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Magnetron Modes and the Chimera State

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Fractional Dynamics, Anomalous Transport and Plasma Science

Abstract

This paper reviews the magnetron electronic valve family development including the: the Barkhausen-Kurz oscillator, split-anode magnetron, cavity-magnetron, rising-sun cavity-magnetron, coaxial cavity-magnetron, relativistic cavity-magnetron and the packaged cavity-magnetron. The paper uses US magnetron patents and original peer-reviewed papers to provide a rich source of mathematical mode competition theory and lumped element equivalent electrical models. Synchronous and asynchronous modes are identified and quantified within the cavity-magnetron, rising-sun cavity-magnetron and relativistic cavity-magnetron. The military imperative (secrecy) that shaped magnetron development is also discussed. It is proposed that this knowledge may have a role in chaos theory when applied to natural and man-made coupled resonator networks.

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References

  1. N.F. Alekseev, D.D. Malairov, Generation of high-power oscillations with a magnetron in the centimeter band. J. Tech. Phys. (USSR) 10, 1297–1300 (1940)

    Google Scholar 

  2. J.T. Randell, H.A. Boot, High-frequency electrical oscillator. US 2,542,966 (issued Feb 20, 1951)

    Google Scholar 

  3. W.W. Hansen, R.D. Richtmeyer, On resonators suitable for klystron oscillators. J. Appl. Phys. 10, 189–199 (1939)

    Article  ADS  Google Scholar 

  4. W.W. Hansen, A type of electrical resonator. J. Appl. Phys. 9(10), 654–663 (1938)

    Article  ADS  Google Scholar 

  5. R.J. Collier, J. Feinstein, Magnetrons. US 2,854,603 (issued Sept 30, 1958)

    Google Scholar 

  6. J. Benford, H. Sze, W. Woo, R.R. Smith, B. Harteneck, Phase locking of relativistic magnetrons. Phys. Rev. Lett. 62(8), 969–971 (1989)

    Article  ADS  Google Scholar 

  7. Y. Shiyu, C. Jingzhong, T. Jianhui, L. Yaoting, A kind of magnetron cavity used in rubidium atomic frequency standards. J. Semicond. 32(12), 122001 (2011)

    Article  ADS  Google Scholar 

  8. C. Stefanucci, T. Bandi, F. Merli, M. Pellaton, C. Affolderbach, G. Mileti, A.K. Skrivervik, Compact microwave cavity for high performance rubidium frequency standards. Rev. Sci. Instrum. 83, 104706 (2012)

    Article  ADS  Google Scholar 

  9. R.G. Andrzejak, G. Ruzzene, I. Malvestio, Generalized synchronization between chimera states. Chaos 27, 053114 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  10. D. Dudkowski, Y. Maistrenko, T. Kapitaniak, Different types of chimera states: an interplay between spatial and dynamical chaos. Phys. Rev. E 90, 032920 (2014)

    Article  ADS  Google Scholar 

  11. V.J. Law, D.P. Dowling, Electronic valve instabilities and mode. CMSIM J. 1, 3–35 (2017)

    Google Scholar 

  12. R.G. Aandrezak. C. Rummel, F. Mormann, K. Schindler, All together now: analogies between chimera state collapses and epileptic seizures. Sci. Rep. 6, 23000 (2016)

    Google Scholar 

  13. M. Leconte, Statistical study of magnetron patents in the early years of electronics between 1920 and 1945; heuristic focusing around the discovery of the cavity magnetron, in Proceedings of CAVMAG 2010 (IEEE, 2010), pp. 11–16. https://doi.org/10.1109/cavmag.2010.5565570

  14. R.M. Page, The Origin of Radar (Anchor Books, Doubleday Garden City, New York, 1962), p. 66

    Google Scholar 

  15. Proceedings of the First International Workshop on Cross-field Devices, Michigan, USA, 15–16 Aug 1995

    Google Scholar 

  16. Proceedings of CAVMAG 2010, International Conference on the Origins and Evolution of the Cavity Magnetron, Bournemouth, UK, 19–20 Apr 2010

    Google Scholar 

  17. L. de Forest, Device for amplifying feeble electrical currents. U.S. 841,387 (issued Jan 15, 1907)

    Google Scholar 

  18. J.A. Fleming, On the conversion of electric oscillations into continuous currents by means of a vacuum valve. Proc. R. Soc. Lond. 74, 476–487 (1904–1905)

    Google Scholar 

  19. J.A. Fleming, Instrument for converting alternating electric currents into continuous currents. US. 803,684 (issued Nov 7, 1905)

