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A Numerical Study on Finite-Bandwidth Resonances of High-Order Axial Modes (HOAM) in a Gyrotron Cavity

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Abstract

Many novel and prospective applications of the gyrotrons as sources of coherent radiation require a broadband and continuous frequency tunability. A promising and experimentally proven technique to achieve it is based on a successive excitation of a sequence of high-order axial modes (HOAM) in the cavity resonator. Therefore, the studies on HOAM are of both theoretical and practical importance and interest. In this paper, we present and discuss the methods and the results of a numerical investigation on the resonances of HOAM in a typical open gyrotron cavity. The simulations have been performed using the existing as well as novel computational modules of the problem-oriented software package GYROSIM (GYROtron SIMulation) for solution of both the homogeneous and the inhomogeneous Helmholtz equation with radiation boundary conditions, which governs the field amplitude along the axis of the resonant structure. The frequency response of the cavity is studied by analyzing several resonance curves (spectral domain analysis) obtained from the numerical solution of the boundary value problem for the inhomogeneous Helmholtz equation with a predefined source term (excitation) by the finite-difference method (FDM). The approach proposed here allows finite-bandwidth resonances of HOAM to be identified and represented on the dispersion diagram of the cavity mode as bands rather than as discrete points, in contrast to the frequently used physical models that neglect the finite width of these resonances. Developed numerical procedures for calculation of the field profiles for an arbitrary frequency and excitation will be embedded in the cold cavity and self-consistent codes of the GYROSIM package in order to study the beam-wave interaction and energy transfer in gyrotron cavities.

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References

  1. G.S. Nusinovich, M.K.A. Thumm, M. Petelin, “The Gyrotron at 50: Historical Overview,” J. Infrared Millimeter and Terahertz Waves 34, 325-381 (2014).

    Article  Google Scholar 

  2. T. Idehara, T. Saito, I. Ogawa, S. Mitsudo, Y. Tatematsu, S. Sabchevski, “The potential of the gyrotrons for development of the sub-terahertz and the terahertz frequency range - A review of novel and prospective applications,” Thin Solid Films 517, 1503-1506 (2008).

    Article  Google Scholar 

  3. M.Yu. Glyavin, G.G. Denisov, V.E. Zapevalov, A.N. Kuftin, A.G. Luchinin, V.N. Manuilov, M.V. Morozkin, A.S. Sedov, and A.V. Chirkov, “Terahertz Gyrotrons: State of the Art and Prospects,” Journal of Communications Technology and Electronics 59, 792–797 (2014).

    Article  Google Scholar 

  4. T. Idehara (Editor) “High Power THz Technologies Opened by High–Frequency Gyrotrons- Special Issue,” J. Infrared Millimeter and Terahertz Waves 33 (2012).

  5. M. Thumm, “State-of-the-Art of High Power Gyro-Devices and Free Electron Masers (Update 2013),” KIT Scientific Reports 7662 (KIT Scientific Publishing), 1-138 (2014).

  6. M. Botton, T.M. Antonsen, B. Levush, K.T. Nguyen, A.N. Vlasov, “MAGY: a time-dependent code for simulation of slow and fast microwave sources,” IEEE Trans. Plasma Science 26, 882-892 (1998).

    Article  Google Scholar 

  7. S. Sabchevski, T. Idehara, M. Glyavin, I. Ogawa, S. Mitsudo, “Modelling and simulation of gyrotrons,” Vacuum 77, 519-525 (2005).

    Article  Google Scholar 

  8. S. Sabchevski, T. Idehara, T. Saito, I. Ogawa, S. Mitsudo, Y. Tatematsu, “Physical Models and Computer Codes of the GYROSIM (GYROtron SIMulation) Software Package,” FIR Center Report FIR FU-99 (Jan. 2010). Available on-line at: http://fir.u-fukui.ac.jp/FIR_FU99S.pdf

  9. S. Sabchevski, I. Zhelyazkov, M. Thumm, S. Illy, B. Piosczyk, T.-M. Tran, J.-Ph. Hogge, J. Gr. Pagonakis, “Recent Evolution of the Simulation Tools for Computer Aided Design of Electron-optical Systems for Powerful Gyrotrons,” Computer Modelling in Engineering and Science 20, 203-220 (2007).

