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研究生： 蘇致皞
Su, Zhi-Hao
論文名稱： 採用二維動力學模擬在磁化等離子體中非線性蘭莫爾孤子之動態變化
Nonlinear Langmuir soliton dynamics in magnetized plasma employing two dimensional kinetic simulation
指導教授： 西村泰太郎
Yasutaro Nishimura
學位類別： 碩士
Master
系所名稱： 理學院 - 太空與電漿科學研究所
Institute of Space and Plasma Sciences
論文出版年： 2016
畢業學年度： 105
語文別： 英文
論文頁數： 78
中文關鍵詞： 蘭莫爾孤子 、札克洛夫方程式 、非線性薛丁格方程式 、粒子網格法(Particle-in-Cell ) 、波數頻譜 、迴轉運動 、E×B漂移
外文關鍵詞： Langmuir solitons, Zakharov equation, Nonlinear Schrödinger equation, Particle-in-Cell simulation, gyromotion, E×B drift
相關次數： 點閱：110  下載：2 
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    • 蘭莫爾孤子( Zakharov, 1972 )和蘭莫爾渦流利用數值模擬在二維周期邊界中探討已是廣泛研究的課題。此論文利用粒子網格法(Particle-in-Cell)來產生蘭莫爾孤子。此論文利用兩種方式產生蘭莫爾孤子，第一利用從札克洛夫和非線性薛丁格方程式得到質子密度、電場的一般解，並利用逆高斯定律來獲得電子密度。第二在勞倫茲力中加入額外射頻電場，此時透過頻率配對現象蘭莫爾波跟離子聲波可以非線性的配對在一起造成共振。透過共振替系統注入能量並產生非週期性的脈波結構，此為二維幾何中的蘭莫爾孤子。在二維或更高維的空間中，因為非線性項的影響超越了分散效應的影響，蘭莫爾孤子可以產生爆發(burn out)現象。詳細討論了在波數頻譜中的動力學變化。再者，透過加入背景均勻磁場到二維系統並觀測帶電粒子如何被迴轉運動跟E×B漂移影響。此影響減緩了爆發的現象並延長了蘭莫爾孤子的存在時限。

    Langmuir soliton ( Zakharov, 1972 ) and Langmuir turbulence in two dimensional periodic geometries are studied by numerical simulation. Particle-in-Cell (PIC) simulation method is employed to generate Langmuir solitons. First, a general solution for electric field and ion density from Zakharov equation and nonlinear Schrödinger equation are obtained, and inverse Gauss’s law is employed to obtain electron density as initial profile. Second, external pumping electric field in Lorentz force is employed. Langmuir waves and Ion-acoustic waves are nonlinearly coupled satisfying frequency matching condition. Through resonance, by pumping energy into system, nonperiodic pulse like structures are generated, that are solitons, are generated in two dimensional geometry. In two dimensional or three dimensional systems, solitons can burn out because the nonlinearity becomes dominant over dispersion effects. The dynamics in k-spectrum of electric field energy is revealed. Furthermore, background magnetic field is superimposed onto the two dimensional system to observe particles’ influence by gyromotion and E×B drift. The background magnetic effect disturbs the process of burn out and elongate the lifetime of solitons.

    摘要 1 Abstract 2 List of Figures 4 Chapter 1 Motivation and introduction of research 8 Chapter 2 Theoretical background of electrostatic plasma 11 2.1 Vlasov equation 11 2.2 Two dimensional sheath formation as a verification of PIC code 12 2.3 Derivation of Zakharov equation and Langmuir soliton solutions 13 2.4 Ponderomotive force 20 Chapter 3 Particle-in-Cell simulation method 22 3.1 Initial loading of particle position and velocity 23 3.2 Linear weighting and nearest grid point method to gather particle density 24 3.3 Solution of Poisson equation in 2D square geometry 26 3.4 Time advance particles’ motion 31 Chapter 4 Numerical simulation results in one dimensional and two dimensional geometries 33 4.1 Formation of sheath in two dimensional geometries 33 4.2 One dimensional solitons by employing analytical soliton solution as an initial profile 37 4.3 Two dimensional solitons by employing analytical soliton solution as an initial profile 44 4.4 Two dimensional plasma oscillation and upper hybrid wave 49 4.5.A Two dimensional soliton with external pumping electric field without magnetic field 52 4.5.B Two dimensional soliton with external pumping electric field and background magnetic field 66 Chapter 5 Summary and discussions 76 Reference 78

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