臺灣博碩士論文加值系統

為實驗驗證在迴旋動力學的理論及模擬結果中的柯爾摩哥洛夫類型的尺度率，我們設計了一系列的量測系統，並欲從得到此尺度率，驗證電漿亂流在迴旋動力學中的普遍性。其中靜電位能擾動的波數相空間的頻譜尺度率，已被國立成功大學 河森榮一郎教授在磁化電漿實驗中驗證。但在二維速度空間中的熵串級，至今仍未被驗證，故此為我們研究的目標，並利用設系之量測系統驗證之。
此研究的目標量測物理量為擾動離子迴旋的速度分佈，為量測此物理量，我們開發了新型的離子軌道篩選量測系統，被稱之為⎾環狀離子分布函數探針⏌，並經由數值模擬計算，得出最適合的結構尺寸。此探針利用不同的離子迴旋半徑，進而塞選出不同的離子速度的分佈。在平衡狀態下的速度分佈數值模擬計算，先前已被設計出來，計算結果為在電漿及量測探針電位差在0.15伏特內，可量測到的誤差範圍在10%~16%。為更貼近計算量測擾動條件下的分佈，我們設計了擾動速度分佈數值模擬計算，藉由不同的速度模數P,去探討原先平衡分佈設計之探針的重建分佈的能力，此計算結果得出，在電漿及量測探針電位差在0.025伏特內及模數4以內，可量測到的誤差範圍在35%。為防止電漿及量測探針間的電位差，我們設計了的電位控制系統，此系統於實驗測中，可維持電位差在0.02伏特以內，因此我們將利用此系統搭配環狀離子分布函數探針於磁化電漿實驗中。
經由完整的設計及建構後，我們應用此量測系統於磁化電漿中。從量測結果中，平衡速度分佈，大約坐落於馬克斯威爾分佈在離子溫度為0.4eV的條件下。速度分佈中的擾動項，在實驗中被認為是低頻的擾動，大約坐落於 1.4 kHz,此頻率被我們認定為是磁化電漿中激發出漂移波頻率。再者利用量測到的擾動的速度分佈做速度空間中的二維傅立葉轉換，我們得到此速度分佈的速度空間中的波數頻譜，此頻譜呈現出在高模數的的情況下，產生了明顯的擾動，此擾動結果與理論及模擬結果不符。從量測數據中，可看出雜訊比例相當高，而這些雜訊的產生，是非預期的電流電壓轉換器及磁場的電源供應器間的交互作用。故研究如何濾掉雜訊，已成為此研究必要的議題。

This research aims at experimentally verifying an entropy cascade in two-dimensional (2D) electrostatic turbulence of laboratory magnetized plasmas by measurement of velocity space structure of the ions, that is considered as universal nature of 2D electrostatic plasma turbulence. Specifically, evaluation of a scaling law E ̂_g (p) ~ p^(-4/3) deduced from a dimensional analysis with the gyrokinetic equations [A. A. Schekochihin, et al., Plasma Phys. Controlled Fusion Vol. 50, 124024 (2008). T. Tatsuno, et al., Phys. Rev. Lett. Vol. 103, 015003 (2009)] is set as a goal, where E_g and p are the power spectrum of fluctuation of g(v_⊥) (g(v_⊥) : ring averaged distribution function of ions at a fixed guiding center position, v_⊥: the velocity component perpendicular to the background magnetic field) and the wavenumber (mode number) in the velocity space, respectively. This scaling law is akin to the Kolmogorov scaling law in three-dimensional turbulence of neutral fluids, which is well-known as an evidence indicating existence of universality in turbulence.
To this end, we have developed a novel diagnostic tool of g(v_⊥) named as ring-averaged ion distribution function probe (RIDFP), which achieves momentum selection of incoming ions by selection of the ion Lamor radii. Through the use of a numerical ion orbit calculation code, we evaluated accuracy of the g(v_⊥) reconstruction by the developed RIDFP. The calculation results indicate that if we can suppress the potential difference ∆ϕ between the body of RIDFP and the target plasma, that is the sheath potential, lower than 0.025V, the velocity mode number p up to 4 can be identified with the error of 35%.
To nullify the sheath potential surrounding RIDFP, we have developed the potential control system of the RIDFP body, which consist of a voltage follower and an emissive probe, through the use of a circuit simulation. After the design of potential control system, we constructed this system, and test it in a bench test and laboratory test. From the test results, it is confirmed that the potential control system has a capability of maintaining the ∆ϕ lower than 0.015V. This is an acceptable range comparing with the calculation results.
After the completion of the developments, we applied the RIDFPs to magnetized plasma experiments in the MPX device. The equilibrium g(v_⟘) measured by the RIDFPs was roughly in accordance with the Maxwellian distribution having T_i=0.4eV. Perturbation components of g(v_⟘) in this experiment indicated low frequency fluctuations at 1.4kHz, which was considered to stem from the drift waves excited in the MPX plasma. A preliminary result of evaluation of the spectrum E ̂_g (p) was obtained from the RIDFP measurements, which showed a significant fluctuation at the high mode number p region unlike the theoretical prediction by Schekochihin et al. The noise induced by an unexpected interaction between the current detection circuits of the RIDFP system and the power supplies for the background magnetic field considerably contaminated the measured spectra of g(v_⊥ ). Further improvement of the signal to noise ratio in the RIDFP measurement is necessary.