    Google Scholar 

  10. M. Damyanova, S. Kern, S. Illy, M. Thumm, S. Sabchevski, I. Zhelyazkov, E. Vasileva, “Modelling and simulation of gyrotrons for ITER,” Journal of Physics: Conference Series 516, 012028. (6 pages) (2014).

  11. F. Braunmueller, T.M. Tran, S. Alberti, J.Genoud, J.-Ph. Hogge, Q. Vuillemin, M.Q. Tran, “Self-consistent, time-dependent gyrotron linear analysis in nonhomogeneous RF-structures,” IEEE Proceedings of the 38th International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz, Mainz, Germany, 1-6 September 2013), 1-2 (2013).

  12. K.A. Avramides, I.Gr. Pagonakis, C.T. Iatrou, J.L.Vomvoridis, “EURIDICE: A code-package for gyrotron interaction simulations and cavity design,” 17th Joint Workshop on Electron Cyclotron Emission and Electron Cyclotron Resonance Heating (Deurne, The Netherlands), Edited by E. Westerhof; P.W.J.M. Nuij; EPJ Web of Conferences 32, id.04016. DOI: 10.1051/epjconf/20123204016 (2012).

  13. P.V. Krivosheev, V.K. Lygin,V.N. Manuilov, Sh.E. Tsimring, “Numerical Simulation Models of Focusing Systems of Intense Gyrotron Helical Electron Beams,” Int. J. of Infrared and Millimeter Waves 22, (2001) 1119-1146.

    Article  Google Scholar 

  14. M.V. Kartikeyan, E. Borie, M.K.A. Thumm, “GYROTRONS High Power Microwave and Millimeter Wave Technology” (Springer, 2003).

  15. G. Nusinovich, “Introduction to the Physics of Gyrotrons” (The Johns Hopkins University Press, 2004).

  16. S.E. Tsimring, “Electron Beams and Microwave Vacuum Electronics” (Wiley-Interscience, 2007).

  17. K. R. Chu, “The Electron Cyclotron Maser,” Rev. of Modern Phys. 76, 489 (2004).

    Article  Google Scholar 

  18. Chao-Hai Du, Pu-Kun Liu, “Millimeter-Wave Gyrotron Traveling-Wave Tube Amplifiers” (Springer, 2014).

  19. M.Yu. Glyavin, T. Idehara, V.N. Manuilov, T. Saito, “Studies of Continuous-Wave Submillimeter-Wave Gyrotrons for Spectroscopy and Diagnostics of Various Media,” Radiophysics and Quantum Electronics 52, 500-509 (2009).

    Article  Google Scholar 

  20. V. Bratman, M. Glyavin, T. Idehara, Y. Kalynov, A. Luchinin, V. Manuilov, S. Mitsudo, I. Ogawa, T. Saito, Y. Tatematsu, V. Zapevalov, “Review of Subterahertz and Terahertz Gyrodevices at IAP RAS and FIR FU,” IEEE Trans. Plasma Science 37, 36-43 (2009).

    Article  Google Scholar 

  21. T. Idehara, S. Sabchevski, “Development and Applications of High—Frequency Gyrotrons in FIR FU Covering the sub-THz to THz Range,” J. Infrared Millimeter and Terahertz Waves 33, 667-694 (2012).

    Article  Google Scholar 

  22. S. Sabchevski, T. Idehara, S. Mitsudo, T. Fujiwara, “Conceptual Design Study of a Novel Gyrotron for NMR/DNP Spectroscopy,” Int. J. Infrared and Millimeter Waves 26, 1241–1264 (2005).

    Article  Google Scholar 

  23. S. Sabchevski, T. Idehara, “Resonant Cavities for Frequency Tunable Gyrotrons,” Int. Journal of Infrared and Millimeter Waves 29, 1-22 (2008).

