磁旋返波震盪器是利用電子迴旋脈射機制(electron cyclotron maser)產生同調電磁波，並且利用電子與波的內部反饋迴路產生振盪，與傳統共振腔結構有所不同，因而具有連續可調的寬頻調頻特性，所以在研究以及實用上都有很大的發展潛力，但是由於非線性場型收縮的特性，能量轉換效率相對較低；操作在四次諧波可以讓軸向靜磁場只需原來的四分之一，大大降低實驗成本困難度，但高次諧波的效率不高，也造成起振電流較高，且又有其他諧波競爭，因此頻寬相對狹小；綜合以上，探討磁旋返波振盪器的效率的提升並且讓頻寬更加寬廣便是本篇論文的主題，並了解其結果背後的物理特性。
本文是以在400GHz頻段下，以後可以應用於MRI、ESR和蛋白質分析等等；選擇 ，並且使用幾乎設計好的CUSP電子槍，由其guiding-center position近乎於零的特性讓 的模式不會被起振，大大降低模式競爭；在線性程式模擬操作下，電子與電磁波不同的優化傳輸角造成不同的優化起振電流，也對應到特徵頻率和電子能量吸吐次數之不同的軸向模式；而在非線性程式模擬操作區間，因為電流的提高，造成場型逐漸往電子入口處集中，而形成效率或起振電流對長度的飽和現象。為了提升振盪器的效率以及頻寬，我們針對波導管的幾何結構進行改變，並且也加入靜磁場的變化，以程式模擬優化效率及頻寬為最終目的。

Harmonic operation could alleviate the requirement of strong magnetic field which is the major difficulty for terahertz gyrotrons. This work presents a theoretical investigation of a 4th harmonic 400 GHz gyrotron backward-wave oscillator (gyro-BWO) with relatively high efficiency and broadening bandwidth. An axis-encircling electron beam is employed to suppress the mode competition. The operating mode is the TE41 mode. The efficiency and bandwidth are optimized for the magnetic field tuning. Simulations suggest that the 4th harmonic circuit is capable of achieving highest interaction efficiency and most broadening bandwidth.

[1] K. R. Chu, Rev. Mod. Phys. “The electron cyclotron maser”, 76, 489 (2004).
[2] K. R. Chu, H.Y. Chen, C.L. Hung et al. “Theory and experiment of ultrahigh-gain gyrotron traveling wave amplifier”, IEEE Trans Plasma Sci27:391-404 (1999).
[3] N. C. Chen, T. H. Chang*, C. P. Yuan, T. Idehara, and I. Ogawa, “Theoretical investigation of a high efficiency and broadband sub-terahertz gyrotron”, Appl. Phys. Lett. 96, 161501 (2010).
[4] C. H. Du, H. Lee, X. B. Qi, P. K. Liu*, and T. H. Chang*, “Theoretical Study of a Fourth-Harmonic 400-GHz Gyrotron Backward-Wave Oscillator”, IEEE Transactions on Electron Devices, 62(1), pp 207-212 (2015).
[5] C. S. Kou, C. H. Chen, and T. J. Wu, “Mechanisms of efficiency enhancement by a tapered waveguide in gyrotron backward wave oscillators”, Phys. Rev. E, vol. 57, no 6, pp. 7162-7168 (1998).
[6] C. S. Kou, and Fouries Tseng, “Linear Theory of Gyrotron Traveling Wave Tubes with Non-Uniform and Lossy Interaction Structures”, Phys. Plasmas 5, 2454-2462 (1998).
[7] C. L. Hung, T. H. Chang, and Y. S. Yeh, “Effects of tapering structures on the characteristics of a coaxial-waveguide gyrotron backward wave oscillator”, Phys. Plasma, vol. 18, 103113 (2011).
[8] K. R. Chu, “Analysis of a basic electron cyclotron maser model”, Journal of the Chinese Institute of Engineers 4.2 (1981): 85-90.
