ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Ryskin N. M., Rozhnev A. G., Minenna D. F., Elskens Y., Andre’ F. Nonstationary discrete theory of excitation of periodic structures and its application for simulation of traveling-wave tubes. Izvestiya VUZ. Applied Nonlinear Dynamics, 2021, vol. 29, iss. 1, pp. 10-34. DOI: 10.18500/0869-6632-2021-29-1-10-34

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
PDF icon ryskin1.pdf
(downloads: 1336)
Language: 
Russian
Heading: 
Applied Problems of Nonlinear Oscillation and Wave Theory
Article type: 
Review
UDC: 
530.182
DOI: 
10.18500/0869-6632-2021-29-1-10-34

Nonstationary discrete theory of excitation of periodic structures and its application for simulation of traveling-wave tubes

Autors: 
Ryskin Nikita Mikhailovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Rozhnev Andrej Georgievich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Minenna Damien F.G., Centre National d’E’tudes Spatiales (CNES)
Elskens Yves, Aix-Marseille Universite’
Andre’ Fre’de’ric, Thales Group
Abstract: 

Aim. This article presents a review of the nonstationary (time-domain) discrete theory of excitation of periodic electromagnetic structures and discusses applications of the theory for simulation of traveling-wave tube (TWT) microwave power amplifiers with slow-wave structures (SWS) of different kind. Methods. The discrete theory is based on a representation of a periodic SWS as a chain of coupled cells. However, these cells are not identical to periods of the structure, and each cell is coupled with not only nearest neighbors, but, in general, with all the other cells. The discrete theory allows useful reformulation of Maxwell equations and simplifies simulation of electromagnetic wave propagation through a periodic structure by a great degree-of-freedom reduction. In this paper, we present the derivation of the basic equations of the discrete model from Maxwell equations and investigate the beam-wave interaction processes by numerical simulation. Results. Derivation of the discrete theory equations in its original form proposed by S.P. Kuznetsov is presented. The results of simulation of the С-band coupled-cavity (CC) TWT are considered, including complicated transients, which accompany spurious self-excitation near cut-off. Further developments of the discrete theory including the Hamiltonian formalism are discussed. The Hamiltonian discrete model is applied for simulation of the 170-W Ku-band helix TWT. The results of simulations are in good agreement with the experimental measurements. Conclusion. The discrete theory proposed by S.P. Kuznetsov in 1980 is a powerful tool for modeling of electromagnetic wave propagation in various periodic slow-wave structures. It allows development of computer codes for time-domain simulation of TWTs, which are promising tools that bears several advantages for industrial and research activities.

Key words: 
nonstationary discrete excitation theory
slow wave structure
traveling wave tube
Hamiltonian formalism
numerical modeling
Acknowledgments: 
Работа выполнена в рамках государственного задания Саратовского филиала ИРЭ им. В.А. Котельникова РАН.
Reference: 
  1. Pierce JR. Traveling Wave Tubes. Princeton, NJ.: Van Nostrand; 1950. DOI: 10.1002/j.1538-7305.1950.tb02352.x.
  2. Gilmour Jr. AS. Principles of Traveling Wave Tubes. Boston, London: Artech House; 1994. P. 644.
  3. Kuznetsov AP, Kuznetsov SP, Rozhnev AG et al. Wave theory of a traveling-wave tube operated near the cutoff. Radiophysics and Quantum Electronics. 2004;47(5/6):356–373. DOI: 10.1023/B:RAQE.0000046310.29763.c1.
  4. Pierce J, Wax N. A note on filter-type traveling-wave amplifiers. Proc. IRE. 1949;38(6):622–625. DOI: 10.1109/JRPROC.1949.233301.
  5. Gould RW. Characteristics of travelling-wave tubes with periodic circuits. IRE Trans. Electron Devices. 1958;5(3):186–195. DOI: 10.1109/T-ED.1958.14419.
  6. Kino GS, Hiramatsu Y, Harman WA, Ruetz JA. Small-signal and large-signal theories for the coupled-cavity TWT // Proc. 6th International Conference оn Microwave and Optical Generation and Amplification. Cambridge, England. 1966:49–53.
  7. Vaughan JRM. Calculation of coupled-cavity TWT performance. IEEE Trans. Electron Devices. 1975;22(10):880–890. DOI: 10.1109/T-ED.1975.18237.
