本研究使用磁性流體力學(Magnetohydrodynamics；MHD)模式來模擬在兩個無窮遠之電極板間，環境為低壓、高氣體密度及低電離率，其瞬間給定一偏壓電位條件下之氬氣(Argon：Ar)電漿的非穩態二維空間之輸送變數。近年來電漿已被廣泛且有效地運用在各種材料加工製造、薄膜製造、核融合發電、光源、蝕刻等；電漿性質更是物理、化學、光電、航空太空、工程科技等熱門之研究範疇，所以電漿輸送現象的研究變得極為重要。本研究將考慮電場及磁場效應、黏滯力效應、以及離子電子及中性粒子動量交換之間的碰撞效應。本模擬之計算結果將顯示極板在瞬間給定負值之直流偏壓電位條件下，電子、離子及中性粒子通過鞘層到達工作表面的密度、速度、電位、溫度、磁場、黏滯係數及熱傳導係數，以及其邊界層和鞘層厚度之增長情形。利用理論與模擬之比較將可以深入瞭解電漿在工作表面之行為。

This study uses the Magnetohydrodynamics (MHD) method to simulate unsteady two-dimensional transport variables in argon (Ar) plasma, under low pressure, high density, and weak ionization between two infinite planar electrodes suddenly biased by a negative voltage. Plasma has been widely used in materials processing, thin film manufacturing, light source, nuclear fusion, and etching, etc. Properties of plasmas are also becoming important area for research in physics, chemistry, photonics, aerospace, engineering science and technology. Studying transport processes of plasmas therefore is important. This research consider by electric fields and magnetic fields, viscous, momentum exchange collisions between electrons ions and neutral particles. The computed results in this work quantitatively show density, velocity, electric potential, temperature, magnetic field, viscosity, thermal conductivity of the electrons ions and neutral particles across the sheath to the surfaces suddenly biased by a DC negative voltage. And increase of the boundary layer and sheath thickness. We can compare the theory and the simulation to know the behavior of the plasma near a surface.

誌謝 i
中文摘要 ii
英文摘要 iii
目錄 iv
圖次 vi
符號說明 viii
第一章 緒論 1
1.1 研究背景與目的 1
1.2 磁性流體力學模擬方法簡介 4
1.3 本論文研究內容簡介 5
1.4 本文架構 5
第二章 理論分析與方法 6
2.1 系統模型與基本假設之條件 6
2.2 統御方程式 7
2.2.1 質量守恆方程式 7
2.2.2 動量守恆方程式 10
2.2.3 能量守恆方程式 18
2.2.4 Maxwell方程式 21
2.3 無因次化 25
2.4 無因次之參數與統御方程式 26
2.4.1 無因次參數 26
2.4.2 無因次質量守恆方程式 28
2.4.3 無因次動量守恆方程式 29
2.4.4 無因次能量守恆方程式 31
2.4.5 無因次Maxwell方程式 33
2.5 研究與模擬之流程圖 34
第三章 研究結果與討論 35
3.1 電位傳遞及影響 35
3.2 震盪影響 37
3.3 密度變化 41
3.4 速度變化 44
3.5 溫度變化 49
3.6 鞘層 52
3.7 動量邊界層 53
3.8 熱邊界層 54
第四章 結論 55
參考文獻 56