    Article  Google Scholar 

  24. S. Sabchevski, T. Idehara, “Design of a Compact Sub-Terahertz Gyrotron for Spectroscopic Applications,” J. Infrared Millimeter and Terahertz Waves 31, 934-948 (2010).

    Google Scholar 

  25. O. Dumbrajs, T. Idehara, S. Sabchevski, “Design of an Optimized Resonant Cavity for a Compact Sub—Terahertz Gyrotron,” J. Infrared Millimeter and Terahertz Waves 31, 1115—1125 (2010).

    Article  Google Scholar 

  26. O. Dumbrajs, G.S. Nusinovich, “To the theory of high-power gyrotrons with uptapered resonators,” Phys. Plasmas 17, 053104 (2010).

    Article  Google Scholar 

  27. T.H. Chang, K.F. Pao, C.T. Fan, S.H. Chen, K.R. Chu, “Study of axial modes in the gyrotron backward-wave oscillator,” Third IEEE International Vacuum Electronics Conference IVEC 2002, 123-124. doi: 10.1109/IVELEC.2002.999293 (2002).

  28. T.H. Chang, T. Idehara, I. Ogawa, L. Agusu, S. Kobayashi, “Frequency tunable gyrotron using backward wave components,” J. Appl. Physics 105, 063304-1–4 (2009).

  29. T. Idehara, K. Kosuga, La Agusu, R. Ikeda, I. Ogawa, T. Saito, Y. Matsuki, K. Ueda, T. Fujiwara, “Continuously Frequency Tunable High Power Sub-THz Radiation Source–Gyrotron FU CW VI for 600 MHz DNP–NMR Spectroscopy,” J. Infrared Millimeter and Terahertz Waves 31, 775–790 (2010).

    Article  Google Scholar 

  30. R. Ikeda, Y. Yamaguchi, Y. Tatematsu, T. Idehara, I. Ogawa, T. Saito, Y. Matsuki, T. Fujiwara, “Broadband Continuously Frequency Tunable Gyrotron for 600MHz DNP-NMR Spectroscopy,” Plasma and Fusion Research: Rapid Communications 9, 1206058 (2014).

    Google Scholar 

  31. M.K. Hornstein, V.S. Bajaj, R.G. Griffin, K.E. Kreischer, I. Mastovsky, M.A. Shapiro, J.R. Sirigiri, R.J. Temkin, “Second harmonic operation at 460 GHz and broadband continuous frequency tuning of a gyrotron oscillator”, IEEE Transactions on Electron Devices 52, 798-807 (2005).

    Article  Google Scholar 

  32. A.C. Torrezan, S.-T. Han, I. Mastovsky, M.A. Shapiro, J.R. Sirigiri, R.J. Temkin, A.B... Barnes, R.G. Griffin, “Continuous—Wave Operation of a Frequency-Tunable 460-GHz Second-Harmonic Gyrotron for Enhanced Nuclear Magnetic Resonance,” IEEE Transactions on Plasma Science 38, 1150-1159 (2010).

  33. A.B... Barnes, E.A. Nanni, J. Herzfeld, R.G. Griffin, R.J. Temkin, “A 250 GHz gyrotron with a 3 GHz tuning bandwidth for dynamic nuclear polarization,” Journal of Magnetic Resonance 221, 147—153 (2012).

  34. S. Jawla, Q.Z. Ni, A. Barnes, W. Guss, E. Daviso, J. Herzfeld, R. Griffin, R. Temkin, “Continuously Tunable 250 GHz Gyrotron with a Double Disk Window for DNP-NMR Spectroscopy,” J. Infrared Millimeter and Terahertz Waves 34, 42-52 (2013).

    Article  Google Scholar 

  35. R.J. Temkin, “Development of terahertz gyrotrons for spectroscopy at MIT,” Terahertz Science and Technology 7, 1-9 (2014).

    Google Scholar 

  36. S. Alberti, J.-Ph. Ansermet, K.A. Avramides, F. Braunmueller, P. Cuanillon, J. Dubray, D. Fasel, J.-Ph. Hogge, A. Macor, E. de Rijk, M. da Silva, M.Q. Tran, T.M. Tran, Q. Vuillemin, “Experimental study from linear to chaotic regimes on a terahertz-frequency gyrotron oscillator”, Physics of Plasmas 19, 123102 (2012).

