準線性理論與線性和弱非線性理論一起構成了等離子體波物理學的最基本理論，它們可以將粒子的平衡速度分佈函數的演變描述為波粒相互作用的結果。準線性理論描述的眾所周知的現象之一是顛簸不穩定性 (BOTI) 後的平台形成。儘管它在廣泛的等離子體物理學中很重要，但到目前為止，很少有實驗能夠清楚地驗證準線性理論。這一事實源於滿足準線性擴散要求的裝置的實驗實現中的一些困難。例如，對於 BOTI 設置，需要具有足夠強度的低能電子束（〜幾倍體電子溫度 T_e）。此外，具有令人滿意的分辨率的高頻靜電波測量和電子速度分佈函數（f_e（v））的測量對於驗證是必不可少的。這種缺乏實驗驗證的情況成為我們進行這項研究的動力。
本研究的目的是通過實驗驗證準線性理論。我們產生 BOTI 條件的想法是將低能電子束（~2-10T_e）注入目標磁化等離子體，其中 T_e 表示目標等離子體的電子溫度。對於我們的等離子體的 T_e ~ 5 eV-10 eV，光束能量應在 10 eV 至 100 eV 之間。為此，我們開發了一種低能電子束注入器。我們的射束噴射器由一個覆蓋有小外殼的燈絲和一個偏置電路組成。將射束注入器浸入目標等離子體中以在 f_e (v) 中產生一個凸起，其中 f_e (v) 是電子速度分佈函數。電子束的強度和能量是可控的。我們通過朗繆爾探針技術測量 f_e (v)。等離子體中的高頻靜電波由浸入等離子體中的高頻接收器（單極天線組）診斷。當注入電子束並在 f_e (v) 中產生凸塊時，我們觀察到高頻靜電波的激發。接收器測得的波的色散（ω-k）關係與朗繆爾波（LWs）的理論色散關係非常吻合。 LW的相速度和電子束的速度與考慮BOTI的準線性理論的預測一致。 f_e (v) 沿光束傳播方向（z 方向）的演變清楚地表明形成了一個速度略低於注入光束的平台，表明準線性理論的有效性。
總之，我們開發了一種用於驗證準線性理論的低能電子束注入器。測量 BOTI 後波粒相互作用的證據與準線性理論的預測一致。 BOTI 產生的波是 LW。另一個顯著的觀察結果是具有長空間相干性的激發 LW 的光譜展寬，表明 LW 超連續譜的產生，這已通過理論和數值模擬進行了預測。

Quasi-linear theory along with the linear and weak nonlinear theories constitutes the most fundamental theories of the plasma wave physics, which can describe evolution of the equilibrium velocity distribution functions of the particles as consequences of wave-particle interactions. One of the well-known phenomena described by the quasi-linear theory is a plateau formation after bump-on-tail instability (BOTI). Despite its importance in wide spectrum of the plasma physics, few experiments have exhibited clear verification of the quasi-linear theory until now. This fact stems from some difficulties in experimental realization of setups which meet requirements of the quasilinear diffusion. For example, for BOTI setting, low energy electron beams (~ a few times the bulk electron temperature T_e) having sufficient intensity are necessary. In addition, high frequency electrostatic wave measurement and measurement of electron velocity distribution function (f_e (v)) with satisfactory resolution are indispensable for the verification. This lack of the experimental verification becomes our motivation to this research.
The purpose of this research is verification of the quasi-linear theory by means of experiment. Our idea for producing a BOTI condition is to inject a low-energy electron beam (~ 2−10T_e) into target magnetized plasmas, where T_e denotes the electron temperature of target plasma. The beam energy should range between 10 eV to 100 eV for T_e ~ 5 eV−10 eV of our plasma. For the purpose, we have developed a low energy electron beam injector. Our beam injector consists of a filament covered with a small casing and a biasing circuit. The beam injector is immersed into the target plasma to produce a bump in f_e (v), where f_e (v) is electron velocity distribution function. The intensity and the energy of the electron beam are controllable. We measure f_e (v) by a Langmuir probe technique. High frequency electrostatic waves in the plasma are diagnosed by high frequency receivers (sets of monopole antennas) immersed into the plasma. We observed excitation of high frequency electrostatic waves when the electron beam was injected and a bump was created in f_e (v). The dispersion (ω-k) relation of the waves measured by the receivers shows a good agreement with the theoretical dispersion relation of Langmuir waves (LWs). The phase velocity of the LWs and the velocity of the electron beam is consistent with the prediction by quasi-linear theory considering BOTI. The evolution of f_e (v) along the beam propagation direction (z-direction) clearly demonstrates a formation of a plateau at the velocity slightly slower than that of the injected beam, indicating that validity of the quasilinear theory.
In summary, we developed a low energy electron beam injector for verification of the quasi-linear theory. Evidences of the wave-particle interaction after BOTI was measured consistent with the prediction of the quasi-linear theory. The waves generated by BOTI are LWs. Another remarkable observation is spectrum broadening of the excited LWs having long spatial coherence, indicating that generation of LW supercontinuum, which has been predicted by theory and a numerical simulation.

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