這項研究的目標是在實驗室等離子體實驗中產生朗繆爾波超連續譜（LWSC）。超連續譜（SC）生成的特徵是種子波通過與介質的非線性交互作用而出現劇烈的光譜展寬，如孤子分裂、自相位調制、拉曼散射和四波混頻（FWM）。這是因為具有有限振幅的朗繆爾波可以通過非線性薛定諤方程（NLSE）來描述，該方程也描述了傳統的光學超連續譜生成。朗繆爾波是等離子體中的靜電波，根據理論預測，它們可能會表現出超連續譜生成。然而，由於朗道阻尼和相位混合效應，實現實驗室朗繆爾波超連續譜一直具有挑戰性。本論文通過將電子束注入目標等離子體中以克服朗道阻尼，成功在實驗室等離子體實驗中產生了朗繆爾波超連續譜。
我們開發了一個低能量電子束注入器（約1.5-6 T_e，其中T_e是目標等離子體的電子溫度），以在我們的實驗室磁化等離子體中激發高頻（0.2～1 GHz）的靜電波。實驗結果展示了電子速度分佈函數的平台形成，並伴隨著朗繆爾波的生成，這與準線性理論的預測相符。電子速度分佈函數、色散關係和激發波的增長率的測量結果與理論預測一致，明確證明了尾凸（BOT）不穩定性的出現，並驗證了準線性理論。根據電子束能量和強度，觀察到了具有相干特性的激發波的光譜展寬。高相干光譜展寬與強電子束輸入相關，而低相干光譜展寬則表明存在朗繆爾波湍流（LWT）。
朗繆爾波的光譜展寬在其傳播過程中發生。隨著朗繆爾波功率的增加，伴隨著電子束功率的增加，波場沿著波傳播方向的相干性增加，同時增強四波混頻（FWM），這是朗繆爾波超連續譜生成的主要機制，表現出調制不穩定性。在電子束強度變化時，從低相干光譜展寬狀態（LWT）到高相干光譜拓寬狀態之間觀察到一種轉變。這個結果表明，朗繆爾波的功率是產生朗繆爾波超連續譜的關鍵因素。

The aim of this research is to generate Langmuir wave supercontinuum (LWSC) in a laboratory plasma experiment. Supercontinuum (SC) generation is characterized by the drastic spectral broadening of a seed wave through nonlinear interactions with the medium, exemplified by soliton fission, self-phase modulation, Raman scattering, and four-wave mixings (FWMs). This is motivated by the fact that LWs having finite amplitude can be described by the nonlinear Schrödinger equation (NLSE), which describes conventional optical SC generation as well. LWs, which are electrostatic waves in plasmas, are theoretically predicted to exhibit SC generation. However, the experimental realization of LWSC has been challenging due to Landau damping and phase mixing effects. This thesis addresses these challenges using electron beam injection into the target plasma to overcome Landau damping and successfully generate LWSC in the laboratory plasma experiment.
We developed a low-energy electron beam injector (~1.5-6 T_e, where T_e is the electron temperature of the target plasma) to excite high-frequency (0.2~1GHz) electrostatic waves in our laboratory magnetized plasmas. The experimental results exhibited the formation of a plateau of the electron velocity distribution function accompanied by the generation of Langmuir waves as predicted by the quasi-linear theory. Measurement results of the electron velocity distribution function, the dispersion relation and the growth rate of the excited waves agree with theoretical predictions, providing clear evidence of the occurrence of the bump-on-tail (BOT) instability and validation of the quasi-linear theory. Spectral broadening of the excited waves having coherent properties was observed depending on the beam energy and intensity. High coherence spectral broadening was associated with strong beam input, while low coherence spectral broadening indicated the presence of Langmuir wave turbulence (LWT).
The spectral broadening of LWs occurs as they propagate. As the power of LWs increases, accompanied by the increase in the power of the electron beam, the coherence of the wave field along the wave propagation direction increases in addition to the enhancement of FWMs, which are the indication of modulational instability, the main mechanism of the LWSC generation A transition between low coherence spectral broadening states (LWT) to high coherence spectral broadening states (LWSC) was observed when the intensity of the electron beam was varied. This result indicates that the power of LWs is a key factor for the generation of LWSC.

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[2] The Plasma Dispersion Function, Burton D. Fried and Samuel D. Conte (Academic Press, London 1961)