    Article  Google Scholar 

  37. J.-P. Hogge, F. Braunmueller, S. Alberti, J. Genoud, T.M. Tran, Q. Vuillemin, M.Q. Tran, J.-P. Ansermet, P. Cuanillon, A. Macor, E. de Rijk, P.V. Saraiva, “Detailed characterization of a frequency-tunable 260 GHz gyrotron oscillator planned for DNP/NMR spectroscopy,” 38th Int. Conf. on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz, 1-6 Sept. 2013) 1-2 (2013).

  38. S. Alberti, F. Braunmueller, T.M. Tran, J. Genoud, J-Ph. Hogge, M.Q. Tran, J-Ph. Ansermet, “Nanosecond Pulses in a THz Gyrotron Oscillator Operating in a Mode-Locked Self-Consistent Q-Switch Regime,” Phys. Rev. Lett. 111, 205101 (2013).

    Article  Google Scholar 

  39. F. Braunmueller, T.M. Tran, S. Alberti, J.-Ph. Hogge, M.Q. Tran,‟Moment-based, self-consistent linear analysis of gyrotron oscillators”, Physics of Plasmas 21, 043105 (2014).

    Article  Google Scholar 

  40. E.S.C. Ching, P.T. Leung, A. Maassen van den Brink, W.M. Suen, S.S. Tong, K. Young, “Quasinormal-mode expansion for waves in open systems,” Rev. Modern Phys. 70, 1545-1554 (1998).

    Article  Google Scholar 

  41. S.N. Vlasov, G.M. Zhisllin, I.M. Orlova, M.I. Petelin, G.G. Rogacheva, “Irregular Waveguides as Open Resonators,” Izv. VUZ, Radiofizika, 12 (8) 1236-1244 (1969) (original paper in Russian). The English version of the paper: S.N. Vlasov, G.M. Zhisllin, I.M. Orlova, M.I. Petelin, G.G. Rogacheva, “Irregular Waveguides as Open Resonators,” Radiophysics and Quantum Electronics 12 972-978 (1969).

  42. A.W. Fliflet, M.E. Read, “Use of weakly irregular waveguide theory to calculate eigenfrequencies, Q values, and RF field functions for gyrotron oscillators,” Int. J. Electronics 51, 475-484 (1981).

    Article  Google Scholar 

  43. B. Engquist, A. Majda, “Absorbing boundary conditions for numerical simulation of waves,” Proc. Nat. Acad. Sci. USA 74 1765-1766 (1977).

    Article  MATH  MathSciNet  Google Scholar 

  44. T.G. Moore, J.G. Blaschak, A. Taflove, G.A. Kriegsmann, “Theory and Application of Radiation Boundary Operators,” IEEE Trans. On Antennas and Propagation 36, 1797-1812 (1988).

    Article  Google Scholar 

  45. G. Baruch, G. Fibich, S. Tsynkov, “A high-order numerical method for the nonlinear Helmholtz equation in multidimensional layered media,” J. Comput. Phys. 228, 3789-3815 (2009).

    Article  MATH  MathSciNet  Google Scholar 

  46. K.R. Chu, H.Y. Chen, C.L. Hung, T.H. Chang, L.R. Barnett, S.H. Chen, T.T. Yang, D. Dialetis, “Theory and experiment of ultrahigh-gain gyrotron traveling wave amplifier,” IEEE Trans. Plasma Sci. 27, 391-404 (1999).

    Article  Google Scholar 

  47. A.V. Gaponov, V.A. Flyagin, A.L. Gol'denberg, G.S. Nusinovich, S.E. Tsimring, V.G. Usov, S.N. Vlasov, “Powerful millimetre-wave gyrotrons (Invited paper)”, International Journal of Electronics, 51:4 277-302 (1981).

