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系統識別號 U0026-1109201715262600
論文名稱(中文) 控制產生的伯恩斯坦–格林–克魯斯卡模式之波於實驗室電漿中
論文名稱(英文) Comtrolled Generation Bernstien-Greene-Kruskal Modes in Laboratory Plasma
校院名稱 成功大學
系所名稱(中) 太空與電漿科學研究所
系所名稱(英) Institute of Space and Plasma Sciences
學年度 105
學期 2
出版年 106
研究生(中文) 李宗懋
研究生(英文) Zong-Mau Lee
學號 LA6021080
學位類別 碩士
語文別 英文
論文頁數 71頁
口試委員 指導教授-河森榮一郎
口試委員-西村泰太郎
口試委員-藏滿康浩
中文關鍵字 BGK模式  非線性摸  蘭摩爾探針  馬赫探針  自動共振 
英文關鍵字 BGK modes  nonlinear waves  magnetized plasma experiment (MPX)  Langmuir probe  autoresonance  triple layer 
學科別分類
中文摘要 如蘭道在線性理論框架中所示,即使在無碰撞電漿,即使沒有相位混合也無法激發不衰減的靜電(ES)波。然而,伯恩斯坦、格林和克魯斯卡(BGK)在非線性範疇中得出靜電波在電漿中不衰減的可能性,且它是穩態弗拉索夫和泊松方程式的解。自BGK模式被發現後,BGK模式的研究已經超過五十年,包含理論、太空觀測、數值模擬和實驗室中的實驗。BGK模式已經被認為是無所不在的存在,雖然它的相位結構是脆弱的。這篇論文描述了我們嘗試用實驗室電漿良好控制的技術生成BGK模式。
我們進行了兩種實驗,以在線性磁化電漿裝置中產生高振幅和穩態靜電波。第一個實驗是通過利用自動共振機制產生相空間電子洞。自動共振是一種非線性現象,振盪器自動調節其振幅,以實現與外部激發器的鎖相。在我們的情況下,振盪器對應於磁鏡中的離子或電子,而激發氣器對應於外加電位源,其目的在於利用桶型電子洞激發電漿中的縱向靜電波。振盪外加電位施加在電漿的一端; 通過沿著場線的下游區域中具有高時間解析度的電位量測探針(emissive probe)監測等離子體的響應(空間電位)。在施加頻率啁啾(chirp)驅動時,觀察到具有負電勢的大振幅脈衝響應。在脈衝傳播期間,我們使用快速電壓掃描蘭摩爾探針觀察到小的相空間電子洞。然而,我們激發的電子洞尺寸不足以防止波衰減。一個可能的原因是電子約束時間短於外部驅動啁啾的持續時間,即生產桶型電子洞所需的時間。
第二個實驗是應用發散磁場在電漿中產生穩態衝擊波。我們發現具有三層(TL)結構電荷密度的強穩態衝擊波。我們從蘭摩爾探針和馬赫探針測量中獲得了電子和離子的相空間圖。TL結構伴隨著大量的電漿密度跳躍。用轉換方法(Druyvesteyn)從蘭摩爾探針測量獲得的電子相空間圖表明,在TL的電位坑中存在被捕獲的電子島,這與BGK圖像一致。發散磁場可能是產生TL的關鍵,這是從電漿中的變化磁場分佈的實驗結果推斷的。
英文摘要 As shown by Landau in a framework of linear theory, it seems considerably difficult to excite undamped electrostatic (ES) waves without suffering from phase-mixing even in collisionless plasmas. The solution of the Vlasov-Poisson equations obtained by Bernstein, Greene and Kruskal in 1957, which is so called BGK modes, is an answer to this question in the framework of the nonlinear theory. In fact, BGK modes have been observed in various circumstances such as in space, numerical simulation and laboratory plasmas. This master thesis describes our attempt at the generation of BGK modes with well-controlled techniques in laboratory plasmas.
We conducted two kinds of experiments to generate high amplitude and steady-state electrostatic waves in the linear magnetized plasma device, MPX. The first experiment is the generation of phase-space electron holes by utilization of the autoresonance mechanism. Autoresonance is a nonlinear phenomenon that an oscillator self-adjusts its amplitude for achieving phase locking with an external exciter [W. Bertsch et al., Phys. Rev. Lett., Vol.91, 265003 (2003)]. In our case, the oscillator corresponds to ions or electrons in a magnetic mirror, and the exciter corresponds to an external potential source, which aims at the excitation of longitudinal electrostatic waves in the plasma with bucket-electron holes. The oscillating external potential was applied at one end of the MPX plasma; responses (space potential) of the plasma were monitored by emissive probes with high temporal resolution in the downstream region along the field lines. A large amplitude pulsed response having a negative potential was observed during the application of the frequency-chirped drive. During the pulse propagation, we observed small phase-space electron holes with the use of a fast voltage scanning Langmuir probe. However, the hole size we excited was not large enough to prevent the wave decay. One possible reason is that electron confinement time was shorter than time duration of the external drive chirp, i.e., the time necessary for production of bucket-electron holes.