    Google Scholar 

  20. E.W. Armstrong, Some recent development in the audion receiver. Proc. IEEE 3(3), 215–247 (1915)

    Google Scholar 

  21. E.W. Armstrong, Some recent development in the audion receiver. Reprinted in Proc. IEEE. 85(4), 658–697 (1997)

    Google Scholar 

  22. E.V. Appleton, M.A.R. Barnett, On some direct evidence for downward atmospheric reflection of electric rays. Proc. R. Soc. Lond. A 109(752), 621–641 (1925)

    Article  ADS  Google Scholar 

  23. I. Langmuir, The effect of space charge and residual gases on thermionic currents in high vacuum. Phys. Rev. 2(6), 450–486 (1913)

    Article  ADS  Google Scholar 

  24. H.G. Barkhaushe, K. Kurz, Die kurzesten, in Vakuumrohren herstellbaren Wellen. Phys. Ztg. 21, 1–6 (1920)

    Google Scholar 

  25. A.W. Hull, The magnetron. JAIEE 40(9), 715–723 (1921)

    Google Scholar 

  26. N.A. Žáček, New method of generating undamped oscillations. J. Cultivation Math. Phys. 53, 378–380 (1924)

    Google Scholar 

  27. E. Habann, Eine neue generatorröhr. Z. Hochfrequenztechnik 24, 115–120 and 135–141 (1924)

    Google Scholar 

  28. K. Okabe, Production of intense extra-short radio waves by a split-anode magnetron. JIEEJ 48(474), 284–290 (1928)

    Google Scholar 

  29. K. Posthumus, Oscillations in a split anode magnetron. Wirel. Eng. 12, 126–132 (1935)

    Google Scholar 

  30. V.J. Law, Plasma harmonic and overtone coupling, in Handbook of Applications of Chaos theory, Chap. 20, ed. by C.H. Skiadas, C. Skiadas (Chapman and Hall/CRC Press, Taylor and Frances, 2016), pp. 405–422. ISBN-10: 1466590432

    Google Scholar 

  31. E.W. Gill, K.G. Britton, The action of a split-anode magnetron. JIEE 11(32), 127–134 (1936)

    Google Scholar 

  32. Discussion on the action of a split-anode magnetron. JIEE 9(476), 224–226 (1936)

    Google Scholar 

  33. G. Heller, The magnetron as a generator of ultra short waves. Philips Tech. Rev. 4(7), 89–197 (1939)

    Google Scholar 

  34. H.E. Hollmann, Magnetron. US. 2,123,728 (issued July 12, 1938)

    Google Scholar 

  35. A.L. Samuel, Electron discharge device. US. 2,063,342 (issued Dec 8, 1936)

    Google Scholar 

  36. E.C.S. Megaw, The high-power pulsed magnetron: a review of early developments. JIEE Part IIIA Radiolocation 93(5), 977–984 (1946)

    Article  Google Scholar 

  37. J. Barbeen, W.H. Brattain, The transistor, a semi-conductor triode. Phys. Rev. 74, 230–231 (1948)

    Article  ADS  Google Scholar 

  38. K. Nosich, I.A. Tishchenko, Development of the first soviet three-coordinate L-band pulsed radar in kharkov before WWII. IEEE Antennas Propag. Mag. 4(3), 29–48 (2001)

    Google Scholar 

  39. M. Elie, H. Gutton, J.H. Jean, M. Ponte, Détection d’obstacles à la navigation sans visibilité [Detection of obstacles in blind navigation]. Bulletin de la Société Française des Electriciens. 5ème série tome IX(100), 345–353 (1939)

    Google Scholar 

  40. M. Elie, H. Gutton, J.H. Jean, M. Ponte, System for object detection and distance measurement. US 2433838 (issued Jan 6, 1948)

    Google Scholar 

  41. K. Shimoda, Theory of split-anode magnetrons by Sin-itiro Tomonaga. AAPPS Bull. 16(2), 17–22 (2006)

    Google Scholar 

  42. S. Nakajima, Japanese radar development prior to 1945. IEEE Antennas Propag. Mag. 34(6), 17–22 (1992)

    Article  Google Scholar 

  43. R.E. Edwards, Historical perspective on magnetron development, in Proceedings of the First International Workshop on Cross-Field Devices, Michigan, USA (1995), pp. 41–50

    Google Scholar 

  44. K. Frizz, Magnetron. US. 2,111,263 (issued Mar 15, 1938)

    Google Scholar 

  45. H. Gutton, S. Berline, Magnetron oscillator and detector. US. 2,147,159 (issued Feb 14, 1939)

    Google Scholar 

  46. A.A. Siddiqi, The Rockets’ Red Glare: technology, conflict, and terror in the soviet union. Technol. Cult. 4(3), 470–501 (2003)

    Article  Google Scholar 

  47. N.F. Alekseev, D.D. Malairov, I.B. Bensen, Generation of high-power oscillations with a magnetron in the centimeter band. Proc. IRE 32, 136–139 (1944)