[9] A. T. Lin, “Mechanism of efficiency enhancement in gyrotron backward-wave oscillator via tapered axial magnetic field”, Appl. Phys. Lett., vol. 54, pp. 514-516 (1989).
[10] N. C. Chen, C. F. Yu, and T. H. Chang*, “A TE21 second harmonic gyrotron backward-wave oscillator with slotted structure”, Phys. Plasmas, 14, 123105 (2007).
[11] G. S. Nusinovich, and O. Dumbrajs, “Theory of gyro-backward wave oscillator with tapered magnetic field and waveguide cross section”, IEEE Trans. Plasma Sci., vol. 24, no. 3, pp. 620-629 (1996).
[12] T. H. Chang, C. H. Du, P. K. Liu, C. P. Yuan, S. J. Yu, and G. F. Liu, “A Magnetic Cusp Gun for Terahertz Gyro-Devices”, IEEE 978-1-4673-1597-5112 (2012).
[13] A. K. Ganguly, and S. Ahn, “Optimization of the efficiency in gyrotron backward-wave oscillator via a tapered axial magnetic field”, Appl. Phys. Lett.., vol. 54, pp. 514-516 (1989).
[14] M. T. Walter, R. M. Gilgenbach, J. W. Luginsland, J. M. Hochman, I. Rintamaki, R. L. Jaynes, Y. Y. Lau, and T. A. Spencer, “Effects of tapering on gyrotron backward-wave oscillator”, IEEE Trans. Plasma Sci., vol. 24, pp. 636-647 (1996).
[15] Idehara, Toshitaka, et al. “A high harmonic gyrotron with an axis-encircling electron beam and a permanent magnet” Plasma Science, IEEE Transactions on 32.3 (2004): 903-909.
[16] M. T. Walter, R. M. Gilgenbach, P. R. Menge, and T. A. Spencer, “Effects of tapered tubes on long-pulse microwave emission from intense e-beam gyrotron-backward-wave-ocillators”, IEEE Trans. Plasma Sci., vol. 22, no. 5, pp. 578-584 (1994).
[17] T. H. Chang, C. H. Du, P. K. Liu, C. P. Yuan, S. J. Yu, and G. F. Liu, “A Magnetic Cusp Gun for Terahertz Gyro-Devices”, IEEE 978-1-4673-1597-5112 (2012).
[18] T. H. Chang, T. ldehara, I. Ogawa, L. Agusu, and S. Kobayashi, “Frequency tunable gyrotron using backward-wave components”, Appl.Phys.105,063304 (2009).
[19] T. H. Chang, C. T. Fan, K. F. Pao, K. R. Chu, and S. H. Chen, “Stability and tunability of the gyrotron backward-wave oscillator”, Appl. Phys. Lett. 90, 191501 (2007).
[20] K. F. Pao, C. T. Fan, T. H. Chang, C. C. Chiu, and K. R. Chu, “Selective suppression of high order axial modes of the gyrotron backward-wave oscillator”, Phys. Plasmas, 14, 093301 (2007).
[21] Y. S. Yeh, T. H. Chang, C. T. Fan, C. L. Hung, J. N. Jhou, J. M. Huang, J. L. Shiao, Z. Q. Wu, and C. C. Chiu, “Nonlinear oscillation behavior of a driven gyrotron backward-wave oscillator”, Phys. Plasmas 17, 113112 (2010).
[22] S. H. Chen, T. H. Chang, K. F. Pao, C. T. Fan, and K. R. Chu, “Linear and Time-Dependent Behavior of the Gyrotron Backward-Wave Oscillator”, Phys.Rev.Lett.89.268303 (2002).
[23] K. R. Chu, “Theory of Electron Cyclotron Maser Interactions in a Cavity at the Harmonic Frequencies”, No. NRL-MR-3672. NAVAL RESEARCH LAB WASHINGTON DC (1978).
