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系統識別號 U0026-0502201317490100
論文名稱(中文) 模擬Vlasov-Poisson高能電子效應
論文名稱(英文) Effects of high energy electrons on electrostatic Vlasov-Poisson simulation
校院名稱 成功大學
系所名稱(中) 太空天文與電漿科學研究所
系所名稱(英) Assistant, Institute of Space, Astrophysical and Plasma Sciences(ISAPS)
學年度 101
學期 1
出版年 102
研究生(中文) 陳岳紘
研究生(英文) Yue-Hung Chen
學號 LA6991073
學位類別 碩士
語文別 英文
論文頁數 53頁
口試委員 指導教授-西村泰太郎
口試委員-談永頤
口試委員-西田靖
口試委員-河森榮一郎
口試委員-陳秋榮
中文關鍵字 Vlasov 模擬  波-粒子交互作用  kappa分布函數  Langmuir孤立波 
英文關鍵字 Vlasov simulation  wave-particle interaction  kappa distribution function  Langmuir solitons 
學科別分類
中文摘要 為了調查高能粒子的生成機制和行為,我們選擇研究在Langmuir 孤立波加入速度分布函數。我們首先採用的是模擬同樣具有在位置空間和速度空間訊息的Vlasov方程式。在模擬Vlsov方程式的時候,我們使用的是在相空間維持穩定的splitting scheme。之後我們模擬了線性和非線性的Landau damping,並跟C. Z. Cheng 一九七六年的論文做對照。在典型的速度分布函數上通常都是Maxwellian分布,我們進一步的選擇了使用kappa分布來做考慮,並且觀察波和粒子的交互作用。要了解電子的 Langmuir 波跟離子聲波發生交互作用以後產生的Langmuir孤立波,我們選擇採用離子的Vlasov 方程式。 在初始狀態下,我們所使用的是流體方程式的Zaharov方程式。之後由Zakharov方程式可以得到一個非線性薛丁格方程式,並由這個方程式來決定孤立波的離子密度,(藉由泊松方程式求得)電子密度和電場分布。當電子的分布函數是Maxwellian分佈時,電子很明顯的在高能量的區域被加熱的情形。此外,在研究Langmuir孤立波的時候,我們也把電子的分布函數從Maxwellian分布改為kappa分布。由於kappa分布本來就有著比較多的高能量分布,因此在分布函數上的改變並沒有像Maxwellian分布那麼明顯。
英文摘要 To investigate the behavior of high-energy electrons and their generation mechanism, Langmuir soliton is studied incorporating the velocity distribution function. For the analysis, the Vlasov equation is employed which has the information in both x-space and v-space. In simulating Vlasov equation, we have employed the phase volume conserving splitting scheme. Linear and nonlinear Landau damping is benchmarked with C. Z. Cheng and G. Knorr paper (1976). On top of typical Maxwellian distribution in v-space, kappa dsitribution function is considered, and the wave-particle interaction (Landau damping) is investigated. The ion Vlasov equation is also employed to study Langmuir solitons which arise from the interaction between electron Langmuir waves and ion acoustic waves. For the initial condition, solutions of Zakharov (fluid) equation is employed. The Zakharov system reduces to the nonlinear Schrodinger equation, and this equation provides us with the ion density, electron density (via Poisson equation), and electric field for the soliton profiles. When electron distribution function is Maxwellian distribution, the electrons' high energy tail are heated significantly. Furthermore, the electron distribution is changed from Maxwellian to kappa distribution in the Langmuir soliton study. Due to the kappa distribution's large high energy tail, it demonstrated that the change in the electrons' distribution function is not as prominent as in the Maxwellian case.
論文目次 摘要 1
Abstract 2
誌謝 3
Contents 4
List of Table 6
List of Figures 7
Chapter 1 Introduction 9
Chapter 2 Simulation model 11
2.1 Normalized Vlasov and Poisson equation 11
2.2 Splitting Scheme 12
Chapter 3 Comparison with analytical solution in free streaming (E=0) case 15
3.1 Numerical results for free streaming case 15
Chapter 4 Benchmark calculation of linear Landau damping 17
4.1 Derivation of Langmuir wave dispersion relation and the mechanism of Landau damping 17
4.2 Field solvers for self-consistent simulation 20
4.3 Linear Benchmark with Cheng and Knorr 21
Chapter 5 Nonlinear Landau damping 23
5.1 The difference between linear and nonlinear simulation 23
5.2 Numerical results for nonlinear Landau damping 23
Chapter 6 Effect of kappa function on Landau damping 26
6.1 What is kappa function? 26
6.2 Numerical results with kappa distribution function 26
Chapter 7 Electron heating by Langmuir Soliton 30
7.1 Soliton as a paradigm of nonlinear wave 30
7.2 Derivation of Zakharov equations for Langmuir soliton 30
7.3 Zakharov soliton as an initial condition 34
7.4 Langmuir soliton interactions with kappa distribution function 41
Chapter 8 Summary and Future work 44
References 46
Appendix 49
A. Fourier interpolation 49
B. Ponderomotive force 50
C. Fokker-Plank equation in velocity space 52
參考文獻 Bezzerides B., & Dubois D. F.(1975).Electron heating and Landau damping in intense localized electric fields. Phys. Rev. Lett. 34, 1381.

