插件磁鐵在同步輻射和自由電子雷射設施上扮演關鍵的光源設備的角色。因此，發展短週期且強磁場的聚頻磁鐵才是提高同步輻射光亮度和縮小加速器設備尺寸的主要目標。為了在短週期之下能產生高磁場，我們使用的材料為高溫超導(high-temperature superconducting)釔鋇銅氧塊材(YBCO Bulk)，半徑和厚度分別為16 mm和2.5 mm。

將塊材組成錯開排列的聚頻磁鐵(staggered undulator)，其週期長(period length)和磁極間隙(magnet gap)分別為5 mm 和4 mm。超導塊材磁列在3.5 T 螺線管磁化系統之下，分別在溫度為77 K和7 K的環境裡被磁化而擄獲磁場。目前在77 K和7 K的條件之下，這種錯開排列的聚頻磁鐵所獲得的平均磁場強度分別約為0.015 T和0.3 T，同時也使用場冷磁化(Field Cool, FC)和零場冷磁化方式(Zero Field Cool, ZFC)，來分析高溫超導塊材錯開排列的聚頻磁鐵(HTS Bulk Staggered Undulator (HTSBSU))被磁化後其所擄獲磁場大小及磁場均勻性的不同特性。對於低溫的實驗環境，利用SolidWorks軟體來設計新的低溫真空腔體，並藉由製冷機(cryocooler)降低塊材溫度達到7 K。

為了獲得一次場積分值(電子角度)和二次場積分值(電子位置)為零，必需想辦法先能計算所能獲得的擄磁場大小及其分佈，因此，尋找一套超導塊材模擬擄磁場的理論與方法，才能去估算擄磁場強度及其橫向上的磁場均勻度分佈，並且利用此方法來優化末端磁極 (end pole optimization)來獲得一次場積分和二次場積分值為零，因此以比恩模型(Bean Model)為基礎而發展出的能量最小化方法(Energy Minimization Method, EM Method)提供了磁場模擬的可行性。最終，以能量最小化方法為理論基礎，並在Mathematica和Radia等的應用程式上發展出一套演算法，去計算感應電流分布來模擬擄獲磁場大小與分佈。

而各顆高溫超導塊材擄磁大小是否相同也是本研究成功與否的主要關鍵因素之一，因此在各顆塊材擄磁大小不相同的情況之下，整理分析並找出一套能滿足「均勻」擄磁場的方法流程，此方法可以解決部分短週期之下高溫超導錯開排列聚頻磁鐵的各顆塊材擄磁大小不相同的問題。從實驗中了解如果各顆塊材擄磁大小不相同時，則以場冷磁化為主並使塊材處於磁化未飽和狀態，如此可以降低各顆塊材擄磁大小不相同的影響因素，並有機會可以獲得較均勻的擄磁場及其縱向磁場分佈。

Insertion device (ID) is the key devices in the facilities of synchrotron radiation and free electron laser. In order to enhance the brightness of synchrotron radiation and minimize the size of accelerator facilities, the development of a short-period undulator with strong magnetic field was launched. For this purpose, we used high-temperature superconducting (HTS) YBCO bulks with diameter of 32 mm and thickness of 2.5 mm as the magnet pole to generate a strong periodic magnetic field in the longitudinal axis.

The HTS bulks were constructed and assembled as the staggered undulator that the period length and magnet gap were 5 mm and 4 mm, respectively. So as to obtain the trapped magnetic field, the staggered undulator with HTS bulks was magnetized at 77 K and 7 K in a 3.5 T solenoid system. The peak field of this HTS bulk staggered undulator is obtained around 0.015 T and 0.3 T at 77 K and 7 K, respectively. Meanwhile, both field cool (FC) and zero field cool (ZFC) were used to analyze properties of trapped magnetic field and uniform field of magnetized HTS bulk staggered undulator (HTSBSU). For low-temperature environment, we used SolidWorks to design a new cryogen-free system which cooled down the HTS bulks to 7 K by cryocooler.

In order to optimize the HTSBSU to let the first field integral (i.e. electron angle) and the second field integral (electron position) be zero, we needed to obtain the exact magnet field strength and the field distribution. Therefore, it was necessary to develop a simulation code to find out the trapped field strength and the field distribution of the HTSBSU magnet. Meanwhile, this simulation code was also used to optimize the end pole configuration and to maximize the homogeneity field range. So, we use the energy minimization method (EM Method) which based on Bean’s model theory to simulate the trapped field on the HTS bulks. This simulation code was developed through the application program of Mathematica and Radia. Consequently, this simulation code was applied to calculate the distribution of induced current density on the bulk array and then to simulate not only the longitudinal periodic fielddistribution, but the magnetic field strength.

