本論文之主要目的為設計出一支速度比(α≈1.5)及較低的速度發散(Δvz/vz < 8%)之溫度限流低電壓(< 30 kV)繞軸式電子槍提供給100 GHz TM11 mode磁旋反波振盪器圓柱形波導管使用。
本實驗室前期的研究顯示，TM模在返波振盪器的操作條件下，可以接近TE模態的轉換效率[1]，且TM11模隨著電壓的降低有更好的效率，此效率隨著電壓從100 kV降低而逐漸變大，至30 kV以下時效率大約達到飽和[2]。這與一般傳統概念相違背，根據電子迴旋脈射機制，越高電壓的電子γ值越大，理論上應該更有利於電子的群聚效應，增加轉換效率。故本論文設計出30 kV及20 kV的電子槍，以利將來提供給磁旋反波振盪器做實驗驗證。
但TM11模與TE01模有相同色散關係，彼此之間易有模式競爭。對於此問題，我們可利用繞軸式電子壓制TE01，讓電子只跟TM11產生耦合。此外，若需要提高磁旋管頻率或是降低磁場需求，而將磁旋管操作在高次諧波時，我們也可用繞軸式電子來避免高次諧波間的競爭[3][4]。
在不需要求超大功率(>100000 W)的前提下，低電壓所提供的功率已足夠提供給一般使用，且利於大幅縮減設備價錢及尺寸，降低能源成本，將來也可朝桌上型裝置發展[5]。

In this paper, we present a low voltage axis-encircling electron gun with pitch factor of 1.5 and axial velocity spread less than 8%, which is suitable for 100 GHz TM11 mode gyro-BWO operation.
According to previous studies of gyrotrons in our lab, the TM mode may be as effective as TE mode for the gyro-BWO interaction. Furthermore, the converting efficiency of TM11 mode become larger when we lower the beam voltage from 100 kV to 30 kV. The result is strange to us since the relativistic factor is typically considered to be a key factor of bunching mechanism. Therefore, a suitable electron gun for future experimental verification is needed.
However, there will be mode competition between TM11 and TE01 due to the same dispersion relation. The axis-encircling beam can suppress TE01 because of the mode selectivity property of the beam. Also, axis-encircling beam provide a great solution to the intense mode competition when gyrotron is operating at high-harmonic modes.
If the above can be realized, lowering the voltage while maintaining a good efficiency can result in a reduction of the cost of energy and the size of the equipment , that make portable gyrotron possible.

[1] T. H. Chang, H.Y. Yao, B.Y. Su, W.C. Chen and B.Y. Wei, “Nonlinear oscillations of TM-mode gyrotrons,” Physics of Plasmas vol. 24,no. 12, p. 122109 (2017).
[2] B. Y. Wei , “Nonlinear and self-consistent simulation of TM-mode gyrotrons,” National Tsing Hua University, Hsinchu, (2018).
[3] V. L. Bratman, Y. K. Kalynov, and V. N. Manuilov, “Large-orbit gyrotron
operation in the terahertz frequency range,” Phys. Rev. Lett., vol. 102, no. 24, pp. 245 101-1–245 101-4 (2009).
[4] S. H. Kao et al., “Competition between harmonic cyclotron maser
interactions in the terahertz regime,” Phys. Rev. Lett., vol. 107, no. 13,
p. 135101 (2011).
[5] Melissa K. Hornstein, Vikram S. Bajaj, Robert G. Griffin, and Richard J. Temkin, “ Efficient Low-Voltage Operation of a CW Gyrotron Oscillator at 233 GHz,” IEEE Trans. Plasma Sci., vol. 35, no. 1, pp. 27–30 (2007).
[6] J.W. Gewartowski, and H.A. Watson, 1965, Principles of electron tubes (Van Nostrand, Princeton, NJ).
[7] K. R. Chu, “The electron cyclotron maser,” Rev. Mod. Phys., vol. 76, no. 2, pp. 489–540 (2004).
[8] C. P. Yuan, T. H. Chang, N. C. Chen, and Y. S. Yeh, “Magnetron injection
gun for a broadband gyrotron backward-wave,” Phys. Plasmas, vol. 16,
no. 7, p. 073109 (2009).
[9] C. H. Du, et al., “Conformal cross-flow axis-encircling electron beam for driving thz harmonic gyrotron,” IEEE Trans. Electron Devices. vol. 36, no.9 (2015).
[10] S. G. Kim, et al., “System development and performance testing of a w-band gyrotron,” J. Infrared, Millim., Terahertz Waves. vol 37, no.3 , pp. 209-229 (2016).
