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系統識別號 U0026-0102201612590100
論文名稱(中文) 利用速度空間量測系統實驗驗證二維迴旋動力學亂流中之熵串級
論文名稱(英文) Experimental Verification of Entropy Cascade in 2-D GyroKinetic Turbulence by Velocity-Space measurement
校院名稱 成功大學
系所名稱(中) 太空與電漿科學研究所
系所名稱(英) Institute of Space and Plasma Sciences
學年度 104
學期 1
出版年 105
研究生(中文) 陳勁廷
研究生(英文) Jin-Ting Chen
學號 LA6021098
學位類別 碩士
語文別 英文
論文頁數 71頁
口試委員 指導教授-河森 榮一郎
口試委員-西村 泰太郎
口試委員-曲宏宇
中文關鍵字 迴旋動力學  靜電亂流  磁化電漿  熵串級  尺度率  柯爾莫哥洛夫定理 
英文關鍵字 gyrokinetic  electrostatic turbulence  magnetized plasma experiment (MPX)  entropy cascade  scaling law  Kolmogorov’s law 
學科別分類
中文摘要 根據迴旋動力學的理論以及模擬,二維靜電亂流在弱碰撞的磁化電漿離子迴旋尺度下可視為熵在相空間的串級。 其中靜電位能微擾的波數空間頻譜尺度率已經被成功大學電漿實驗室在磁化電漿實驗中驗證出來,這些理論、模擬以及實驗接露了二維磁化電漿的柯爾莫哥洛夫類型的普遍性性質。 雖然磁化電漿實驗以及理論互相吻合但至今仍沒有證據證明二維靜電亂流中速度空間的柯爾莫哥洛夫熵串級。
而本研究的目地是利用速度空間量測系統實驗驗證二維迴旋動力學亂流中之熵串級,特別是透過實驗來檢驗速度空間結構的尺度率。 為此我們開發了一種新型量測速度空間分布結構的探針 ⎾環狀離子分布函數探針⏌。環狀離子分布函數探針是離子速度分析儀,藉由不同的離子拉莫爾半徑達到傳入離子的動量選擇。另一個關鍵想法是無效化環狀離子分布函數探針探頭的外體和等離子體之間的電位差(鞘),因為電位差會導致從純離子迴旋軌道的偏差。為達到電位差無效化,我們採用額外的電位控制系統控制探針探頭的外體電位。環狀離子分布函數探針系統由三個部分所組成一個探針探頭,電位控制系統和電流檢測電路,其中探針探頭經由二維離子軌道計算的數值程式碼(我們開發的)設計以及優化。最後的設計結果顯示在電位差0.1伏特之下我們的探針有足夠的能力去重建速度空間的分布並且誤差範圍在10%~16%。
在建構完整個環狀離子分布函數探針系統後,我們在磁化電漿實驗中使用這個新型探針並且量測離子電流數值和數值計算結果差異不大,另外我們也發現所蒐集到的離子電流有著2000赫茲的頻率的微擾存在,而這個頻率範圍差不多跟磁化電漿實驗中飄移波的頻率一樣。雖然我們並沒有在磁化電漿實驗中完成全部尺度的量測,但我們可以說環狀離子分布函數探針是一個強而有力的量測儀器並且已經準備好用於迴旋動力學亂流熵串級的調查。
英文摘要 Two-dimensional (2D) electrostatic turbulence in weakly-collisional magnetized plasma at ion gyro scales can be illustrated by cascades of entropy through phase space dynamics according to a theory and gyrokinetic simulations [A. A. Schekochihin, et al., Plasma Phys. Controlled Fusion Vol. 50, 124024 (2008). T. Tatsuno, et al., Phys. Rev. Lett. Vol. 103, 015003 (2009)]. The scaling law of wave number spectrum of electrostatic potential fluctuations E_∅ (k_⟘ ) ∝ k_⟘^(-10/3) deduce by the theory was verified in a subsequent laboratory experiment with the use of the magnetized plasma experiment (MPX) device at NCKU [E. Kawamori, Phys. Rev. Lett., Vol. 110, 095001 (2013)], where E_∅ and k_⟘ are the power spectrum of potential fluctuations and wave number, respectively. These theoretical, numerical and experimental results have revealed Kolmogorov-like universal property of 2D magnetized plasma gyrokinetic turbulences. Although the observations in MPX were consistent with those in the theory, there have been no experimental evidence to support the Kolmogorov type cascade in velocity space in 2-D electrostatic gyrokinetic turbulences, which is the central part of the theory.
