Surface Electron Cyclotron O-Mode Waves

  • Volodymyr GirkaEmail author
  • Igor Girka
  • Manfred Thumm
Part of the Springer Series on Atomic, Optical, and Plasma Physics book series (SSAOPP, volume 107)


This chapter complements the previous studies by investigating the possibility of surface electron cyclotron O (SCO)-mode wave propagation. The external stationary magnetic field is assumed to be oriented parallel to the plasma interface. SCO-modes can propagate in the plasma–dielectric–metal structures at the harmonics of the electron cyclotron frequency. Change in the direction of the external static magnetic field does not influence their dispersion properties unlike in the case of SCX-modes. As in the case of SCTM-modes, decrease of the thickness of the dielectric coating (or increase of the dielectric constant of this coating) results in worsening the conditions for SCO-mode excitation. Electron beam excitation of SCO-modes is studied theoretically for two scenarios: resonant beam-plasma and beam-dissipative instabilities. In the range of long wavelengths (compared to Larmor radius), the growth rates of SCO-modes are larger than those of SCX-modes. In addition, the electrodynamic model of a stationary gas discharge, which is sustained by SCO-modes, is constructed in this chapter. The dimensions of the uniform plasma region are calculated for different discharge conditions. Increase of the external static magnetic field is found to increase the discharge length and volume. The discharge length increases as well with increasing SCO-mode wavelength.


  1. 1.
    Aleksandrov, A. F., Bogdankevich, L. S., & Rukhadze, A. A. (1984). Principles of plasma electrodynamics. Berlin: Springer.CrossRefGoogle Scholar
  2. 2.
    Kondratenko, A. N. (1976). Plasma waveguides. Moscow: Atomizdat. (in Russian).Google Scholar
  3. 3.
    Kondratenko, A. N. (1979). Penetration of a field into plasmas. Moscow: Atomizdat. (in Russian).Google Scholar
  4. 4.
    Kondratenko, A. N. (1985). Surface and bulk waves in bounded plasmas. Moscow: Energoatomizdat. (in Russian).Google Scholar
  5. 5.
    Beletski, N. N., Bulgakov, A. A., Khankina, S. I., & Iakovenko, V. M. (1984). Plasma instabilities and non-linear phenomena in semi-conductors. Kyiv: Naukova Dumka. (in Russian).Google Scholar
  6. 6.
    Vandenplas, P. E. (1968). Electron waves and resonances in bounded plasmas. London, N.Y.: Interscience Publishers.Google Scholar
  7. 7.
    Azarenkov, N. A., Kondratenko, A. N., & Ostrikov, K. N. (1993). Surface waves in plasma-metal structures. Radiophysics and Quantum Electronics, 36(5), 213–247.ADSCrossRefGoogle Scholar
  8. 8.
    Beletski, N. N., Svetlichnyj, V. M., Khalamejda, D. D., & Iakovenko, V. M. (1991). Electromagnetic phenomena in HF range in inhomogeneous semi-conductor structures. Kyiv: Naukova Dumka. (in Russian).Google Scholar
  9. 9.
    Ganguli, A., Akhtar, M. K., & Tarey, R. D. (1998). Theory of high-frequency guided waves in a plasma-loaded waveguide. Physics of Plasmas, 5(5), 1178–1189.ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    Kaner, E. A., & Skobov, V. G. (1967). Electromagnetic waves in metals in a magnetic field. Soviet Physics Uspekhi, 9(4), 480–503.ADSCrossRefGoogle Scholar
  11. 11.
    Vedenov, A. A. (1965). Solid state plasma. Physics-Uspekhi, 7(6), 809–822.MathSciNetCrossRefGoogle Scholar
  12. 12.
    Lifshits, I. M., Azbel, M., & Kaganov, M. I. (1973). Electron theory of metals. New York: Consultants Bureau.zbMATHGoogle Scholar
  13. 13.
    Steele, M., & Vural, B. (1969). Wave interactions in solid state plasmas. New York: McGraw Hill.zbMATHGoogle Scholar
  14. 14.
    Vladimirov, V. V., Volkov, A. F., & Ye Meylikhov, Z. (1979). Plasma of semiconductors. Moscow: Atomizdat. (in Russian).Google Scholar
  15. 15.
    Dmitruk, N. L., Litovchenko, V. G., & Strizhevskiy, V. L. (1989). Surface polaritons in semiconductors and dielectrics. Kiev: Naukova Dumka. (in Russian).Google Scholar
  16. 16.