  8. Chernin D, Antonsen TM, Chernyavskiy IA, Vlasov AN, Levush B, Begum R, Legarra JR. Large-signal multifrequency simulation of coupled-cavity TWTs. IEEE Trans. Electron Devices. 2011;58(4):1229–1240. DOI: 10.1109/TED.2011.2106504.
  9. Chernin D, Antonsen TM, Vlasov AN, Chernyavskiy IA, Nguyen KT, Levush B. 1-D large signal model of folded-waveguide traveling wave tubes. IEEE Trans. Electron Devices. 2014;61(6): 1699–1706. DOI: 10.1109/TED.2014.2298100.
  10. Qiu W, Lee HJ, Verboncoeur JR, Birdsall CK. A time-domain circuit simulator for coupled-cavity traveling-wave tubes. IEEE Trans. Plasma Sci. 2001;29(6):911–920. DOI: 10.1109/27.974979.
  11. Freund HP, Antonsen TM, Zaidman EG, Levush B, Legarra J. Nonlinear time-domain analysis of coupled-cavity traveling-wave tubes. IEEE Trans. Plasma Sci. 2002;30(3):1024–1040. DOI: 10.1109/TPS.2002.802148.
  12. Curnow HJ. A general equivalent circuits for coupled-cavity slow-wave structures. IEEE Trans. Microwave Theory Tech. 1965;3(5):671–675. DOI: 10.1109/TMTT.1965.1126062.
  13. Carter RG. Representation of coupled-cavity slow-wave structures by equivalent circuits. IEE Proc. I (Solid-State and Electron Devices). 1983;130(2):67–72.
  14. Christie VL., Kumar L, Balakrishnan N. Improved equivalent circuit model of practical coupledcavity slow-wave structures for TWTs. Microwave Optical Technol. Lett. 2002;35(4):322–326. DOI: 10.1002/mop.10596.
  15. Malykhin AV, Konnov AV, Komarov DA. Synthesis of six-pole network simulating of coupled cavity chain characteristics in two passbands. 4th IEEE International Conference of Vacuum Electronics. 2003:159–160. DOI: 10.1109/IVEC.2003.1286199.
  16. Antonsen TM, Vlasov AN, Chernin DP, Chernyavskiy IA, Levush B. Transmission line model for folded waveguide circuits. IEEE Trans. Electron Devices. 2013;60(9):2906–2911. DOI: 10.1109/TED.2013.2272659.
  17. Dialetis D, Chernin DP, Cooke SJ, Antonsen TM, Chang CL, Levush B. Comparative analysis of the Curnow and Malykhin-Konnov-Komarov (MKK) circuits as representations of coupled-cavity slow-wave structures. IEEE Trans. Electron Devices. 2005;52(5):774–782. DOI: 10.1109/TED.2005.846353.
  18. Byulgakova LV, Trubetskov DI, Ficher VL, Shevchik VN. Lectures on the Electronics of Microwave Devices O-type. Saratov: Saratov State Univ.; 1974. P. 221 (in Russian).
  19. Gavrilov MV, Trubetskov DI, Fisher VL. Theory of chains of active multipoles with electronic excitation. Lectures on Microwave Electronics and Radiophysics. The 5th Winter Workshop of Engineers, Book 1. Saratov: Saratov State Univ.; 1981. P. 173–197 (in Russian).
  20. Bulgakova LV, Gavrilov MV, Pishik LA, Trubetskov DI, Fisher VL. Application of the theory of active multipoles to the analysis of a TWT and EIK. Lectures on Microwave Electronics and Radiophysics. The 5th Winter Workshop of Engineers, Book 1. Saratov: Saratov State Univ.; 1981. P. 198–215 (in Russian).
  21. Chernyavskiy IA, Antonsen TM, Rodgers JC, Vlasov AN, Chernin D, Levush B. Modeling vacuum electronic devices using generalized impedance matrices. IEEE Trans. Electron Devices, 2017;64(2):536–542. DOI: 10.1109/TED.2016.2640205.
  22. Connolly DJ, O’Malley TA. A contribution to computer analysis of coupled-cavity traveling wave tubes. IEEE Trans. Electron Devices, 1977;24(1):27–31. DOI: 10.1109/T-ED.1977.18673.
  23. Connolly DJ, O’Malley TA. Computer program for analysis of couple-cavity traveling wave tube. Rep. NASA, TND-8492. Cleveland, USA; 1977. P. 52.
  24. Solntsev VA, Osin AV. Theory of interaction in O-type devices with periodic structure. Lectures on Microwave Electronics and Radiophysics. The 5th Winter Workshop of Engineers, Book 4. Saratov: Saratov State Univ.; 1981. P. 142–178 (in Russian).