One of the eventual goals of this research (thesis) is to experimentally verify the entropy cascade in 2D electrostatic turbulence of laboratory magnetized plasmas by means of velocity space structure measurement of ions. Specifically, we attempt to experimentally examine a scaling law of the velocity space structure predicted by the gyrokinetic entropy cascade theory E ̂_g (p) ~ p^(-4/3) in 2-D electrostatic turbulences in MPX, where E ̂_g (p) and p are power spectrum of fluctuation of g(v) (g(v) : the ion distribution function at a fixed guiding center) and wavenumber in the velocity space.
To this end, we have developed a novel diagnostic instrument of g(v), which is named as ring ion distribution function probe (RIDF probe). RIDF probe is an ion velocity analyzer, which achieves momentum selection of incoming ions by selection of the ion Lamor radii. Another key idea applied to the RIDF probe is nullification of a potential drop (sheath) between the body of RIDF probe and a target plasma, which causes deviation of ion orbits from the pure ions gyro orbit. To that end, we employ an external control of potential of the chassis of the RIDF probe with a feedback system using a space potential measurement with an emissive probe. The RIDF probe consist of three parts, a sensor head, the potential control system and current detection circuits. The sensor head of RIDF probe was designed through particle orbit calculations with the numerical code, we have developed from scratch. Specifically, by particle orbit calculations, (a) dimensions of the sensor heads, (b) the number of velocity channels and (c) dimensions of the ion collectors were determined under some physical constraints. Also we optimized the other details such as detailed positions of the collectors and so on from the results of the calculations. The final design of sensor head has ability of reconstructing ion velocity distribution function with an error of 10%~16% if the potential difference between the probe body and the space potential of the target plasma is controlled within 0.1V. The typical ion current detected by RIDF probe ranges between 10pA~100pA.
We constructed two sensor heads based on the numerical calculation, a multichannel small current detection system and the potential control system. After the completion of the RIDF probe development, we applied the RIDF probe to MPX to measure fluctuation of ring averaged ion distribution. We have confirmed that the amplitude of ion current signals in the RIDF probe measurement was consistent with our particle orbit calculation results. As a preliminary result, we observed fluctuation in the ion current in RIDF probe measurement, whose frequency~ 2 kHz, was consistent with the drift wave frequency range of the MPX plasma.
Although we have not yet initiated a full scale measurement of velocity structures of ions in MPX, it can be said that a powerful diagnostic tool of the 2D gyrokinetic turbulence is almost ready for investigation of entropy cascade in gyrokinetic turbulences.