[24] 范肇達，磁旋返波振盪之穩定性與調變性研究，,國立清華大學博士論文 (2005)
[25] 姚仁傑，400GHz TE41第四諧波磁旋返波振盪器之CUSP電子槍設計，國立清華大學碩士論文 (2009).
[26] 張存續， “高功率可調頻太赫茲波源---電子磁旋脈射” , 物理雙月刊, 四月號 (2009).
[27] 張存續*，陳乃慶，杜朝海、袁景濱，真空電子學之磁旋管發展，真空科技　25 卷‧第 1 期 (2012)
[28] T. H. Chang*, C. T. Fan, K. F. Pao, S. H. Chen, and K. R. Chu, “Stability and Tunability of the Gyrotron Backward-Wave Oscillator”, Appl. Phys. Lett. 90, 191501 (2007)
[29] C. T. Fan, T. H. Chang*, K. F. Pao, S. H. Chen, and K. R. Chu, “Stable, high efficient gyrotron backward-wave oscillator”, Phys. Plasmas, 14, 093102 (2007)
[30] T. H. Chang*, C. F. Yu, C. L. Hung, Y. S. Yeh, M. C. Msiao, and Y. Y. Shin, “W-band TE01 gyrotron backward-wave oscillator with distributed loss”, Phys. Plasmas 15, 073105 (2008)
[31] T. H. Chang*, T. Idehara, I. Ogawa, L. Agusu, C. C. Chiu, and S. Kobayashi, “Frequency tunable gyrotron using backward-wave components”, J. Appl. Phys. 105, 063304 (2009).
[32] N. C. Chen, C. F. Yu, C. P. Yuan, and T. H. Chang*, “A mode-selective circuit for TE01Gyrotron Backward-wave Oscillator with wide-tuning range”, Appl. Phys. Lett. 94, 101501 (2009).
[33] C. P. Yuan, T. H. Chang*, N. C. Chen, and Y. S. Yeh, “Magnetron injection gun for a broadband gyrotron backward-wave oscillator”, Phys. Plasmas, 16, 073109 (2009).
[34] P. Sprangle, and A. T. Drobot, “The Linear and Self ─ consistent Nonlinear Theory of the Electron Cyclotron Maser Instability”, IEEE Trans. Microwave Theory Tech., vol. 25, no. 6, pp. 528-544 (1977).
[35] K. R. Chu, A. T. Drobot, H. H. Szu, and P. Sprangle, “Theory and Simulation of the Gyrotron Traveling Wave Amplifier Operating at Cyclotron Harmonics”, IEEE Trans. Microwave Theory Tech., vol. 28, no. 4, pp. 313-317 (1980).
[36] K. R. Chu, and A. T. Lin, “Gain and Bandwidth of the Gyro ─ TWT and CARM Amplifiers,” IEEE Trans. Plasma Sci., vol. 16, no. 6, pp. 90-104 (1988).
[37] L. R. Barnett, L. H. Chang, H. Y. Chen, K. R. Chu, Y. K. Lau, and C. C.
Tu,“Absolute instability compentition and suppression in a millimeter-wave gyrotron traveling-wave tube”, Phys. Rev. Lett.,vol. 63, pp. 1062-1065 (1989).
[38] A. T. Lin, K. R. Chu, C. C. Lin, C. S. Kou, D. B. McDermott, and N. C. Luhmann, “Marginal stability design criterion for gyro-TWT, and comparison of fundamental with second harmonic operation”, Int. J. Electron., vol. 72, no. 5, pp. 813-885 (1992).
[39] Q. S. Wang, C. S. Kou, D. B. McDermott, A. T. Lin, K. R. Chu, and N. C.
Luhmann, “High-power harmonic gyro-TWT-part Ⅱ: nonlinear theory and design” IEEE Trans. Microwave Theory Tech. vol. 20, no. 3, pp. 163-169 (1992).
