The Cool-down TASEH 013 . . . . . . . . . . . . . . . . . . . . . . . . . . 52
6.4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
6.4.2 CDT013 test setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
6.4.3 Test results of CDT013 . . . . . . . . . . . . . . . . . . . . . . . . . 55
Constant displacement for each motor step . . . . . . . . . . . . . 57
Determination of the motor displacement for a 1 MHz frequency
change . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
6.4.4 The test for CDT013 setup at room temperature . . . . . . . . . . 60
6.5 The test result and experiment setup of CDT015 . . . . . . . . . . . . . . 60
6.5.1 CDT015 test result of room temperature . . . . . . . . . . . . . . . 64
6.5.2 CDT015 test result of low temperature in DR . . . . . . . . . . . . 64
7 Calibration for the amplification chain and test of the LC circuit performance 67
7.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
7.1.1 Component test for amplification chain . . . . . . . . . . . . . . . 67
Room Temperature amplifier test . . . . . . . . . . . . . . . . . . 67
Cryogenic amplifier test at the room temperature . . . . . . . . . 69
The electric circuit diagram of LC circuit and amplification chain 70
Noise level test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
7.1.2 LC circuit test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Strong coupling port reflection . . . . . . . . . . . . . . . . . . . 73
7.2 Calibration of the amplification chain . . . . . . . . . . . . . . . . . . . . 75
7.2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
7.2.2 Calibrate the amplifier chain with the LC circuit . . . . . . . . . . 77
7.2.3 Calibrate the amplifier chain without the LC circuit . . . . . . . . 77
8 Conclusion 81
8.1 The limit of the expected gaγγ . . . . . . . . . . . . . . . . . . . . . . . . . 81
8.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
A 87
A.1 Axion field equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
A.2 Combining these Equations . . . . . . . . . . . . . . . . . . . . . . . . . . 89
A.3 The B field solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
A.4 The E field solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
A.5 The long-wavelength limit . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
bibliography 97

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