論文目次 摘要.....................................................Ⅰ Abstracts.................................................Ⅲ
致謝......................................................Ⅵ
Constant .................................................Ⅶ
List of Figure............................................Ⅹ
Chapter 1 Introduction....................................1
1.1 What turbulence is................................1
1.2 Turbulence studies in plasma research.............3
1.3 Purpose of this research..........................6
Chapter 2 Magnetized Plasma eXperiment (MPX) device.......7
2.1 Vacuum chamber and pumping system...................8
2.2 Magnet system.......................................8
2.2.1 Pick coils....................................9
2.3 Langmuir Probe (LP).................................9
2.4 Data acquisition system............................10
2.5 Plasma Emitter-Hot cathode mode....................11
2.6 Electron cyclotron resonance (ECR) mode plasma.....12
Chapter 3 Chapter 3 Theoretical description of entropy cascade in the framework of gyrokinetic theory...........13
3.1 Introduction of GyroKinetic theory.................13
3.2 Derivation of gyrokinetic equation.................14
3.3 Nonlinear phase-mixing.............................18
3.4 Scaling law of gyrokinetic turbulences.............18
3.5 Summary of derivation of gyrokinetic...............20
Chapter 4 Design of ring ion distribution function probe (RIDFP)..................................................21
4.1 Basic idea of ring ion distribution function probe (RIDFP)..................................................21
4.1.1 Actual configuration of RIDF probe...........22
4.1.1.1 Sensor head..........................23
4.1.1.2 Current detection circuit............24
4.1.1.3 Potential control circuit............24
4.2 Procedure of measurement and analysis for obtaining spectrum in the physical and velocity spaces.............25
4.3 Basic idea of ring ion distribution function probe (RIDFP)..................................................26
4.4 Two-dimensional particle orbit calculation for the design of RIDF probe.....................................27
4.5 Validity check of simulation code....................35
4.6 Calculationresult for an appropriate sensor configuration design.....................................38
4.6.1 Investigation of calculation parameters......38
4.6.2 Investigation of parameters of RIDF probe....42
4.7 Summary of calculations work.......................49
Chapter 5 Development of ring ion distribution function probe (RIDFP) system.....................................50
5.1 Design of detection circuit of ring ion distribution function probe (IDFP) system.............................50
5.2 Development of RIDF probe sensor...................52
5.3 Development of Detection circuit and its validity check....................................................53
5.3.1 Current Voltage converter....................53
5.3.2 Validity check of Current Voltage converter..54
5.4 Development of potential control circuit and its validity check...........................................56
5.4.1 Buffer amplifier.............................56
5.4.2 Model of potential control system by circuit simulation...............................................56
5.4.3 Validity check of potential control circuit..57
5.5 Summary of development of ring ion distribution function probe (RIDFP) system............................59
Chapter 6 Application of Ring Ion Distribution Function probe to MPX.............................................60
6.1 Experimental setup of RIDFP system and the MPX device...................................................60
6.2 First test of RIDFP in the MPX.....................61
6.3 Discussion of First test of RIDFP in the MPX.......67
6.4 Summary of MPX.....................................67
Chapter 7 Summary........................................69
Reference................................................71
參考文獻 [1] A.N. Kolmogorov, Dokl. Akad. Nauk SSSR 30, 301(1941); 31, 538(1941).
[2] Steve Cowley, Gyro-Kinetic Lectures.
[3]AstroGK Manual, http://newton.physics.uiowa.edu/~ghowes/astrogk/source
/agk_manual.pdf
[4] A. A. Schekochihin, S. C. Cowley, W. Dorland, G. W.Hammett, G. G. Howes, G. G. Plunk, E. Quataert, and T.Tatsuno, Plasma Phys. Controlled Fusion 50, 124024 (2008).
[5] T. Tatsuno, W. Dorland, A. A. Schekochihin, G. G. Plunk,M. Barnes, S. C. Cowley, and G. G. Howes, Phys. Rev.Lett. 103, 015003 (2009).
[6] T. Tatsuno, M. Barnes, S. C. Cowley, W. Dorland, G. G.Howes, R. Numata, G. G. Plunk, and A. A. Schekochihin,J. Plasma Fusion Res. Ser. 9, 509 (2010).
[7] G. G. Plunk, S. C. Cowley, A. A. Schekochihin, T. Tatsuno, Plasma Phys.
[8] R.H. Kraichnan, Phys. Fluid 10, 1417 (1967).
[9] S.D. Bale, P.J. Kellogg, F.S. Mozer, T.S. Horbury, and H. Reme, Phys. Rev. Lett. 94, 215002 (2005).
[10] J. M. Beall, Y. C. Kim, and E. J. Powers, J. Appl. Phys. 53,
3933 (1982).
[11] H. Xia and M.G Shats, Phy. Rev. Lett. 91,155001 (2003).
[12] E. Kawamori, Phys. Rev. Lett., 110, 095001 (2013).
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