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姓名 鄧力文(Lee-Wen Teng) 查詢紙本館藏 畢業系所 物理學系 論文名稱 非線性微粒聲波的相空間動力行為
(Phase Space Dynamics of Nonlinear Dust Acoustic Wave)相關論文 檔案 [Endnote RIS 格式]
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摘要(中) 自然界中，波的非線性成長與波破碎是流體中常見的現象。例如風吹水面，興起的水波波振幅會持續增長終至破碎；然而這類非線性行為並不只是發生在橫波上，亦可於縱波中被觀測。在電漿中，當電漿波（疏密波）以雷射產生後，波從高電漿密度往低電漿密度區運動時，電漿波之波強度將非線性提升，在此過程中更生成高速電子，第二協振和X-射線，此結果被提議作為電子加速器。因此，電漿波破碎行為在雷射電漿尾跡場加速器中，佔有高度的重要性。儘管波破碎在物理學上是重要的議題，實驗上，仍未有這類波破碎行為的微觀研究。也就是說，是甚麼原因促成波動系統從波成長轉變為波破碎，就我們所知這類問題至今仍未有答案。
直到我們利用微粒電漿系統，藉由觀測微粒在自發微粒聲波場中的高速震盪行為，才從其中得到了明確的解答。在實驗上，我們首先在電漿中生成微粒庫侖液體，微粒庫侖液體由於受到離子風(ion wind)的拖曳力(drag force)加速，藉由調降系統壓力，在系統耗散被降低的情況下，微粒聲波能夠自發地產生，在這樣的系統中不僅聲波場影響了微粒的運動，微粒本身亦是密度波的一部分。在觀測上我們輔以高速數位攝影機深入探討波形隨時空的變化，波的運動及與波相互作用的微粒的關聯。
研究的目標在於回答以下的問題：（1）微粒的運動如何構成密度波波振幅的成長？（2）微粒的運動做了甚麼樣的轉變，造成密度波從成長變成波破碎？（3）波破碎後，聲波場對微粒的運動有甚麼影響？實驗結果顯示，如果微粒在空間中震盪的振幅或是不同微粒震盪的相位差被提升，則聲波振幅被提升。但是若過度提升微粒運動的振幅或相位差，使得微粒和微粒彼此在空間上的拓墣關係（微粒震盪軌跡交錯）被改變，則改變的瞬間即是波破碎的開始。另外，聲波波前在被壓縮的同時會加熱微粒，使微粒的震盪變紊亂，而變紊亂則會阻礙之前提及的波震幅成長。最後，我們發現波破碎後，波加熱微粒並產生高速微粒，而這樣的行為可在微粒的相空間分布圖上被清楚地看見。
摘要(英) The nonlinear growth and breaking of waves in nature are fundamental phenomena. For example, the waveform of growing waves driven by the strong wind on the water surface will steepens and breaks finally. These nonlinear phenomena not only occur in transverse waves but also in longitudinal waves. In plasmas, the electron plasma wave generated by a pulse laser grows nonlinearly as it propagates from higher plasma density region to low plasma density region. As the electron plasma wave breaks, higher order harmonics, X-ray emission and fast electrons are generated. Therefore, the wave breaking which is applied to accelerate electrons by laser wake field in plasmas is an important issue. However, to our knowledge, the experimental study of wave breaking in microscopic discrete level is not conducted. Namely, the micro-origin that causes the changing of growing waves to breaking waves is still a mystery.
The dust acoustic wave propagates in dusty plasmas composed of negatively charged micro-meter dust particles can be observed directly through a high speed CCD camera (sampling rate = 500 Hz). By tracking the motion of dusts which oscillate in the dust acoustic wave field, the particle-wave dynamics and the micro-origin of wave breaking are investigated. In the experiment, the dust particles introduced to the plasma are charged negatively due to the higher electron mobility. The dust particles suspended in the vicinity of the bottom electrode are confined by the electric field of a hollow cylindrical glass cell. The floating dust particles driven by the downward ion flow line up vertically and form a dust Coulomb liquid. The ion stream also provides a free energy source to spontaneously excite the dust acoustic wave. In the system, the dust acoustic wave field affects the dust particle motion which constitutes the waveform evolution of the dust acoustic wave. The main subjects of this work are answering the following questions: (1) How the wave field affects the particle motion? (2) How the particle motion constitutes the wave propagation and growing. (3) What is the microscopic origin of the breaking of growing waves.
In order to find out the answers, the waveform evolution and the corresponding particle motion are analyzed. It is found that the dust acoustic wave amplitude grows as the dust oscillation amplitude or the inter-dust phase lag is increased. However, the wave onsets breaking as the inter-dust topological relation is changed during the increasing of dust oscillation amplitude/ inter-dust phase lag. On the other hand, the growing wave also heats up the dust particles and causes chaotic dust motion. The chaotic motion opposes the growing trend of dust acoustic wave. Finally, it is found that, after wave breaking, the wave also generates fast particles. The corresponding fast particles, wave heating phenomena can be clearly observed in phase space.
關鍵字(中) ★ 相空間動力學
★ 波破碎關鍵字(英) ★ wave breaking
★ nonlinear growth
★ phase space dynamics論文目次 Contents
1. Introduction 1
2. Background and theory 6
2.1 Dusty Plasma System...…………………………………….…...6
2.2 Dust Acoustic Wave……………………………………….….…8
2.2.1 History……………………………………………….……8
2.2.2 Previous study of dust acoustic wave……………….…….9
2.2.3 Instabilities in dust acoustic waves……………..…….…...9
2.2.4 Microscopic study of dust acoustic wave…………….…..11
2.3 Wave breaking…………………………………………….…….13
2.3.1 Longitudinal wave breaking………………………….…...13
2.3.2 Transverse wave breaking…………………………….…...15
3 Experimental Methods 17
3.1 Experimental setup……………………………………………...18
3.2 Analysis Methods………………………………………………..20
4 Result and Discussion 23
4.1 DAW Waveform evolution……………….……………………...24
4.2 Particle motion-
breaking induced dust heating and liquid-to-gas transition…….27
4.3 Micro-origin of wave breaking…………………………….…....31
4.4 Phase space dynamics of the DAW:
corkscrew distribution and resonant dust crest trapping…….....36
4.5 Wave induced anisotropic motion and heating..…………………39
4.6 Summary of nonlinear wave breaking…………………………...43
5. Conclusion 47
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