摘要................................................................................................................... I
Abstracts……………………………………………………………………... III
致謝………………………………………………………………………….. IV
Content………………………………………………………………………. VI
List of Figures……………………………………………………………….. IX
Chapter 1 Introduction…………………………………………………………. 1
1.1 Turbulence……………………………………………………………… 1
1.2 Previous studies of plasma turbulence………………………………….. 4
1.3 Purpose of this research……………………………………………….... 6
Chapter 2 Theoretical description of entropy cascade in the gyrokinetic theory..8
2.1 Introduction of gyrokinetic theory………………………………………. 8
2.2 Derivation of gyrokinetic equation……………………………………… 9
2.3 Nonlinear phase-mixing……………………………………………….. 14
2.4 Derivation of scaling laws in gyrokinetic turbulences………………… 15
2.5 Summary of Chapter 2………………………………………………… 18
Chapter 3 Magnetized Plasma eXperiment (MPX) device…………………… 19
3.1 Vacuum chamber and pumping system………………………………… 20
3.2 Magnet system…………………………………………………………. 20
3.3 Langmuir Probe (LP)…………………………………………………... 21
3.4 Emissive probe (EP)…………………………………………………… 22
3.5 Data acquisition system………………………………………………... 24
3.6 Plasma Emitter-Hot cathode mode…………………………………….. 25
3.7 Electron cyclotron resonance (ECR) mode plasma……………………. 25
Chapter 4 Design of Ring Ion Distribution Function Probe (RIDFP) by numerical particle orbit calculation……………………………………………………… 26
4.1 Basic idea of Ring Ion Distribution Function Probe (RIDFP)…………. 26
4.1.1 Actual configuration of RIDFP……………………………………. 27
4.1.1.1 Sensor head…………………………………………………… 28
4.1.1.2 Current detection circuit……………………………………… 29
4.1.1.3 Potential control circuit………………………………………. 29
4.2 Procedure of measurement and analysis for obtaining spectrum in the
physical and velocity spaces…………………………………………… 30
4.3 Required specification of RIDFP………………………………………. 31
4.4 Two-dimensional numerical particle orbit calculation for the design of RIDFP…………………………………………………………………. 32
4.4.1 Calculation of potential distribution use of Gauss-Seidel method… 34
4.4.2 Preparation of ions following distribution functions including fluctuation components…………………………………………... 35
4.4.3 Electric field evaluation by interpolation method…………………. 36
4.4.4 Calculation of particle motion by using fourth-order Runge-Kutta method………………………………………………………….… 36
4.5 Evaluation of velocity resolution of RIDFP………………………….… 40
4.5.1 Resolution test of RIDFP at different ion temperatures…………… 40
4.5.2 Evaluation of reconstruction error of the ring-averaged ion distribution function containing fluctuations……………………... 43
4.6 Summary of Chapter 4…………………………………………………. 48
Chapter 5 Development of ring ion distribution function probe (RIDFP)
system………………………………………………………………………... 49
5.1 Development of RIDFP sensor………………………………………… 51
5.2 Development of detection circuit and its frequency response test……... 52
5.3 Development of potential controller and its validity check…………….. 54
5.3.1 The configuration of the potential controller and its validity test by means of circuit simulations……………………………………….. 54
5.3.2 Circuit simulation for emulation of the real plasma experiment…... 56
5.3.3 Validity check of potential controller circuit……………………… 57
5.3.4 Validity check of potential controller system in MPX…………….. 59
5.4 Summary of Chapter 5…………………………………………………. 60
Chapter 6 Application of Ring Ion Distribution Function Probe (RIDFP) in Magnetized Plasma eXperiment (MPX)……………………………………… 61
6.1 Experimental set-up of dual RIDFP system in MPX device…………… 61
6.2 Application of dual RIDFP in MPX…………………………………… 62
6.3 Discussion of full channels test of dual RIDFP in MPX………………. 71
6.4 Summary of Chapter 6…………………………………………………. 80
Chapter 7 Summary…………………………………………………………... 81
Reference…………………………………………………………………….. 83

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