    Article  Google Scholar 

  48. B.G. Danly, R.J. Temkin, “Generalized nonlinear harmonic gyrotron theory,” Physics of Fluids 29, 561-567 (1986).

    Article  Google Scholar 

  49. K.E. Kreischer, R.J. Temkin, “Mode excitation in a gyrotron operating at the fundamental,” International Journal of Infrared and Millimeter Waves 2, 175-196 (1981).

    Article  Google Scholar 

  50. N. Froeman, P.O. Froeman, “JWKB Approximation: Contributions to the Theory”. (Amsterdam: North-Holland, 1965).

    MATH  Google Scholar 

  51. B.Z. Katsenelenbaum, L.M. Del Rio, M. Pereyaslavets, M.S. Ayza, M. Thumm, “Theory of nonuniform waveguides-The cross-section method”, IEE Electromagnetic Waves 44 (IEE Press London, UK, 1998).

  52. I. Ederra, M.S. Ayza, M. Thumm, B.Z. Katsenelenbaum, “Comparative Analysis of Mode Reflection and Transmission in Presence of a Cutoff Cross Section of Nonuniform Waveguide by Using the Cross Section and the Mode-Matching and Generalized Scattering-Matrix Methods,” IEEE Trans. Microwave Theory and Techniques 49, 637-645 (2001).

    Article  Google Scholar 

  53. G.S. Nusinovich, M. Walter, “Linear theory of multistage forward-wave amplifiers,” Phys. Rev. 60, 4811-4822 (1999).

    Google Scholar 

  54. G.S. Nusinovich, R. Pu, O.V. Sinitsyn, J. Yu, T.M. Antonsen, V.L. Granatstein, “Self-Excitation of a Tapered Gyrotron Oscillator,” IEEE Trans. Plasma Sci. 38, 1200-1207 (2010).

    Article  Google Scholar 

  55. Lezhu Zhou, Chenghe Xu, Zhonglin Gong, “General theory and design of microwave open resonators,” International Journal of Infrared and Millimeter Waves 3, 117-136 (1982).

  56. Anshi Xu, Chenghe Xu, “A theory of complex open resonators in the form of cavity chain,” International Journal of Infrared and Millimeter Waves 7, 487-512 (1986).

    Article  Google Scholar 

  57. Chenghe Xu, Lezhu Zhou, Anshi Xu, “An improved theory of microwave open resonators,” International Journal of Infrared and Millimeter Waves 10, 55-62 (1989).

    Article  Google Scholar 

  58. Anshi Xu, Lezhu Zhou, Chenghe Xu, “A method for the synthesis of microwave open resonators,” International Journal of Electronics 57, 887-899 (1984).

  59. G. Nusinovich, M. Read, L. Song, “Excitation of “monotron” oscillations in klystrons”, Phys. Plasmas 11, 4893-4903 (2004).

    Article  Google Scholar 

  60. J.J. Barroso, A. Montes, G.O. Ludwig, “RF field profiles in weakly irregular open resonators,” International Journal of Electronics 61, 771-794 (1986).

    Article  Google Scholar 

  61. E. Borie, “Self-consistent code for a 150 GHz gyrotron”, International Journal of Infrared and Millimeter Waves 7, 1863-1879 (1986).

    Article  Google Scholar 

  62. Q.F. Li, K.R. Chu, “Analysis of open resonators,” International Journal of Infrared and Millimeter Waves 3, 705-723 (1982).

    Article  Google Scholar 

  63. E. Borie, O. Dumbrajs, “Calculation of eigenmodes of tapered gyrotron resonators,” International Journal of Electronics 60, 143-154 (1986).

    Article  Google Scholar 

  64. E. Borie, B. Jodicke, H. Wenzelburger, O. Dumbrajs, “Resonator design studies for a 150 GHz gyrotron at Kf K,” International Journal of Electronics 64, 107-126 (1988).

    Article  Google Scholar 

  65. J.J. Barroso, R.A. Correa, A. Montes, “Optimization of RF field profiles for enhanced gyrotron efficiency,” International Journal of Electronics 67, 457-484 (1989).

    Article  Google Scholar 

  66. O. Dumbrajs, B. Piosczyk, “Resonator for a frequency-step tunable gyrotron,” International Journal of Electronics 68, 885-890 (1990).

