伯恩斯坦，格林和克魯斯卡（BGK）模式是一種在非碰撞電漿中不會衰減的非線性靜電波，且他是穩態弗拉索夫和泊松方程式的解。自從BGK模式被發現並發表成論文後，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。這是因為BGK模式已經被認為無所不在地存在自然界中，雖然他的相位結構是脆弱的。本研究的目的是第一次直接量測BGK模式的相位分布圖 - 電子洞,藉由這個量測我們可以確認BGK模式在我們的磁化電漿中被成功創造與否。
我們的構思是將一根蘭摩爾探針固定在一個位置,並放入移動的BGK波中去量測它的相位分布圖，而BGK波是由自動共振機制所產生的。一根快速掃頻的蘭摩爾探針需要夠高的時間解析度去覆蓋整個相位構造。
為了完成這項量測,我們設計一個快速掃頻的蘭摩爾探針包含了兩個電流電壓轉換器和一個插分放大器,這個系統是為了消除在高頻時產生的寄生電容。在完成這項設計後,我們將它應用在磁化電漿實驗中的BGK波,結果顯示出沒有清楚的電子洞相位構造圖,可能的原因是電子約束時間比製造BGK波的時間短。在未來我們將改善製造BGK波的頻率和延展電子的約束時間來製造出電子洞。

Bernstein, Greene and Kruskal (BGK) modes are nonlinear electrostatic undamped waves in collisionless plasmas, which are exact solutions of the steady state Vlasov-Poisson equations. Since the seminal paper by BGK, numerous studies have been conducted for sixty years in theory, space observations, numerical simulations and laboratory experiments. This is because waves that are considered BGK modes have been ubiquitously observed in nature (in space) regardless of its seemingly fragile structure in phase space. A target of this study is the first direct measurement of phase space structures f (x,v) of the phase space electron hole, that is a type of BGK modes in laboratory magnetized plasmas, where f, x and v represent the electron distribution function, coordinates of the physical space and the velocity space, respectively.
Our idea to achieve the target is to apply a voltage-sweeping Langmuir probe (LP) at a fixed position into propagating periodic BGK modes having electron hole structures in the phase space, which are generated by a chirped-frequency drive. A fast voltage sweep of the LP enables to cover the phase space with a satisfactory time resolution. f (x,v) is obtained by Druyveteyn method with a digital differentiation of current-voltage curves measured by LP.
For this purpose, we designed a fast voltage sweep LP (FVSLP) which consists of two probe channels including a dummy channel and a differential amplifier. The dummy channel is employed for cancellation of the stray current induced by the fast voltage sweep. After the development of the FVSLP, we applied it to plasma experiments on electron-hole excitations with the use of the autoresonance technique in the magnetized plasma experiment (MPX) device. The results of the FVSLP measurement in the BGK mode-excitation experiment in MPX indicated no clear evidence of emergence of a hole structure in the electron phase space during propagating of a pulse train of the excited waves. One possible reason is that electron confinement time was shorter than the time duration of the external drive chirp, i.e., the time necessary for production of bucket-electron holes. In near future, we improve the situation by increase in the chirp rate of the external drive and extension of the confinement time for generating BGK modes.

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