  25. Solntsev VA and Mukhin SV. Difference Form of the Periodic Wave-Guides Exitation Theory. J. Commun. Technol. Electron. 1991;36(11):2161–2166 (in Russian).
  26. Solntsev VA. Theory of waveguides excitation. Izvestiya VUZ. Applied Nonlinear Dynamics. 2009;17(3):55–89 (in Russian). DOI: 10.18500/0869-6632-2009-17-3-55-89.
  27. Solntsev VA, Koltunov RP. Analysis of the equations of discrete electron-wave interaction and electron-beam bunching in periodic and pseudoperiodic slow-wave structures. J. Commun. Technol. Electron. 2008;53(6):700–713. DOI: 10.1134/S1064226908060120.
  28. Solntsev VA. Beam–wave interaction in the passbands and stopbands of periodic slow-wave systems. IEEE Trans. Plasma Sci. 2015;43(7):2114–2122. DOI: 10.1109/TPS.2015.2440479.
  29. Vainshtein LA, Solntsev VA. Lectures on Microwave Electronics. Moscow: Sov. Radio; 1973. P. 400. (in Russian).
  30. Bevensee RM. A unified theory of electron beam interaction with slow wave structures, with application to cut-off conditions. Journal of Electronics and Control. 1960;9(6):401–437. DOI: 10.1080/00207216008962774.
  31. Bahr AJ. A coupled-monotron analysis of band-edge oscillations in high-power traveling-wave tubes. IEEE Trans. Electron Devices. 1965;12(10):547–556. DOI: 10.1109/T-ED.1965.15606.
  32. Ginzburg NS, Kuznetsov SP, Fedoseeva TN. Theory of transients in relativistic backward wave tubes. Radiophysics and Quantum Electronics. 1978;21(7):728–739. DOI: 10.1007/BF01033055.
  33. Kuznetsov SP. On one form of excitation equations of a periodic waveguide Sov. J. Commun. Technol. Electron. 1980;25(2):419–421 (in Russian).
  34. Gel’fand IM. Expansion in eigenfunctions of an equation with periodic coefficients. Proceedings of the Academy of Sciences of the USSR. 1950;73(6):1117–1120 (in Russian).
  35. Kittel C. Quantum Theory of Solids. University of California, Berkeley. John Wiley and Sons, Inc. New York; 1963. P. 435.
  36. Kuznetsov AP, Kuznetsov SP. Nonlinear nonstationary equation of interaction between an electron beam and electromagnetic field near the Brillouin zone boundary. Radiophysics and Quantum Electronics. 1984;27(12):1099–1105. DOI: 10.1007/BF01039225.
  37. Bulgakova LV, Kuznetsov SP. Unsteady-state nonlinear processes accompanying the interaction of an electron beam with an electromagnetic field near the boundary of a transmission band. I. The high-frequency boundary. Radiophysics and Quantum Electronics. 1988;31(2):155–166. DOI: 10.1007/BF01039179.
  38. Bulgakova LV, Kuznetsov SP. Nonstationary nonlinear processes in the interaction оf an electron beam with an electromagnetic field near the limit of the transmission band of an electrodynamic system. II. Low-frequency limit. Radiophysics and Quantum Electronics. 1988;31(5):452–460. DOI: 10.1007/BF01043610.
  39. Bulgakova LV, Kuznetsov AP, Kuznetsov SP, Rozhnev AG. Amplification and parasitic selfexcitation of TWT-amplifier near the limit of the transmission band of slow-wave structure. Sov. Electron Tech. Microw. Electron. 1988;3(407):7–12. (in Russian).
  40. Ryskin NM, Titov VN, Yakovlev AV. Nonstationary nonlinear discrete model of a coupled-cavity traveling-wave-tube amplifier. IEEE Trans. Electron Devices. 2009;56(5):928–934. DOI: 10.1109/TED.2009.2016690.
  41. Collier RJ, Helm GD, Laico JP, Striny KM. The ground station high-power traveling-wave tube. Bell Syst. Tech. J.. 1963;42(4):1829–1861. DOI: 10.1002/j.1538-7305.1963.tb04052.x.
  42. Hockney RW, Eastwood JW. Computer Simulation Using Particles. NY, London, Paris: McGrowHill; 1981. P. 540.
  43. Birdsall CK, Langdon AB. Plasma Physics, via Computer Simulation. NY: McGrow-Hill; 1985. P. 479.
  44. Rowe JE. Nonlinear Electron Wave Interaction Phenomena. NY, London: Academic Press; 1965. P. 606. DOI: 10.1016/C2013-0-08102-9.
