介電質微波加熱是個歷史悠久的研究議題，其應用也出現在許多研究領域中。以加熱均勻性、加熱效率、熱點、微波化學合成技術與害蟲防治等為探討主題的論文更是不計其數。然而，就我們目前所知，關於極化電荷屏蔽效應的討論卻是罕見於文獻資料中。

在本文中，我們首先以在均勻靜電場中的介電質物體這個物理問題介紹即化電荷屏蔽效應。接著，我們考慮平面波入射介電質物體作為微波加熱的簡化模型。利用變數分離法來解析解出圓球與圓柱坐標系的漢姆霍茲方程式。本文依照此方程式的標準解法，但為求完整性，我們列出各個步驟。當電磁波波長遠大於物體尺寸時，極化電荷屏蔽效應將大幅降低物體內電場大小。此外，若考慮細長型的介電質，物體主軸的方向會對屏蔽效應有極大的影響。在最後一章，我們探討微波共振效應，此效應發生於波長略等於物體尺寸時。

Dielectric heating by microwave has been studied for a long period and its applications are widely used in a variety of research fields. There are a plenty of papers discussing about the uniformity of heating, heating rate, hotspot, microwave synthesis, pest control, etc. However, best to our knowledge, it seems that the shielding effect of polarization charges have been overlooked.

In this thesis, we first introduce the shielding effect of polarization charges by reviewing the problem of dielectric objects immersed in static uniform E-field. Next, we focus on the problem of dielectric objects hit by uniform plane waves which serves as a simplified model of microwave dielectric heating; solve the Helmholtz equations with separation of variables in spherical and cylindrical coordinates. The procedure of solving the Helmholtz equations is standard, but for completeness we point out the steps. We find out that when the wavelength is much longer than the geometry size of the object, shielding effects take place. And for elongate objects, orientations of objects have a great influence on polarization charge shielding. When wavelength has the same order as the size of the object, microwave resonance phenomenon will occur.

致謝 i
中文摘要 ii
Abstract iii
Contents iv
List of Figures vi
List of Tables viii
Chapter 1 Introduction -1
1.1 Microwave Dielectric Heating -1
1.2 Penetration Depth -2
1.3 Polarization Charges Shielding Effect -3
1.4 Dielectric Objects with High Permittivity as Resonant Cavities -6
Chapter 2 Static Cases: Analytical Analysis -7
2.1 A Dielectric Sphere Immersed in a Uniform Electric Field -7
2.2 A Dielectric Cylinder with Infinite Length Immersed in a Uniform Electric Field -9
2.3 Comparison between the Two Cases -11
Chapter 3 Dielectric Objects with simple geometry hit by plane waves: Analytical Analysis -13
3.1 Dielectric Sphere -13
3.2 Dielectric Cylinder with Infinite Length -17
Chapter 4 Long-Wavelength-Limit: Demonstration of Polarization Charges Shielding Effect -21
4.1 Dielectric Sphere -21
4.2 Dielectric Cylinder with Infinite Length -24
4.3 Microwave Heating on Water Spheres: Observation of the Shielding Effect of Polarization Charge -26
4.4 Microwave Heating on Water Cylinder: The Orientation Effect -28
Chapter 5 Dielectric Electromagnetic Resonators -31
5.1 Resonant Modes of Water Spheres Excited by 2.45 GHz Plane Wave -31
5.2 Spectral Responses and Quality Factors -33
Appendix A Detailed derivation of equations in chapter 3 -35
A.1 Evaluation of fields components from vector potentials: Sphere -35
A.2 Find the coefficients bn, cn, dn, and en satisfying the boundary conditions: Sphere -39
A.3 Find the coefficients an and cn satisfying the boundary conditions of TM mode: Cylinder -40
A.4 Find the coefficients bn and dn satisfying the boundary conditions of TE mode: Cylinder -41
Appendix B Detailed derivation of equations in chapter 1 -43
B.1 Penetration depth -43
Appendix C Special thanks -45
REFERENCE -46

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