    Platzman, P. M., & Wolff, P. A. (1973). Waves and interactions in solid state plasmas. New York: Academic Press.Google Scholar
  17. 17.
    Bass, F. G., Bulgakov, A. A., & Tetervov, A. P. (1989). High-frequency properties of semiconductors with superlattices. Moscow: Nauka. (in Russian).Google Scholar
  18. 18.
    Nikitin, A. K., & Tishchenko, A. A. (1983). Surface electromagnetic waves and their application. Zarubezhnaya elektronika, 3, 38–55.Google Scholar
  19. 19.
    Wallis, R. F. (1972). Theory of surface magnetoplasmons in semiconductors. Physical Review Letters, 28(22), 1455–1458.ADSCrossRefGoogle Scholar
  20. 20.
    Bajbakov, V. I., & Datsko, V. N. (1981). Propagation of surface magneto-plasma waves in a semiconductor. Fizika i tehnika poluprovodnikov, 15(11), 2261–2263. (in Russian).Google Scholar
  21. 21.
    Brazis, R. S. (1981). Active and nonlinear interactions at the excitation of plasma-like polaritons in semiconductors. Litovskiy Fizicheskiy Sbornik, 21(4), 73–117. (in Russian).Google Scholar
  22. 22.
    Prozorovski, V. D., & Ocheret’ko, V. I. (1990). Determining the zonal and kinetic parameters of semiconductors with the help of magnetoplasma waves. Zhurnal Tehnicheskoj Fiziki, 60(2), 192–195. (in Russian).Google Scholar
  23. 23.
    Vukovic, S. (Ed.) (1986). Surface waves in plasmas and solids. Singapore: World Scientific.Google Scholar
  24. 24.
    Azarenkov, N. A., & Ostrikov, K. N. (1999). Surface magnetoplasma waves at the interface between a plasma-like medium and a metal in a Voigt geometry. Physics Reports, 308, 333–428.ADSCrossRefGoogle Scholar
  25. 25.
    Moisan, M., & Zakrzewski, Z. (1986). Plasmas sustained by surface waves at microwave and RF frequencies: Experimental investigation and applications. In J. M. Proud & L. H. Luessen (Eds.), NATO Advanced Study Institute, Series B: Physics: Vol. 149. Radiative processes in discharge plasmas (pp. 381–430).Google Scholar
  26. 26.
    Zhelyazkov, I., Atanasov, V., & Benova, E. (1986). Axial structure of a plasma column produced by a large-amplitude electromagnetic surface wave. In S. Vucovic (Ed.), Surface waves in plasmas and solids (pp. 467–489). Singapore: World Scientific.Google Scholar
  27. 27.
    Ferreira, C. M., & Moisan, M. (1993). Microwave discharges: Fundamentals and applications. In NATO Advanced Study Institute, Series B: Physics: Vol. 302 (pp. 187–544).Google Scholar
  28. 28.
    Zhelyazkov, I., & Atanasov, V. (1995). Axial structure of low-pressure high-frequency discharges sustained by travelling electromagnetic surface waves. Physics Reports, 255, 79–201.ADSCrossRefGoogle Scholar
  29. 29.
    Nonaka, S. (1992). Mode identification of electromagnetic waves for large-area planar RF plasma productions. Journal of the Physical Society of Japan, 61(5), 1449–1452.ADSCrossRefGoogle Scholar
  30. 30.
    Nonaka, S. (1994). Proposal of non-cylindrical and large-area RF plasma production by surface waves. Journal of the Physical Society of Japan, 63, 3185–3186.Google Scholar
  31. 31.
    Nonaka, S. (1994). Very long and large-area RF plasma production by odd surface waves for online mass production of amorphous silicon solar cells or mirrors. Japanese Journal of Applied Physics, 33, 4226–4231.ADSCrossRefGoogle Scholar
  32. 32.
    Margot, J., & Moisan, M. (1992). Surface wave sustained plasmas in static magnetic fields for study of ECR discharge mechanisms. In M. Moisan & J. Pelletier (Eds.), Microwave exited plasmas (pp. 229–48). Amsterdam: Elsevier.Google Scholar
  33. 33.
    Moisan, M., & Zakrzewski, Z. (1986). Surface wave discharges in trapped tubes. In S. Vukovic (Ed.), Surface waves in plasmas and solids (pp. 605–608). Singapore: World Scientific.Google Scholar
  34. 34.
