臺灣博碩士論文加值系統

，系統中的能量可以廣泛的分布到不同波長與頻率的波中。此時，系統所展現的波動現象不再是規律的週期震盪，而是呈現出高度不規則的運動狀態，同時，系統達到了一個高自由度且非平衡的紊流態。橫波的紊流態動力行為在不同系統中已充分的被發掘與研究，內容包括其波動的間歇性與碎形的動力行為研究；然而，縱波的紊流態動力行為卻很少被探討。
微粒電漿系統由微米大小的顆粒在弱游離的電漿中所組成，微粒因電漿中電子的高移動性而攜帶大量負電荷，使得系統成為一強耦合之多體系統。透過微粒的慣性力、屏蔽效應下的庫倫作用力、背景電漿的壓力與離子風所產生之不穩定性，此微粒電漿系統會自發地產生微粒電漿聲波，或稱微粒電漿疏密波。在這樣的系統中，聲波場將會影響微米粒子的運動，微米粒子本身亦是構成聲波的成份。藉由微粒與聲波的交互作用，即微粒縱向來回之震盪伴隨著週期性密度的變化，導致微粒聲波在時空中的傳遞。透過高速數位攝影機，微粒電漿聲波的研究可提供一個平台，用於了解疏密波(縱波)的微觀動力學行為。
在這個研究之中，我們透過精細的調控系統參數，首度觀測到微粒電漿聲波轉變至間歇性紊流態，並透過統計分析與利用其結構方程式，探討微粒電漿聲波與其他波動系統在紊流態下相同與相異之處。首先，我們觀察到隨著波從規律週期性的傳播轉變為紊流態，其時間中功率頻譜的分佈從窄的諧波往兩旁擴散，最後成為連續的冪次尺度分佈，驗證了此微粒電漿系統達到紊流態。在紊流態下，由於在波峰區間強大的壓縮現象與在波谷區間微粒數量的約束，因而導致波高呈現不對秤的非高斯分佈。此外，微粒電漿紊流波中存在著強烈且間歇性的突發波，這些短時間內生滅的突發波使短間隔的波高差呈現非高斯分佈，並破壞了原先自我相似性的規則。隨著時間間隔上升，波高差回到高斯分佈，導致系統擁有不同時間尺度下不同的冪次尺度率與多重碎形的特性。

Dusty plasma system composed of negatively charged micrometer sized dust particles in a low pressure laboratory discharge background is a nonlinear open dissipative system. The nonlinear dust acoustic wave with longitudinal dust oscillations can be self-excited by the free streaming energy of the vertical ion flow through the interplay of dust inertial and screened electric field. In this thesis, the direct observation of the transition from the coherent dust acoustic wave to the dust acoustic wave turbulence through optical video microscopy by decreasing neutral pressure is demonstrated. The mutlifractal scaling behaviors of the turbulent dynamics are investigated using structure function analysis.
When the nonlinearity increases, the irregular dust oscillations cause the broadening of the peaks in the power spectrum.The local dust density follows the power law scaling S(f) ~ f ^ -2.6 over a broad range showing the dynamical selection rule is found. The non-Gaussian histogram of wave height has higher degree of asymmetry than other transverse wave turbulences due to the strong compression in the crest region and the lower bound of dust particles in the trough region. Through the statistical analyses of the different moments of wave height increments, it is found that the intense bursts of the local dust density break the strict self-similar condition and cause the short time intermittent property. The scaling behaviors evolves from monoscaling into multiscaling. This work evidences that the acoustic type wave can also exhibit multifractal intermittent wave turbulence. It should be able to not only inspire future related theoretical works for dust acoustic wave turbulence, but also intrigue the readers in the dusty plasma, plasma, and turbulence communities.

1 Introduction 1
2 Background and theory 5
2.1 Wave turbulence 5
2.1.1 Resonant wave-ave interaction 5
2.1.2 Power spectrum 7
2.1.3 PDF of turbulent wave height 8
2.2 Intermittency 9
2.2.1 Fractal 10
2.2.2 High moment statistical analyses 11
2.3 Dust acoustic wave 13
2.3.1 Dusty plasma system 13
2.3.2 Dust acoustic wave 16
3 Experiment and data analysis 19
3.1 Experimental setup 19
3.2 Data analysis 22
4 Result and discussion 23
4.1 Transition from the coherent to the irregular DAW 24
4.2 Characteristics of DAWT 27
4.2.1 Power law scaling 27
4.2.2 Asymmetric distribution of local dust densities 31
4.3 Intermittency 32
4.3.1 Shape deformation with time interval 32
4.3.2 Identifying multiscaling nature through structure functions 35
5 Conclusion 40
Bibliography 42

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