In the end, the key to successful construction of HTSBSU is the uniformity of all HTS bulks. If the field homogeneity of all HTS bulks is not good enough, we have to find a solution to solve the issue of non-uniform trapped field. If the quality of all HTS bulks is different, the field-cooled is selected for the magnetized method and bulks are maintained at unsaturated state, then it is able to reduce the effect from the non-uniformity of each HTS bulks. Consequently, there is opportunity to get better homogenous trapped magnetic field on each bulk and good period field in the longitudinal axis.

1 前言 1
1.1 同步輻射加速器 1
1.2 研究目的與目標 5
1.3 研究方法與架構 12

2 理論和數值模擬 14
2.1 前言 14
2.2 比恩模型(Bean Model) 14
2.3 能量最小化方法(Energy Minimization Method, EM Method) 15
2.3.1 幾何描述和方程式 15
2.3.2 能量最小化方法步驟 17
2.4 能量最小化方法套用於錯開排列之高溫超導塊材聚頻磁鐵的數值計算
(High Temperature Superconducting Bulk Staggered Undulator, HTSBSU) 21
2.4.1 模擬磁化HTSBSU，以單顆似半圓塊材為一組 23
2.4.2 模擬磁化HTSBSU，以五顆似半圓塊材為一組 25
2.4.3 模擬磁化HTSBSU，以十顆似半圓塊材為一組 26
2.5 結果與討論 28
2.5.1 超導量子干涉儀(Superconducting Quantum Interference Device, SQUID)和臨界電流密度Jc (critical current density) 28
2.5.2 HTSBSU實驗結果和能量最小化方法模擬HTSBSU之間
的比較 33
2.5.3 比恩模型和能量最小化方法在模擬擄磁場不同之處 37
2.6 結論 39

3 HTSBSU末端磁極優化(End pole optimization) 40
3.1 前言 40
3.2 各顆塊材擄磁大小相同下的末端磁極優化 40
3.2.1 HTSBSU週期數為5，裁切塊材尺寸 40
3.2.2 HTSBSU週期數為5，移動塊材位置 46
3.3 各顆塊材擄磁大小不相同下的末端磁極優化 49
3.3.1 HTSBSU週期數為5，改變末端四顆塊材的臨界電流密度Jc 49
3.3.2 HTSBSU週期數為5，改變末端六顆塊材的臨界電流密度Jc
，最末端兩顆塊材尺寸縮小並移動位置 51
3.4 討論 53
3.4.1 不同溫度和不同磁化狀態之下的末端磁極設計 55
3.4.2 改變間隙(gap) 62
3.4.3 增加週期數目 69
3.5 結論 74

4 低溫系統腔體設計 76
4.1 前言 76
4.2 熱分析 83
4.3 降溫結果與討論 86
4.4 結論 88

5 HTSBSU實驗與塊材篩選 89
5.1 塊材篩選 89
5.1.1 塊材篩選設備與步驟 90
5.1.2 塊材篩選結果 92
5.2 HTSBSU實驗設備 97
5.2.1 磁化系統和測量系統 100
5.2.2 低溫系統和測量系統 104
5.3 HTSBSU實驗步驟和注意事項 105
5.4 HTSBSU末端磁極優化實驗 107
5.4.1 77 K磁化飽和的結果與討論 107
5.4.1.1 FC和ZFC結果 131
5.4.1.2 LN2和Cryocooler結果 132
5.4.2 77 K磁化未飽和的結果與討論 133
5.4.2.1 一次場積分和二次場積分結果 140
5.4.2.2 FC和ZFC結果 143
5.4.3 7 K磁化未飽和的結果與討論 144
5.5 討論 148
5.5.1 各局部峰值磁場值的相對差距 148
5.5.2 溫度影響各局部峰值磁場值的大小和相對差距 149
5.5.3 聚頻磁鐵內塊材的磁化方向影響擄磁場大小 150
5.6 結論 152

6 結論 154
6.1 總結 154
6.2 建議和改善 157
6.3 未來展望 159

參考文獻 160

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