介電質微波加熱之特性探討: 極化電荷之屏蔽效應與微波共振現象

An Investigation on Microwave Dielectric Heating: Polarization charge shielding Effect and Microwave Resonance Phenomenon

陳冠文(Kuan-Wen Chen)

指導教授 ： 朱國瑞

國立臺灣大學/理學院/物理學研究所/碩士(2019年)

https://doi.org/10.6342/NTU201900802

摘要

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。

關鍵字

介電質微波加熱 ； 極化電荷 ； 屏蔽效應 ； 複變數借電常數 ； 介電質耗損 ； 漢姆霍茲方程式 ； 拉普拉斯方程式 ； 平面波 ； 均勻靜電場 ； 常波長極限 ； 介電質電磁共振腔

並列摘要

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.

並列關鍵字

Dielectric microwave heating ； Polarization charge ； Shielding effect ； Complex permittivity ； Dielectric loss ； Helmholtz equation ； Laplace equation ； Plane wave ； uniform static electric field ； Long-wavelength-limit ； Dielectric electromagnetic resonators

參考文獻

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