[11] Toshitaka Idehara, et al., “Development of frequency tunable, medium
power gyrotrons (gyrotron FU series) as submillimeter wave radiation sources,” IEEE Trans. Plasma Sci., vol. 27, no. 2 (1999).

[12] Z. H. Geng, et al., “Experiment and simulation of a W-band cw 30 kW low-voltage conventional gyrotron,” IEEE Trans. Electron Devices. vol. 61, no.6 (2014).
[13] D. B. McDermott, R. C. Statzman, A.J. Balkcum , and N. C. Luhmann “94-GHz 25-kW cw low-voltage harmonic gyrotron,” IEEE Trans. Plasma Sci., vol. 26, no. 3 (1998).
[14] M. Yu. Glyavin, A. G. Luchinin, and G. Yu. Golubiatnikov, “Generation of 1.5-kw, 1-THz coherent radiation from a gyrotron with a pulsed magnetic field,” Phys. Rev. Lett., vol. 100, no. 1 (2008).
[15] M. Yu. Glyavin, et al., “Experimental demonstration of the possibility to expand the band of smooth tuning of frequency generation in short-cavity gyrotrons,” Radiophysics and Quantum Electronics , vol.61, no.11 (2019).
[16] X.B.Qi, C. H. Du, et al., “Terahertz broadband-tunable minigyrotron
with a pulse magnet,” IEEE Trans. Electron Devices. vol. 64, no.2 (2017).
[17] T.H.Chang, et al.,“Frequency tunable gyrotron using backward-wave components,”J. Appl. Phys. , vol. 105, no. 6 (2009).
[18] Andrey Fokin, et al.,“High-power sub-terahertz source with a record frequency stability at up to 1Hz,” scientific reports. vol. 8 (2018).
[19] M. Yu. Glyavin, et al., “Experimental tests of a 263 GHz gyrotron
for spectroscopic applications and diagnostics of various media,” Rev. Sci. Instrum., vol 86, no.5(2015).
[20] Melissa K. Hornstein, et al., “Second harmonic operation at 460 GHz and
broadband continuous frequency tuning of a gyrotron oscillator,” IEEE Trans. Electron Devices. vol. 52, no.5 (2005).
[21] Toshitaka Idehara, et al., “Gyrotron FU cw VII for 300 MHz and 600 MHz DNP-NMR spectroscopy,” J. Infrared, Millim., Terahertz Waves. vol 31, no.7 (2010).
[22] Tao Song, et al., “Study on the effect of electron beam quality on a continuously frequency-tunable 250-GHz gyrotron,” IEEE Trans. Electron Devices. vol. 65, no.4 (2018).
[23] A. L. Goldenberg, M.Yu.Glyavin, N. A. Zavolsky, and V.N.Manuilov , “Technological gyrotron with low accelerating voltage,” Radiophysics and Quantum Electronics , vol.48, no.10-11 (2005).
[24] M. K. Hornstein, V. S. Bajaj, R. G. Griffin, and R. J. Temkin,“Efficient Low-Voltage Operation of a CW Gyrotron Oscillator at 233 GHz,” IEEE Trans. Plasma Sci., vol. 35, no. 1 (2007).
[25] Sergey A. Kishko, et al.,“Low-voltage cyclotron resonance maser,” IEEE Trans. Plasma Sci., vol. 49, no. 9, pp. 2475–2479 (2013).
[26] V. L. Bratman, et al., “Operation of a sub-terahertz CW gyrotron with an extremely low voltage,” Phys. Plasmas, vol. 24, no. 11 (2017).
[27] V. L. Bratman, et al., “Smooth Wideband Frequency Tuning in
Low-Voltage Gyrotron With Cathode-End Power Output,” IEEE Trans. Electron Devices. vol. 64, no.12 (2017).
[28] W. He, et al., “Axis-encircling electron beam generation using a smooth magnetic cusp for gyrodevices,” Appl. Phys. Lett. 93, pp. 121 501-1–121 501-3 (2008).
[29] V. N. Manuilov, S. V. Samsonov, S. V. Mishakin, A. V. Klimov, K. A. Leshcheva , “Cusp guns for helical-waveguide gyro-twts of a high-gain high-power w-band amplifier cascade,” J. Infrared, Millim., Terahertz Waves , vol.39, no.5, pp.447-455 (2018).
[30] W.Lawson,“Design of low velocity‐spread cusp guns for axis encircling beams,” Appl. Phys. Lett., vol. 50, no. 21 (1987)
[31] C. H. Du, X.B. Qi, B.L. Hao, T.H. Chang, and P.K. Liu, “Development of a magnetic cusp gun for tetrahertz harmonic gyrodevices,” IEEE Trans. Electron Devices, vol. 59, no. 12 (2012).