The second experiment is production of steady-state shock in MPX plasmas with the application of diverging magnetic fields. We discovered a strong steady–state strong shock (∆φ_s> T_e/e ) having a triple-layer (TL) of charge density, where ∆φ_s, Te and e are the potential depth, the electron temperature and elementary charge, respectively. We obtained the phase space diagram of the electrons and ions from the Langmuir probe and Mach probe measurements. The TL was accompanied a density jump by approximately on order. The electron phase space diagram obtained from LP measurement with the Druyvesteyn method indicates that trapped electron islands exist behind the potential dip of TL, which is consistent with a BGK picture. The diverging magnetic fields may be a key to produce the TL, which inferred from experimental results of the varied field profile of MPX plasma.
論文目次 摘要........................................I
Abstracts..................................III
List of Figures............................VIII
Chapter 1 Introduction......................1
1.1 History of research on BGK modes........1
1.2 Purposes of this research...............3
Chapter 2 Theory of BGK modes...............6
2.1 Description of Steady-state ES waves in collision-free plasma.................................6
2.2 Pseudo potential........................7
2.3 Energy Distribution function of charge particle of BGK modes...................................10
2.4 The example of preparation of BGK solution...11
2.5 Summary.................................12
Chapter 3 Magnetized Plasma eXperiment (MPX) devic.......................................14
3.1 Vacuum chamber and pumping system.......14
3.2 Magnetic coil system....................15
3.3 Data acquisition system.................16
3.4 Plasma Emitter-Hot cathode mode.........17
3.5 Electron cyclotron resonance (ECR) mode plasma......................................17
Chapter 4 Measurement of the phase space structure and electrostatic potential.....................18
4.1 Requirements for resolutions in measurements of propagating BGK modes and static shock structures..................................19
4.2 Potential measurement...................20
4.2.1 Emissive probe........................20
4.2.2 Principle of emissive probe...........21
4.2.3 Development of emissive probe.........23
4.2.4 Test of emissive probe................26
4.3 Velocity distribution of elections......29
4.3.1 Druyvesteyn method....................29
4.3.1.1 IV measurement of plasma............30
4.3.1.2 Energy distribution.................31
4.3.2 FVSLP- Measurement ideas of phase space measurement of BGK modes................................31
4.3.3 LPAz..................................32
4.4 Flow measurement of ions................34
4.4.2 Principle of Mach probe...............35
4.4.2 Correction mechanism of Mach probe....36
4.5 Summary of measurement..................37
Chapter 5 Autoresonance mechanism for exciting BGK modes.......................................38
5.1 Introductions...........................38
5.2 Set up..................................40
5.2 Behaves of ES Waves Excited in MPX Plasma through Autoresonance Mechanism.....................43
5.3 Phase Space Diagram.....................45
5.4 Discussion of results...................50
5.5 Summary.................................52
Chapter 6 Experiment of steady state shock formation in MPX plasma..................................53
6.1 Introduction............................53
6.2 Experiment of shock formation using diverging magnetic field and discovery of triple layer.......................................53
6.3 Phase Space Diagram of steady-state shock ............................................55
6.4 Control of shock profile................62
6.5 Summary.................................68
Chapter 7 Summary...........................69
Reference...................................71
參考文獻 [1] A. Vlasov, J. Phys., 9, 25 (1945).
[2]L. D. Landau, J. Phys. 10, 25 (1946)
[3]I. B. Berstein, J. M. Greene, and M. D. Kruskal, Phys. Rev. Lett. 108, 546 (1957).
[4]K.V Roberts and H. L. Berk, Phys. Rev. Lett. 19, 297 (1967).
[5] R. L. Morse and C. W. Nielson, Phys. Fluids. 12, 2418 (1969).
[6] H. Matsumo, et. Geophys. Rev. Lett., 21 2915 (1994).
[7] A. Mangeney, et. Ann. Geophysicae 17, 307 (1999).
[8] Giovanni Manfredi and Pierre Bertrand, Phys. Plasmas 7, 2425 (2000).
[9] K. Saeki, et. Phys. Rev. Lett. 42, 501 (1978).
[10] J.R. Danielson, et. Phys. Rev. Lett. 92 , 245003. (2004) .
[11] O'Neil, Phys. Fluids 8, 2255 (1965)
[12] W. Bertshe, J. Fajwns, and L. Friedland, Phys Rev Lett. 91, 265003 (2003).
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