    Article  Google Scholar 

  67. R.M. Rozental, N.S. Ginzburg, N.I. Zaitsev, E.V. Ilyakov, I.S. Kulagin, “Controllable Spectrum of an Axial-Mode Gyrotron with External Reflections,” Technical Physics 51, 78–81 (2006).

    Article  Google Scholar 

  68. T. Idehara, I. Ogawa, S. Mitsudo, Y. Iwata, S. Watanabe, Y. Itakura, K. Ohashi, H. Kobayashi, T. Yokoyama, V.E. Zapevalov, M.Y. Glyavin, A.N. Kuftin, O.V. Malygin, S.P. Sabchevski, “A High Harmonic Gyrotron With an Axis-Encircling Electron Beam and a Permanent Magnet,” IEEE Trans. Plasma Sci. 32, 903-909 (2004).

    Article  Google Scholar 

  69. M. Thumm, “Effective Cavity Length of Gyrotrons”, J. Infrared Millimeter and Terahertz Waves, doi:10.1007/s10762-014-0102-z (2014)

    Google Scholar 

  70. J.W. Thomas, “Numerical Partial Differential Equations: Finite Difference Methods,” vol. 1 (Springer, 1995) 437 pages.

  71. Markus Götz, “Zur mathematischen Modellierung und Numerik eines Gyrotron Resonators” (Universität München, Dissertation Dr. rer. nat., 2006) 129 pages. Available online: https://mediatum.ub.tum.de/doc/602036/602036.pdf

  72. “LAPACK 3.2 Release Notes”. 16 November 2008, (http://www.netlib.org/lapack/lapack-3.2.html).

  73. D. Hinton, P. W. Schaefer, “Spectral theory and computational methods of Sturm-Liouville problems” (Marcel Dekker, Inc., New York, 1997).

    MATH  Google Scholar 

  74. W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, “Numerical Recipes: The Art of Scientific Computing (3rd ed.),” New York: Cambridge University Press (2007).

    Google Scholar 

  75. K.R. Chu, C.S. Kou, J.M. Chen, Y.C. Tsai, C. Cheng, S.S. Bor, L.H. Chang, “Spectral Domain Analysis of Open Cavities,” International Journal of Infrared and Millimeter Waves 13, 1571-1598 (1992).

    Article  Google Scholar 

  76. C.L. Hung, Y.C. Tsai, K.R. Chu, “A Study of Open-End Cavities by the Field-Energy Method,” IEEE Trans. Plasma Sci. 26, 931-939 (1998).

    Article  Google Scholar 

  77. Chien Lun Hung, Yi Sheng Yeh, “Spectral Domain Analysis of Coaxial Cavities,” International Journal of Infrared and Millimeter Waves 24, 2025-2041 (2003).

    Article  Google Scholar 

  78. L.A. Vainshtein, “Open Resonators for Lasers,” Soviet Physics JETP 17, 709-719 (1963). Available on-line at: http://www.jetp.ac.ru/cgi-bin/dn/e_017_03_0709.pdf

  79. QtiPlot-DataAnalysis and Scientific Visualization (visit: www.qtiplot.com).

Download references

Acknowledgments

This work was supported partially by the Special Fund for Education and Research from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) in Japan and was carried out in the framework of the collaboration of an international consortium on the project “Promoting international collaboration for development and application of high-power THz gyrotrons” of the FIR UF Research Center (Fukui, Japan).

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  1. Institute of Electronics of the Bulgarian Academy of Sciences, 1784, Sofia, Bulgaria

    Svilen Petrov Sabchevski

  2. Research Center for Development of Far-Infrared Region, University of Fukui, 910-8507, Fukui, Japan

    Toshitaka Idehara

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Sabchevski, S.P., Idehara, T. A Numerical Study on Finite-Bandwidth Resonances of High-Order Axial Modes (HOAM) in a Gyrotron Cavity. J Infrared Milli Terahz Waves 36, 628–653 (2015). https://doi.org/10.1007/s10762-015-0161-9

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