    Longinov, A. V., & Stepanov, K. N. (1992). Radio-frequency plasma heating in tokamaks in the ion-cyclotron frequency range. In A. G. Litvak (Ed.), High-frequency plasma heating (pp. 93–237). New York: AIP.Google Scholar
  35. 35.
    Becoulet, A. (1996). Heating and current drive regimes in the ion cyclotron range of frequency. Plasma Physics and Controlled Fusion, 38(12A), 1–12.ADSCrossRefGoogle Scholar
  36. 36.
    Laqua, H. P., Erckmann, V., Hartfuβ, H. J., et al. (1996). Resonant and non-resonant electron cyclotron heating at densities above the plasma cut-off by O–X–B mode conversion at W7-AS. In 23rd European Physical Society Conference on Controlled Fusion and Plasma Physics (pp. 847–850), Ukraine.Google Scholar
  37. 37.
    Grigor’eva, L. I., Smerdov, B. I., Stepanov, K. N., et al. (1970). Plasma instability in a strong alternating electric field. Soviet Physics JETP, 31(1), 26–28.ADSGoogle Scholar
  38. 38.
    Korzh, A. F., & Stepanov, K. N. (1988). Parametric instability of plasma in electric field of two pumping waves. Fizika Plazmy, 14(6), 698–705. (in Russian).Google Scholar
  39. 39.
    Akhiezer, A. I., Akhiezer, I. A., Polovin, R. V., Sitenko, A. G., & Stepanov, K. N. (1975). Plasma electrodynamics. Oxford: Pergamon Press.Google Scholar
  40. 40.
    Ginzburg, V. L., & Rukhadze, A. A. (1972). Waves in magnetoplasma. Heidelberg: Springer.Google Scholar
  41. 41.
    Lominadze, D. G. (1981). Cyclotron waves in plasma. Oxford: Pergamon Press.Google Scholar
  42. 42.
    Sitenko, O. G., & Mal’nev, V. M. (1994). Principles of plasma theory. Kyiv: Naukova Dumka. (in Ukrainian).Google Scholar
  43. 43.
    Gross, E. P. (1951). Plasma oscillations in a static magnetic field. Physical Review, 82(2), 232–242.ADSMathSciNetCrossRefGoogle Scholar
  44. 44.
    Sen, H. K. (1952). Solar “enhanced radiation” and plasma oscillations. Physical Review, 88(4), 816–822.ADSCrossRefGoogle Scholar
  45. 45.
    Sitenko, A. G., & Stepanov, K. N. (1957). On the oscillations of an electron plasma in a magnetic field. Soviet Physics JETP, 4(4), 512–520.MathSciNetzbMATHGoogle Scholar
  46. 46.
    Bernstein, J. B. (1958). Waves in a plasma in a magnetic field. Physical Review, 109(1), 10–21.ADSMathSciNetCrossRefGoogle Scholar
  47. 47.
    Drummond, W. E., & Rosenbluth, M. N. (1962). Anomalous diffusion arising from microinstabilities in a plasma. Physics of Fluids, 5(12), 1507–1513.ADSCrossRefGoogle Scholar
  48. 48.
    Stix, T. H. (1990). Waves in plasmas: Highlight from the past and present. Physics of Fluids B, 2(8), 1729–1743.ADSCrossRefGoogle Scholar
  49. 49.
    Azbel, M. I., & Kaner, E. A. (1957). Theory of cyclotron resonance in metals. Soviet Physics JETP, 5(4), 730–744.zbMATHGoogle Scholar
  50. 50.
    Kaner, E. A. (1958). Cyclotron resonance in plasma. Soviet Physics JETP, 6(2), 425–427.ADSzbMATHGoogle Scholar
  51. 51.
    Kaner, E. A. (1958). Theory of cyclotron resonance. Journal of Experimental and Theoretical Physics, 6(6), 1135–1138.ADSzbMATHGoogle Scholar
  52. 52.
    Girka, V. O. (2000). Propagation of the surface cyclotron O-modes at harmonics of ion and electron cyclotron frequencies. Plasma Physics and Controlled Fusion, 42, 999–1011.ADSCrossRefGoogle Scholar
  53. 53.
    Abramowitz, M., & Stegun, I. A. (1964). Applied Mathematics, Series 55. Handbook of mathematical functions. New York: National Bureau of Standards.Google Scholar
  54. 54.