    Article  Google Scholar 

  48. H.A.H. Boot, J.T. Randall, Historical notes on the cavity magnetron. IEEE Trans. Electron Devices 23(7), 724–729 (1976)

    Article  ADS  Google Scholar 

  49. R.H. Varian, S.F. Varian, A high frequency oscillator and amplifier. J. Appl. Phys. 10, 321–327 (1939)

    Article  ADS  Google Scholar 

  50. R.W. Burns, Communications: an international history of the formative years. Chap 22 (IEE, London, UK, 2004), pp, 592–593. ISBN 0863413307

    Google Scholar 

  51. W.W. Hansen. High efficiency resonant circuit. US 2,190,712 (issued Feb, 1940)

    Google Scholar 

  52. Y. Blanchard, G. Galati, P. van Genderen, The cavity magnetron: not just a british invention. IEEE Antennas Propag. Mag. 55(5), 244–254 (2013)

    Article  ADS  Google Scholar 

  53. A.E. Austin, Precursors to radar—the Watson-Watt Memorandum and the Daventry experiment. IJEEE 36, 365–372 (1999)

    Google Scholar 

  54. W. Froncisz, J.S. Hyde, Microwave resonator. US 4,446,429 (issued May 1, 1984)

    Google Scholar 

  55. D.R. Hartree, Mode selection in a magnetron by a modified resonance criterion. CVD Report Mag. 17 (Manchester University)

    Google Scholar 

  56. V.J. Law, S.D. Anghel, Compact atmospheric pressure plasma self-resonant drive circuits. J. Phys. D Appl. Phys. 45(7), 075202 (2012)

    Article  ADS  Google Scholar 

  57. R.H. Levy, Two new results in cylindrical diocotron theory. Phys. Fluids 11(4), 920–921 (1968)

    Article  ADS  Google Scholar 

  58. K.S. Fine, Simple theory of a nonlinear diocotron mode. Phys. Fluids B4(12), 3981–3984 (1992)

    Article  ADS  Google Scholar 

  59. S. Riyopoulos, Magnetron instability in the low-space-charge limit. Phys Rev. Letts. 81(14), 3026–3029 (1998)

    Article  ADS  Google Scholar 

  60. R.I. Wilkinson, Short survey of Japanese radar-I. Electr. Eng. 65, 455–463 (1946)

    Article  Google Scholar 

  61. R.I. Wilkinson, Short survey of Japanese radar-II. Electr. Eng. 65, 370–377 (1946)

    Article  Google Scholar 

  62. H. Döring, Microwave tube development in Germany from 1920–1945. Int. J. Electron. 70(5), 955–978 (1991)

    Article  ADS  Google Scholar 

  63. G. Galati, On the Italian contribution to radar, in European Radar Conference (EuRAD) (2014), pp. 37–40

    Google Scholar 

  64. P.L. Spencer, Electron discharge device. US. 2,466,060 (issued Apr 5, 1949)

    Google Scholar 

  65. J. Sayers, High-frequency electrical oscillator. US 2,546,870 (issued Mar 27, 1951)

    Google Scholar 

  66. E.C. Okress, R.R. Reed, Echelon strapping system. US. 2,785,340 (issued Mar 12, 1957)

    Google Scholar 

  67. W.J. Dodds, Electron discharge device of the cavity resonator type. US. 2,607,019 (issued Aug 12, 1952)

    Google Scholar 

  68. A.A. Flowers, System for automatically aging of magnetrons and suppression of arcing thereof. US. 2,804,365 (issued Aug 27, 1957)

    Google Scholar 

  69. P.L. Spencer, Method of treating foodstuffs. US. 2495429 (issued. Jan 24, 1950)

    Google Scholar 

  70. J.F. Corbani, Cathode sputtering apparatus. US. 3,878,085 (issued Apr 5, 1975)

    Google Scholar 

  71. K. Suzuki, et al., Plasma etch device. US. 4,101,411 (issued Jul 18, 1978)

    Google Scholar 

  72. A. Ribner, Microwave plasma etching machine and method of etching. US 4,804,431 (issued Feb 14, 1989)

    Google Scholar 

  73. V.J. Law, D. Tait, Microwave plasma cleaning of ion implant ceramic insulators. Vacuum 49(4), 273–278 (1998)

    Article  Google Scholar 

  74. S. Millman, A.T. Nordsieck, The rising sun magnetron. J. Appl. Phys. 19, 156–165 (1948)

    Article  ADS  Google Scholar 

  75. N.M. Kroll, W.E. Lamb Jr., The resonant modes of the rising sun and other unstrapped magnetron. J. Appl. Phys. 19, 166–186 (1948)

