本研究建立了電壓源驅動變壓器耦合環形放電電漿源—2D TCTD voltage source coil model，同時考慮到流場的影響，建立了有進出氣口的電壓源驅動的變壓器耦合環形放電電漿源－2D TCTD voltage source coil (flow) model，並探究電漿特性，以及不同線圈電壓對於電漿特性的影響。
在2D TCTD voltage source coil model中，在氣壓為2 Torr，線圈電壓1200 V下，達到穩態時，氫氣電漿密度約為7.84×1017 m-3，電漿的吸收功率為65.75 kW/m。模擬結果顯示，線圈電壓從1000V增大到1600V，電漿吸收功率提高1.1倍，電子密度提高1.5倍。
在2D TCTD voltage source coil (flow) model中，探討了加入流場對電漿特性的影響。在氣壓為2 Torr，線圈電壓1200 V下，達到穩態時，電子密度為5.9×1017 m-3，相較於2D TCTD voltage source coil model，在相同線圈電壓下，穩態時電子密度下降2 ×1017 m-3。電漿達到穩態後，分布與2D TCTD voltage source coil model相同，都為環狀分布。達到穩態時，電漿吸收功率為56.75 kW/m，電漿吸收功率佔全部功率的45%。模擬結果顯示，線圈電壓從1000V增大到3000V，出氣口H原子流量增大5.2倍。
模擬結果顯示，電漿可以順利點燃並達到穩態，主電漿區滿足準電中性條件，在腔體中呈現環狀分布，符合預期。另外，線圈的終端和接地端之間有電壓差，形成電容性阻抗，因此，系統阻抗在低電壓的情況下為電容性。增大線圈電壓，腔體中的電漿密度增加，電漿區產生感應電流和感應電場，模型系統的阻抗會從電容性轉換為電感性。

In this study, a voltage source-driven transformer-coupled toroidal discharge plasma source-2D TCTD voltage source coil model is built, and a voltage source-driven transformer-coupled toroidal discharge plasma source-2D TCTD voltage source coil (flow) model with inlet and outlet is developed, and investigate the plasma characteristics of these two models and the effect of different coil voltages on the plasma characteristics.
In the 2D TCTD voltage source coil model, the hydrogen plasma density is about 7.84×1017 m-3 and the absorbed power of the plasma is 65.75 kW/m at a steady state of 2 Torr and 1200 V. The simulation results show that the plasma absorbed power increases by 1.1 times and the electron density increases by 1.5 times when the coil voltage increases from 1000 V to 1600 V.
In the 2D TCTD voltage source coil (flow) model, the effect of adding a flow field on the plasma characteristics was investigated. The electron density at steady state is 5.9 × 1017 m-3 at 2 Torr and 1200 V coil voltage, compared with the 2D TCTD voltage source coil model, the electron density at steady state decreases by 2 × 1017 m-3 at the same coil voltage. the distribution is the same as that of the 2D TCTD voltage source coil model. At steady state, the absorbed power of the plasma is 56.75 kW/m, and absorbed power of the plasma accounts for 45% of the total power. The simulation results show that the coil voltage increases from 1000 V to 3000 V, and the H-atom flux at the outlet increases by 5.2 times.
The simulation results show that the plasma can be ignited and reach a stable state, and the main plasma region meets the quasi-electrically neutral condition with a ring-like distribution in the cavity as expected. In addition, there is a voltage potential difference between the terminal of the coil and the ground, forming a capacitive impedance, so the impedance is capacitive at low voltages. By increasing the coil voltage, the plasma density in the cavity increases, and the inductive current and field are generated in the plasma area, and the impedance of the model changes from capacitive to inductive.

[1] K. N. Kim, J. H. Lim, J. K. Park, J. T. Lim, and G. Y. Yeom, "Characteristics of Plasma Using a Ferromagnetic Enhanced Inductively Coupled Plasma Source," Japanese Journal of Applied Physics, vol. 47, no. 9, pp. 7339-7342, 2008.
[2] V. Godyak, "Ferromagnetic enhanced inductive plasma sources," Journal of Physics D: Applied Physics, vol. 46, no. 28, 2013.
[3] I. M. Ulanov, M. V. Isupov, and A. Y. Litvintsev, "Experimental study of transformer-coupled toroidal discharge in mercury vapour," Journal of Physics D: Applied Physics, vol. 40, no. 15, 2007.
[4] S. Rauf, A. Balakrishna, Z. Chen, and K. Collins, "Model for a transformer-coupled toroidal plasma source," Journal of Applied Physics, vol. 111, no. 2, 2012.
[5] J. J. Han, A. Abliz, and D. Wan, "<p>Impact of hydrogen plasma treatment on the electrical performances of ZnO thin-film transistors & nbsp;</p>," Chinese Journal of Physics, vol. 77, pp. 327-334, Jun 2022.
[6] Y. X. Zheng, J. Lapano, G. B. Rayner, and R. Engel-Herbert, "Native oxide removal from Ge surfaces by hydrogen plasma," Journal of Vacuum Science & Technology A, vol. 36, no. 3, May 2018, Art. no. 031306.
[7] V. I. Kolobov and V. A. Godyak, "Inductively coupled plasmas at low driving frequencies," Plasma Sources Science and Technology, vol. 26, no. 7, 2017.
[8] 張晏榕, "鐵磁增強電感耦合電漿放電數值模擬計算分析,"碩士, 工程與系統科學系, 國立清華大學, 新竹市, 2019
[9] 周子傑, "變壓器耦合環形電漿源數值模擬計算分析."碩士, 工程與系統科學系, 國立清華大學, 新竹市, 2020
[10] R. S. Brokaw, "Predicting Transport Properties of Dilute Gases," pp. p. 240–253, 1969.
[11] P. Colpo, T. Meziani, and F. Rossi, "Inductively coupled plasmas: Optimizing the inductive-coupling efficiency for large-area source design," Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films, vol. 23, no. 2, pp. 270-277, 2005.
[12] G. J. M. Hagelaar, "Modeling Of Microdischarges for Display Technology," 2000.
[13] L. I. Stiel and G. Thodos, "The Viscosity of Polar Substances in the Dense Gaseous and Liquid Regions," AIChE Journal, 1964.
[12] "http://www.lxcat.net."
[13] K. Hassouni, S. Farhat, and C. D. Scott, M. A. Prelas, G. Popovici, and L. K. Bigelow, Eds. Handbook of Industrial Diamond and Diamond Films. New York: Marcel Dekker, Inc, 1998.
[14] K. Hassouni, T. A. Grotjohn, and A. Gicquel, "Self-consistent microwave field and plasma discharge simulations for a moderate pressure hydrogen discharge reactor," Journal of Applied Physics, Article vol. 86, no. 1, pp. 134-151, Jul 1999.
[15] R. K. Janev, W. D. Langer, J. K. Evans, and D. E. Prost, Elementary Processes in Hydrogen-Helium Plasmas. Berlin: Springer, 1987.
[16] "www.quantemoldb.com."