[32] S. B. Harriet, D. 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, pp. 909–914 (2002)
[33] S. V. Samsonov, et al., “Ka-Band gyrotron traveling-wave tubes with the highest continuous-wave and average power,” IEEE Trans. Electron Devices. vol. 61, no.12 (2014).
[34] W. He, C. R. Donaldson, L. Zhang, K. Ronald, A. D. R. Phelps, and A. W. Cross, “Broadband amplification of low-terahertz signals using axis-encircling electrons in a helically corrugated interaction region,” Phys. Rev. Lett., vol. 119, no. 24, p.184801 (2017).
[35] C. R. Donaldson, et al., “A cusp electron gun for millimeter wave gyrodevices,” Appl. Phys. Lett., vol. 96, no. 14, p141501-1–141 501-3 (2010).
[36] V.N. Manuilov, “Cusp guns for helical-waveguide Gyro-TWTs of a high-gain high-power w-band amplifier cascade,” J. Infrared, Millim., Terahertz Waves vol. 39, no. 5 (2018).
[37] C. R. Donaldson, W. He, A. W. Cross, A. D. R. Phelps, F. Li, K. Ronald,
C. W. Robertson, C. G. Whyte, and A. R. Young, “Design and numerical
optimization of a cusp-gun-based electron beam for millimeter-wave
gyro-devices,” IEEE Trans. Plasma Sci., vol. 37, no. 11, pp. 2153–2157,
(2009).
[38] L. Zhang, C. R. Donaldson, and W. He, “Optimization of a triode-type cusp electron gun for a W-band gyro-TWA,” Phys. Plasmas, vol. 25, no. 4, (2018).
[39] T. Idehara, et al.,“A high harmonic gyrotron with an axis-encircling electron beam and a permanent magnet,” IEEE Trans. Plasma Sci., vol. 32, no. 3, pp. 903–909 (2004).
[40] S. G. Jeon, C. W. Baik, D. H. Kim, G. S. Park, N. Sato, and K. Yokoo,
“Study on velocity spread for axis-encircling electron beams generated by single magnetic cusp,” Appl. Phys. Lett., vol. 80, no. 20, pp. 3703–3705 (2002).
[41] S. G. Jeon, C. W. Baik, D. H. Kim, G. S. Park, N. Sato, and K. Yokoo,
“Experimental verification of low-velocity spread axis-encircling electron beam,” Appl. Phys. Lett., vol. 84, no. 11, pp. 1994–1996 (2004).
[42] C. Q. Jiao, J. R. Luo, “Linear theory of electron cyclotron maser based on TM circular waveguide mode,” Phys. Plasmas, vol. 13, no. 7, p.073104 (2006).
[43] C. S. Kou and Fouries Tseng, “ Linear theory of gyrotron traveling wave tubes with nonuniform and lossy interaction structures,” Phys. Plasmas, vol. 5, no.6, p.2454 (1998).
[44] C.S. Kou, “Starting oscillation conditions for gyrotron backward wave oscillators,” Phys. Plasmas, vol.1, no.9, p.3093 (1994).
[45] Baird, J. Mark, and W.Lawson, “Magnetron injection gun (MIG) design for gyrotron applications,” Int. J.Electronics, vol. 61, no. 6, pp. 953-967 (1986).
[46] Sh.E. Tsimring, “On the spread of velocities in helical electron beams,” Radiophysics and Quantum Electronics , vol.15,no.8, pp.952-961 (1972).
[47] A. L.Gol’denberg, and M. I.Petelin , “The formation of helical electron beams in an adiabatic gun,” Radiophysics and Quantum Electronics , vol.16, no.1, pp.106-111 (1972).
[48] Avdoshin, E. G., Nikolaev, L. V., Platonov, I. N., and Sh. E.Tsimring , “Experimental investigation of the velocity spread in helical electron beams,” Radio physics and Quantum Electronics 16, pp. 416-466 (1973).
[49] Sh. E. Tsimring, “Gyrotron electron beams: velocity and energy spread and beam instabilities,” J. Infrared, Millim., Terahertz Waves 22, 1433 (2001).
[50] Y. Yamaguchi et al., “Formation of a laminar electron flow for 300 GHz
high-power pulsed gyrotron,” Phys. Plasmas, vol. 19, no. 11, p. 113113
(2012).
[51] Sh. E. Tsimring, “Synthesis of systems for the formation of helical electron beams,” Radiophysics and Quantum Electronics, vol. 20, no. 10, pp. 1068-1076 (1977).
[52] W. B. Herrmannsfeldt, “EGUN electron optics program”,Standford Linear Accelerator Center (1996).