葉超雄Yeh, Chau-Shioung臺灣大學:應用力學研究所鄭怡芬Cheng, Yi-FenYi-FenCheng2010-06-022018-06-292010-06-022018-06-292008U0001-2103200813353000http://ntur.lib.ntu.edu.tw//handle/246246/184706依據先前學者們對半空間電漿介質的研究，發現幾乎沒有研究採用無因次化法來討論擾動磁場對非相對論性且非等向性電漿頻率產生的物理特性變化效應。此發現推動我們設想如何採用無因次化方法去分析出在巨觀尺度下，經由推導非相對論性下非等向性時電漿的無因次化特徵頻散曲線關係，而得到前述結果。 經由基本方程式推導與無因次化處理，我們定義出一組處理電磁理論的無因次化參數，我們解出存在於介質內不同型態的磁性擾動源對非相對論性且非等向性電漿頻率產生的物理特性變化效應；接下來，我們將磁性擾動源改置於介質外部，利用電漿物質本身特性與天線理論概念近似解出對應的瞬間無因次化頻散曲線，以及電漿頻率變化特徵，並且不需運用複雜的微分幾何處理。 結論，我們得到部分情形下電漿介質頻率擾動與外部磁場擾動的關係式；並提及無因次化參數於整體數學模型所扮演的角色，歸類出許多由控制方程式所推演出不同條件下的簡化模式，可對於不同假設條件下的問題提出可參考的簡單解析與預測；對於電漿內部存在不同的化學組成時，則可以運用改變推演式中的參數，令其符合不同的組成特徵密度函數，而修正出所要的介質頻率擾動與外部磁場擾動的關係式；最後提及尺度應用方面，在這裡所推展的函數與方程式，經由無因次化所得的結果，理論上可以超越尺度的限制，大到結構長度相對遠大於激源波長，如高頻電磁波、光波、微波，小至毫微米、次毫微米電磁波，皆可大膽運用，唯獨運用於微觀尺度時，例如核融合電漿，在擾動尺度接近或小於7個德拜長度，於量子尺度範圍內，則此模式不能完全套用，必須引入量子力學概念；另外，應用於微連體力學分析或微流體生物力學分析時，必須考量其他假設條件，引入其他控制方程式，才能修正出較為合理的對應模式。 未來，我們可以配合數值模擬、實驗設計，提出修正參數，進一步將理論推展並延伸此套理論於其他物理電漿相關應用、微奈米尺度工業設計與控制、跨尺度力學系統建制等相關的研中。According to the previous studies, a large number of the half-space plasma research have been made. But it is little to know about that the relation between the characteristic frequency of plasma and the change of the mangetic field. This key point drives us to the question to develop this thesis. From the nondimensional fundamental equations, the non-dimensionalized parameters for the electromagnetic fields and the magneto-hydrodynamics have been made. Then, the fundamental solutions to the inner field perturbation for the plasma half-space have been showed in chapter 3. We solve the relation between the characteristic frequency of plasma and the perturbed mangetic fields from the non-dimensional dispersion equations. In Chapter 4 , we obtain the similar relation between the frequency and the magnetic field when we move the excitation out off the medium instantaneously. By doing the further discussion, the roles of the non-dimensional parameters in the whole model are indicated. The last subtopic which we also discuss in the thesis is the role of the density variable in the medium and the usable range. The minimum usable range is . And it is the threshold limit value (TLV) of the quasi-neutrality in the plasma medium. In conclusion, this mathematical and physical model can figure out the different micro-nano effects on the manufacture procedures or other research with proper parameters revised. By supplying the relation between the characteristic frequency of the plasma and the perturbed magnetic fields, this research will set the further steps in the future studies. And it can be used on the other application, such as the experiments or numerical simulations.Contents of Thesiscknowledgement…………………………………………………………ibstract & Keywords in Chinese…………………………………..vbstract & Keywords in English……………………………………….viiontents of Thesis………………………………………………………..ixontents of Figures……………………………………………………xiiontents of Tables………………………………………….…………xvih1 Introduction………………………………………………………….1.1 Preview and Motivation…………………...………………………1.2 Focus of the research ….…...……………..………………………2.3 Previous studies……………………………...……………………4h2 Fundamental Equations and Non-dimensional Method…………8.1 Fundamental Definitions………….……………………………8.2 Governing Equations………...…………………………………10.3 Non-dimensional Method…………………..……………………13.3.1 Non-dimensional Parameters for MHD………….…………13.3.2 Non-dimensional Parametersfor Electromagnetic Fields………………………………...16.3.3 Non-dimensional form of the Governing Equations…….…17h3 Fundamental Solutions -- Inner field Disturbance & Plasma Characteristic Frequency……………...………………………….22.1 Solution Induced By Basic Fundamental Disturbance.………….22.2 Solutions Induced By Inner Field Disturbance.………………..30h4 Solutions Induced By Outer Fields Disturbance…………………36.1 Fundamental Definitions: Magnetic Dipoles……………….……36.2 Solution From The Vertical Field Disturbance.……...…………..41.3 Solution From The Transverse Field Disturbance…….…………45h5 Discussion -- Characteristic Frequency of Plamsand Other Physical Properties……………...……..48.1 Relation between Perturbed Magnetic Fieldnd Characteristic Frequency of Plasma…………………………48.2 Dispersion equation and curves…………………………………58.3 Non-dimensional Parameters………………………………….62.4 Other Applications……………………………………………….63h6 Conclusion and Future Works…………………………………..67.1 Conclusions………………..…………………………………….67.2 Future Works…………………………………………………….71eference………………………………………………………………ref-1h1………………………………………………………………..ref-1h2………………………………………………………………..ref-4h3………………………………………………………………..ref-5h4………………………………………………………………..ref-6ppendices………………………………………………………….…A-1. The physical constants and formulae……………………………A-1. Tables…………………………….………………………….…B-1. Figures……………………………………………………….