[40] Q. S. Wang, D. B. McDermott, and N. C. Luhmann, Jr., “Demonstration of
marginal stability theory by a 200-kW second-harmonic gyro-TWT amplifier”, Phys. Rev. Lett., vol. 75, no. 23, pp. 4322-4325 (1995).
[41] Q. S. Wang, H. E. Huey, D. B. McDermott, Y. Hirata, and N. C. Luhmann, Jr., “Design of a W-band second-harmonic TE02 gyro-TWT amplifier”, IEEE Trans. Plasma Sci., vol. 28, no. 6, pp. 2232-2237 (2000).
[42] Q. S. Wang, D. B. McDermott, and N. C. Luhmann, Jr., “Operation of a stable 200-kW second-harmonic gyro-TWT amplifier”, IEEE Trans. Microwave Theory Tech., vol. 24, no. 3, pp. 700-706. (1996).
[43] K. R. Chu, H. Guo and V. L. Granatstein, “Theory of the Harmonic Multiplying Gyrotron Traveling Wave Amplifier”, Phys. Rev. Lett., vol. 78, pp. 4461-4464 (1997).
[44] Q. S. Wang, D. B. McDermott, C. K. Chong, K. R. Chu, and N. C. Luhmann,“Stable 1 MW, Third-Harmonic Gyro-TWT Amplifier”, IEEE Transactions on Plasma Science, vol. 22, no. 5, pp. 608-615 (1994).
[45] C. W. Baik, S. G. Jeon, D. H. Kim, N. Sato, K. Yokoo and G. S. Park, “Third-harmonic frequency multiplying of a two-stage tapered gyrotron TWT amplifier,” IEEE Trans. Electron Devices (2005).
[46] S. B. Harriet, David B. McDermott, D. A. Gallagher, and N. C. Luhmann, Jr., “Cusp Gun TE21 Second-Harmonic Ka-Band Gyro-TWT Amplifier”, IEEE Trans. Plasma Sci. Vol. 30, No. 3 (2002).
[47] D. B. McDermott, B. H. Deng, K. X. Liu, J. Van Meter, Q. S. Wang, and N. C. Luhmann, Jr., “Stable 2 MW, 35 GHz, Third-Harmonic TE41 Gyro-TWT Amplifier”, IEEE Trans. Plasma Sci. Vol. 26, No. 3 (1998).
[48] K. R. Chu, L. R. Barnett, H. Y. Chen, Ch. Wang, Y. S. Yeh, Y. C. Tsai, T. T. Yang, and T. Y. Dawn, “Stabilizing of absolute instabilities in gyrotron traveling wave
amplifier”, Phys. Rev. Lett., vol. 74, no. 7, pp. 1103-1106 (1995).
[49] Y. S. Yeh, T. S. Wu, Y. T. Lo, C. W. Su, and S. C. Wu, “Stability Analysis of TE01 Gyrotron Traveling Wave Amplifier”, Int. J. Electron., vol. 90, no. 8, pp.517-532 (2003).
[50] A. V. Gaponov-Grekhov and V. L. Granatstein, Eds., Applications of High Power Microwaves (Artech House, Norwood, MA, 1994).
[51] C. S. Kou, Q. S. Wang, D. B. McDermott, A. T. Lin, K. R.Chu, and N. C. Luhmann, Jr., “High-power harmonic gyro-TWT. Part I: Linear theory and oscillation study”, IEEE Trans. Plasma Sci. 20, 155 (1992).
[52] Q. S. Wang, C. S. Kou, D. B. McDermott, A. T. Lin, K. R. Chu, and N. C. Luhmann, Jr., “High-power harmonic gyro-TWTs—Part II: Nonlinear theory and design”, IEEE Trans. Plasma Sci. 20, 163 (1992).
[53] C. H. Du, et al. “Development of a magnetic cusp gun for terahertz harmonic gyrodevices,” IEEE Transactions on Electron Devices, 59.12 (2012): 3635-3640.