  45. Miller SM, Antonsen TM, Levush B, Bromborsky A, Abe DK, Carmel Y. Theory of relativistic backward wave oscillator operating near cutoff. Phys. Plasmas. 1994;1(3):730–740. DOI: 10.1063/1.870818.
  46. Levush B, Antonsen TM, Bromborsky A, Lou WR, Carmel Y. Theory of relativistic backwardwave oscillators with end reflectors. IEEE Trans. on Plasma Sci., 1992;20(3):263–280. DOI: 10.1109/27.142828.
  47. Ryskin NM. Study of the nonlinear dynamics of a traveling-wave-tube oscillator with delayed feedback. Radiophysics and Quantum Electronics. 2004;47(2):116–128. DOI: 10.1023/B:RAQE.0000035693.16782.94.
  48. Ryskin NM, Titov VN. Self-modulation and chaotic regimes of generation in a relativistic backward-wave oscillator with end reflections. Radiophysics and Quantum Electronics. 2001; 44(10):793–806. DOI: 10.1023/A:1013717032173.
  49. Andre F, Bernardi P, Ryskin NM, Doveil F, Elskens Y. Hamiltonian description of self-consistent ´ wave-particle dynamics in a periodic structure. Europhys. Lett. 2013;103(2):28004. DOI: 10.1209/0295-5075/103/28004.
  50. Minenna DFG, Elskens Y, Andre F, Doveil F. Electromagnetic power and momentum in ´ N-body Hamiltonian approach to wave-particle dynamics in a periodic structure. Europhys. Lett. 2018;122(4):44002. DOI: 10.1209/0295-5075/122/44002.
  51. Hairer E, Lubich C, Wanner G. Geometric Numerical Integration. Vol. 31. Springer-Verlag, Berlin, Heidelberg; 2006. P. 644. DOI: 10.1007/3-540-30666-8.
  52. Andre F, Racamier JC, Zimmermann R, Trung Le Q, Krozer V, Ulisse G, Minenna DFG, ´ Letizia R, Paoloni C. Technology, assembly, and test of a W-band traveling wave tube for new 5G high-capacity networks. IEEE Trans. Electron Devices. 2020;67(7):2919–2924. DOI: 10.1109/TED.2020.2993243.
  53. Bernardi P, Andre F, David JF, Le Clair A, Doveil F. Efficient time-domain simulation of a helix ´ traveling-wave tube. IEEE Trans. Electron Devices. 2011;58(6):1761–1767. DOI: 10.1109/TED.2011.2125793.
  54. Bernardi P, Andre F, David JF, Le Clair A, Doveil F. Control of the reflections at the terminations ´ of a slow wave structure in the nonstationary discrete theory of excitation of a periodic waveguide. IEEE Trans. Electron Devices. 2011;58(11):4093–4097. DOI: 10.1109/TED.2011.2163410.
  55. Bernardi P, Andre F, Bariou D., David JF, Le Clair A, Doveil F. Efficient 2.5-D nonstationary ´ simulations of a helix TWT. 2011 IEEE International Vacuum Electronics Conference (IVEC). 21–24 Feb. 2011, Bangalore, India. P. 307–308. DOI: 10.1109/IVEC.2011.5746998.
  56. Minenna DFG, Terentyuk AG, Elskens Y, Andre F, Ryskin NM. Recent discrete model for small- ´ signal analysis of traveling-wave tubes. Physica Scripta. 2019;94(5):055601. DOI: 10.1088/1402-4896/ab060e.
  57. Minenna DFG, Elskens Y, Andre F, Poy ´ e A, Puech J, Doveil F. DIMOHA: A time-domain ´ algorithm for traveling-wave tube simulations. IEEE Trans. Electron Devices. 2019;66(9): 4042–4047. DOI: 10.1109/TED.2019.2928450.
  58. Karetnikova TA, Rozhnev AG, Ryskin NM, Fedotov AE, Mishakin SV, Ginzburg NS. Gain analysis of a 0.2-THz traveling-wave tube with sheet electron beam and staggered grating slow wave structure. IEEE Trans. Electron Devices. 2018;65(6):2129–2134. DOI: 10.1109/TED.2017.2787960.
Received: 
23.12.2020
Accepted: 
30.12.2020
Published: 
01.02.2021
  • 3336 reads