[1] F.F. Chen, Introduction to Plasma Physics and Controlled Fusion. New York and London: Plenum Press, second edition, 1983.
[2] L. Tonks and I. Langmuir, “A general theory of the plasma of an Arc,” Phys. Rev. , Vol. 34, pp. 876 - 922, 1929.
[3] D. Bohm, The Characteristics of Electrical Discharges in Magnetic Fields, A. Guthrie and R.K. Wakerling, Eds. New York and London: McGraw-Hill, 1949.
[4] R.N. Franklin, “The plasma-sheath boundary region,” J. Phys. D: Appl. Phys., vol. 36, pp. 309 - 320, 2003.
[5] R.N. Franklin, “Where is the ‘sheath edge’ ?,” J. Phys. D: Appl. Phys., vol. 37, pp. 1342 - 1345, 2004.
[6] K.-U. Riemann, “Kinetic theory of the plasma sheath transition in a weakly ionized plasma,” Physics of Fluids, vol. 24, pp. 2163 - 2172, 1981.
[7] K.-U. Riemann, “The plasma sheath transition of a weakly ionized plasma with reflecting walls,” Proc. XVIIth Int. Conf. on Phenomena in Ionized Gases, Budapest, pp. 519 - 521, 1985.
[8] K.-U. Riemann, “The Bohm criterion and the field singularity at the sheath edge,” Physics of Fluids B, vol. 1, pp. 961 - 963, 1989.
[9] K.-U. Riemann, “The Bohm criterion and boundary conditions for a multicomponent system,” IEEE Transactions on Plasma Science, vol. 23, pp. 709 - 716, 1995.
[10] Anders, A., 2004, “Fundamentals of Pulsed Plasmas for Materials Processing,” Surface and Coating Technology, vol. 183, pp. 301 - 311.
[11] S.I. Braginskii, 1965, Review of Plasma Physics, vol. 1(ed. M.A. Leontovich) pp. 205 - 311. Consultants Bureau, New York.
[12] Widner, M., Alexeff, I., Jone, W.D., and Lonngren, K.E., 1970, “Ion Acoustic Wave Excitation and Ion Sheath Evolution,” Physics of Fluids, vol. 13, pp. 2532 - 2540.
[13] Lieberman, M.A., 1989, “Model of Plasma Immersion Ion Implantation,” J. Applied Physics, vol. 66, pp. 2926 - 2929.
[14] Vahedi, V., Lieberman, M.A., Alves, M.V., Verboncoeur, J.P., and Birdsall, C.K., 1991, “A One-Dimensional Collisional Model for Plasma-Immersion Ion Implantation,” J. Applied Physics, vol. 69, pp. 2008 - 2014.
[15] Stewart, R.A., and Lieberman, M.A., 1991, “Mode of Plasma Immersion Ion Implantation for Voltage Pluses with Finite Rise and Fall Times,” J. Applied Physics, vol. 70, pp. 3481 - 3487.
[16] Riemann, K.-U. and Daube, Th., 1999, “Analytical Model of the Relaxation of a Collisionless Ion Matrix Sheath,” J. Applied Physics, vol. 86, pp. 1202 - 1207.
[17] Daube, Th., Meyer, P., Riemann, K.-U., and Schmitz, H., 2002, “Relaxation Phenomena in Pulsed Discharges,” J. Applied Physics, vol. 91, pp. 1787 - 1796.
[18] Riemann, K.-U., 1991, “The Bohm criterion and sheath formation,” J. Physics D: Applied Physics, vol. 24, pp. 493 - 518.
[19] Hsu, K.C., and Pfender, E., 1983, “Analysis of the Cathode Region of a Free-Burning High Intensity Argon Arc,” J. Applied Physics, vol. 54, pp. 3818 - 3824.
[20] Montierth, L.M., Neuman, W.A., and Morse, R.L., 1992, “Fluid Model Treatment of Surface Plasma Structures,” Physics of Fluids B, vol. 4, pp. 784 - 795.
[21] Scheuer, J.T. and Emmert, G.A., 1990, “A Fluid Treatment of the Plasma Presheath for Collisionless and Collisional Plasmas,” Physics of Fluids B, vol. 2, pp. 445 - 451.
[22] Stangeby, P.C., 2000, The Plasma Boundary of Magnetic Fusion Devices, Institute of Physics Publishing, Bristol, UK.
[23] Bissell, R.C., Johnson, P.C., and Stangeby, P.C., 1989, “A Review of Models for Collisionless One-Dimensional Plasma Flow to a Boundary,” Physics of Fluids B, vol. 1, pp.1133 - 1140.
[24] Hong, M.P., and Emmert, G.A., 1995, “Two-Dimensional Fluid Simulation of Expanding Plasma Sheaths,” J. Applied Physics, vol. 78, pp. 6967 - 6973.
[25] Sheridan, T.E. and Alport, M.J., 1994, “Two-dimensional Model of Ion Dynamics during Plasma Source Ion Implantation,” Applied Physics Lett, vol. 64, pp. 1783 - 1785.
[26] Kim, H.C., Iza, F., Yang, S.S., Radmilovi′c-Radjenovi′c, M., and Lee, J.K., 2005, “Particle and Fluid Simulations of Low-Temperature Plasma Discharges: Benchmarks and Kinetic Effects,” J. Physics D: Applied Physics, vol. 38, pp. R283 - R301.
[27] Wei, P.S, and Yeh, F.B.,2000, “Fluid-like Transport Variables in a Kinetic, Collisionless Plasma near a Surface with Ion and Electron Reflection,” IEEE Transactions on Plasma Science, vol. 28, pp. 1233 - 1243.