Chateau, Y.F.,& N. Meyer-Vernet (1991).Electrostatic noise in non Maxwellian plasmas: generic properties and kappa distributions. J. Geophys. Res. 96.

Chen, Y. H., Nishimura, Y., & Cheng, C. Z. (2012). Effect of kappa distribution function on Landau damping in electrostatic Vlasov simulation. To be published in Terrestrial, Atmospheric and Oceanic Sciences.

Cheng, C. Z., & Knorr, G. (1976).Integration of Vlasov equation in configuration space. J. Comput. Phys. 22, 330-351.

Fried, B. D., & S. D. Conte (1961). The Plasma Dispersion Function, Academic Press, 1pp.

Gorev, V.V., & Kingsep, A. S. (1974). Interaction of Langmuir solitions with plasma particles. Sov. Phys. JETP 39, 1008-1011.

Hamming, R.W. (1987). Numerical methods for scientist and engineer, Dover Pubns, 515pp.

Jackson, J. D. (1960). Longitudinal plasma oscillations. J. Nuclear Energy, Part C 1, 171-189.

Kim, C. H. (1974). Development of Cavitons and Trapping of rf Fields. Phys. Rev. Lett. 33, 886-889.

Landau, L. D. (1946). On the vibration of the electronic plasma. J. Phys. (U.S.S.R) 10, 25.

Leubner, M. P. (2004). Fundamental issues on kappa-distributions in space plasmas and interplanetary proton distributions. Phys. Plasmas 11, 1308-1316.

Li, C. H., Chao J. K., & Cheng, C. Z. (1995). One-dimensional Vlasov simulation of Langmuir solitons. Phys. Plasmas 2, 4195.

Morales, G. J., & Lee, Y. C.(1974). Effect of localized electric fields on the evolution of the velocity distribution function. Phys. Rev. Lett. 33, 1534.

Nicholson, D. R. (1992). Introduction to Plasma Theory 2nd ed, Krieger Publishing, 82 pp. and 120 pp.

Pereira, N. R., Sudan, R. N., & Denavit, J. (1977). Numerical simulations of one-dimensional solitons. Phys. Fluids 20, 271.

Ruth, R. D. (1983). A canonical integration technique. IEEE Transactions on Nuclear Science 30, 2669-2671.

Summers, D., & Thorne, R. M. (1991). The modified plasma dispersion function. Phys. Fluids B 3, 1835-1847.

Thorne, R. M., & Summers, D. (1991). Landau damping in space plasmas. Phys. Fluids B 3, 2117-2123.

Tsallis, C., & Stat, J. (1988). Possible generalization of Boltzmann-Gibbs statistics. Phys. 52, 479-487.

Van Kampen, N. G. (1955).On the theory of stationary waves in plasmas. Physic 21, 949-943.

Vasyliun, V.M. (1968). A survey of low-energy electrons in evening sector of magnetosphere with OGO 1 and OGO 3. J. Geophys. Res. 73, 2839-2884.

Wang, J. G., Pain G. L., Dubois D. F., & Rose H. A. (1994). One-dimensional simulation of Langmuir collapse in a radiation-driven plasma. Phys. Plasmas 1, 2531

Wang, J. G., Pain G. L., Dubois D. F., & Rose H. A. (1995). Vlasov simulation of modulational instability and Langmuir collapse. Phys. Plasmas 2, 1129

Wang, J. G., Pain G. L., Dubois D. F., & Rose H. A. (1996). Comparison of Zakharov simulation and open boundary Vlasov simulation of strong Langmuir turbulence. Phys. Plasmas 3, 111-121.

Zakharov, V. E. (1972). Collapse of Langmuir waves. Sov. Phys. JETP 35, 908-914.
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