    Article  ADS  Google Scholar 

  76. A.V. Hollenberg, N. Kroll, S. Millman, Rising sun magnetrons with large numbers of cavities. J. Appl. Phys. 19, 624–635 (1948)

    Article  ADS  Google Scholar 

  77. R.R. Moats, Interaction of modes in magnetron oscillators. Ph.D. Thesis, MIT, 1950

    Google Scholar 

  78. B. Van de Pol, On oscillation hysteresis in a triode generator with two degrees of freedom. Philos. Mag. 4, 700–719 (1922)

    Google Scholar 

  79. D.C. Buck, Ferrite tuned coaxial magnetron. US. 3,333,148 (issued Dec 12, 1967)

    Google Scholar 

  80. D.E. Blank, G. Thornber, P. Wyann, Tunable coaxial magnetron. US. 3,590,312 (issued Jun 29, 1971)

    Google Scholar 

  81. G. Bekefi, T.J. Orzechowaski, Giant microwave bursts emitted from a field-emission, relativistic-electron beam magnetron. Phys. Rev. Lett. 37(6), 379–381 (1976)

    Article  ADS  Google Scholar 

  82. G. Bekefi, T.J. Orzechowaski, Relativistic electron beam cross-field device. US. 4,200,821 (issued Apr 29, 1980)

    Google Scholar 

  83. A. Palevsky, G. Bekefi, Microwave emission from pulsed, relativistic e-beam diodes. II. The multiresonator magnetron. Phys. Fluids. 22, 986–996 (1979)

    Article  ADS  Google Scholar 

  84. H.-W. Chen, C. Chen, R.C. Davidson, Numerical study of relativistic magnetrons. J. Appl. Phys. 73(11), 7053–7060 (1993)

    Article  ADS  Google Scholar 

  85. A.D. Andreev, K.J. Hendricks, First multi-cavity magnetrons were built in NII-9, Leningrad during the spring of 1937 PIC Simulations of the First 4-Cavity S-Band CW Magnetron (2010). https://doi.org/10.1109/cavmag.2010.5565560

  86. V.J. Law, Knowledge domain information and the impact on process control. IUVSTA #49 Workshop, Dublin City University, Ireland, 4–6 Sept 2006. CD-rom published by the organizing Committee

    Google Scholar 

  87. A. Pagliarani, A.J. Kenyon, N.F. Thornhill, E. Sirisena, K. Lee, V.J. Law, Process harmonic pulling in a RIE plasma-tool. Electron. Lett. 42(2), 120–121 (2006)

    Article  Google Scholar 

  88. V.J. Law, Process induced oscillator frequency pulling and phase noise within plasma systems. Vacuum 82(6), 630–638 (2008)

    Article  ADS  Google Scholar 

  89. V.J. Law, N. Macgearailt, Visualization of a dual frequency plasma etch process. Meas. Sci. Technol. 18(3), 645–649 (2007)

    Article  ADS  Google Scholar 

  90. H.W. Welch, W.G. Dow, Analysis of synchronous conditions in the cylindrical magnetron space charge. J. Appl. Phys. 22(4), 433–438 (1951)

    Article  ADS  Google Scholar 

  91. J.L. Stewart, Theory of frequency modulation noise in tubes employing phase focusing. J. App. Phys. 26(4), 409–413 (1955)

    Article  ADS  Google Scholar 

  92. T. Mitani, N. Shinohara, H. Matsumoto, K. Hashimoto, Improvement of spurious noises generated from magnetrons driven by DC power supply after turning off filament current. IEICE Trans. Electron. E86-C(8), 1556–1563 (2003)

    Google Scholar 

  93. V.B. Neculaes, R.M. Gilgenbach, Y.Y. Lau, M.C. Jones, W.M. White, Low-noise microwave oven magnetrons with fast start-oscillation by azimuthally varying axial magnetic fields. IEEE Trans. Plasma Sci. 32(3), 1152–1159 (2004)

    Article  ADS  Google Scholar 

  94. T. Mitani, N. Shinohara, H. Matsumoto, M. Aiga, N. Kuwahara, T. Ishii, Noise-reduction effects of oven magnetron with cathode shield on high-voltage input side. IEEE Trans. Electron Devices 53(8), 1929–1935 (2006)

    Article  ADS  Google Scholar 

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Acknowledgements

The authors would like to acknowledge support of the SFI funded I-Form Advanced Manufacturing Research Centre.

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Law, V.J., Dowling, D.P. (2018). Magnetron Modes and the Chimera State. In: Skiadas, C. (eds) Fractional Dynamics, Anomalous Transport and Plasma Science. Springer, Cham. https://doi.org/10.1007/978-3-030-04483-1_2

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