…C-1. Dispersion Equations & Analytic Solutions of the Inner Field Excitation – 3.2 & 3.3 Derivations……………D-1. Dispersion Equations & Analytic Solutions of he Outer Field Excitation – Sections 4.1 ~ 4.3 Derivations…...E-1ppendix Reference…………………………………………App.ref-1ontents of Figuresigure 2.1 Closed contour C and surface S associated with Faraday’s law …………………………………….……….…………..……………C-1igure 2.3 Fields, currents, and surface charge at a general interface between two media …………………….…………………………...…...C-1igure 2.2 Arbitrary volume, surface, and line currents.……….…C-2igure 3.1 General geometry of half-space plasma medium…....C-3igure 3.2 General geometry of half-space plasma medium with the boundary ………………………………………………………………...C-3igure 4.1 Electrical potential function and its source vector in general form ………………………………………..…………………………..C-4igure 4.2 Image in a infinity ground plane (a) magnetic current element perpendicular to the ground plane……………...…………...…………...C-4igure 4.2 Image in a infinity ground plane (b) magnetic current element parallel to the ground plane ……………………..…………………...….C-5igure 5.1.A The disturbed plasma frequency of (3-38) vs. the different wave number of the disturbed magnetic field under different permittivity ratios………………………..…………………...…… ……C-6igure 5.1.B The disturbed plasma frequency of (3-38) vs. the different frequency of the disturbed magnetic field under the different permittivity ratios ……………….......…………....…………………..…C-7igure 5.1.C The disturbed plasma frequency of (3-38) vs. the different structure lengthes under the different permittivity ratios …C-8igure 5.1.D The disturbed plasma frequency of (3-38) vs. the differnet under the different permittivity ratios……………….…C-9igure 5.1.E The disturbed plasma frequency of (3-38) vs. the differnet under the different permittivity ratios……………………C-10igure 5.1.F The disturbed plasma frequency of (3-38) vs. the different medium velocity under the different permittivity ratios.…C-11igure 5.2 The disturbed plasma frequency of (3-38), (3-46) , (3-47), (3-49), (3-51), (3-53), (3-54) vs. the differnet frequency of the disturbed magnetic fields when the permittivity ratio equals to 0.5…..C-12igure 5.3 The disturbed plasma frequency of (5-6) vs. the variation of plasma refraction index under the different permittivity ratios……………………………………………………………………C-13igure 5.4 the disturbed plasma frequency of (3-55), (4-54), (4-57), (4-65) vs. the different frequency of the disturbed mangetic fields when permittivity ratio equals to 0.5…………………………….…C-14igure 5.5 The disturbed plasma frequency of (4-54) vs. the different frequency of the disturbed mangetic fields when permittivity ratio equals to 0.5…………………………….......…………………….C-15igure 5.6 The disturbed plasma frequency of (4-57) vs. the different frequency of the disturbed mangetic fields when permittivity ratio equals to 0.5…………….........................................……………...C-16igure 5.7 The disturbed plasma frequency of (4-65) vs. the different frequency of the disturbed mangetic fields when permittivity ratio equals to 0.5………………………………………………………C-17igure 5.8 The diagram of the dispersion curve for (3-32) under different permittivity ratios………………………………………………………C-18igure 5.9 The diagram of the dispersion curve for (3-35) under different permittivity ratios………………………………………………………C-19igure 5.10 The diagram of the dispersion curve for (5-1) & (5-2) under different permittivity ratios……………………………………………..C-20igure 5.11 The diagram of the dispersion curve for (5-3) under different permittivity ratios………………………………………………………C-21igure 5.12 The diagram of the dispersion curve for (5-4) & (5-5) under different permittivity ratios……………………………………………C-22igure 5.13 The diagram of the dispersion curve for (5-6) under different permittivity ratios………………………………………………………C-23igure 5.14 The diagram of the dispersion curve for (5-1), (5-7), and (5-8) under permittivity ratio equals to 0.1…………………………………..C-24igure 5.15 The diagram of the dispersion curve for (4-46), (4-49), (4-63) under permittivity ratio equals to 0.5…………………………………..C-25ontents of TablesableA.1 Physical constants………………………………………A-1able 1.2 The parameters for different units of plasma…….……...B-1able 2.1 Primary dimensions and associated SI units………………B-1able 2.2 Dimensions of physical parameters………………………...B-2able 2.3 Magneto-fluid-dynamic parameters……………………...B-3able 2.4 Dimensions of the m.k.s.a. units……………….……..B-3application/pdf2147174 bytesapplication/pdfen-US非相對論性非等向性半空間電漿介質無因次化參數頻散曲線電漿特有頻率擾動磁場Non-relativeAnisotropicHalf-space plasmaNon-dimensional parametersDispersion curvePlasma frequencyPerturbed magnetic fieldsthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/184706/1/ntu-97-R95543002-1.pdf