    Girka, V. O., Girka, I. O., & Pavlenko, I. V. (1997). HF surface cyclotron waves in planar waveguide structures with nonuniform plasma filling. Journal of Plasma Physics, 58(1), 31–39.ADSCrossRefGoogle Scholar
  55. 55.
    Azarenkov, N. A., Girka, V. A., & Sporov, A. E. (1997). Ion cyclotron surface waves at the plasma-metal interface. Plasma Physics Reports, 23(3), 231–236.ADSGoogle Scholar
  56. 56.
    Azarenkov, N. A., Girka, V. O., Kondratenko, A. M., et al. (1997). Surface waves on the harmonics of the electron cyclotron frequency propagating along a plasma–metal interface. Plasma Physics and Controlled Fusion, 39, 375–388.ADSCrossRefGoogle Scholar
  57. 57.
    Girka, V., Girka, I., Pavlenko, I., et al. (1996). Surface ion cyclotron propagation as a possible cause of plasma contamination during ion cyclotron resonance heating. In Book of Abstracts 12-th International Conference on Plasma Surface Interactions in Controlled Fusion Devices (pp. 199), France.Google Scholar
  58. 58.
    Dnestrovskii, Y. N., & Kostomarov, D. P. (1961). Electromagnetic waves in a half-space filled with a plasma. Soviet Physics JETP, 12(3), 587–591.MathSciNetGoogle Scholar
  59. 59.
    Arsenin, V. Y. (1963). On the absorption of an electromagnetic wave incident upon the plasma halfspace. Izvestiya Vysshikh Uchebnykh Zavedenii Radiofizika, 6, 457–460. (in Russian).zbMATHGoogle Scholar
  60. 60.
    Bogomolov, Y. V. (1970). On the absorption of an electromagnetic wave in a bounded magnetically active plasma. Radiophysics and Quantum Electronics, 13(10), 1147–1151.ADSCrossRefGoogle Scholar
  61. 61.
    Meierovich, B. E. (1970). Influence of the sample surface on the cyclotron resonance in metals. Soviet Physics JETP, 31(1), 175–180.ADSGoogle Scholar
  62. 62.
    Girka, V. O. (1998). Excitation of the surface type X-modes by charged particles beams. Journal of Plasma Physics, 60(2), 413–420.ADSCrossRefGoogle Scholar
  63. 63.
    Girka, V. O. (1984). Surface cyclotron waves in plasmas. Thesis for awarding candidate of sciences degree in Physics and Mathematics, Kharkiv State University, Ukraine. (in Russian).Google Scholar
  64. 64.
    Girka, V. A., & Kondratenko, A. N. (1982). Excitation of surface ion-cyclotron waves in a gyrotropic plasma by charged-particle beams. Radiotekhnika i Elektronika, 27(3), 534–539. (in Russian).ADSGoogle Scholar
  65. 65.
    Girka, V. A., & Kondratenko, A. N. (1982). Excitation of surface cyclotron waves in a solid state plasma by charged-particle beams. Zhurnal Tehnicheskoj Fiziki, 52(8), 1521–1525. (in Russian).ADSGoogle Scholar
  66. 66.
    Girka, V. A., & Peneva, J. K. (1982). Excitation of surface cyclotron waves in a plasma slab. Ukrainskij Fizicheskij Zhurnal, 27(8), 1246–1247. (in Russian).Google Scholar
  67. 67.
    Girka, V. O., Kondratenko, A. M., & Peneva, J. K. (1982). Surface cyclotron waves. In Proceeding Conference on Surface Waves in Plasmas (pp. 366–369), Bulgaria.Google Scholar
  68. 68.
    Girka, V. O. (2002). Excitation of surface cyclotron O modes by charged-particle beams. Journal of Plasma Physics, 68(2), 129–136.ADSCrossRefGoogle Scholar
  69. 69.
    Hiyamay, S., Onoz, T., Iizukaz, S., et al. (1996). Wide-area uniform plasma processing in an ECR plasma. Plasma Sources Science and Technology, 5, 299–304.ADSCrossRefGoogle Scholar
  70. 70.
    Miyazaway, W., Taday, S., Itoy, K., et al. (1996). A large-area ECR processing plasma. Plasma Sources Science and Technology, 5, 265–267.ADSCrossRefGoogle Scholar
  71. 71.
    Ganguli, A., Akhtar, M. K., & Tarey, R. D. (1999). Investigation of microwave plasmas produced in a mirror machine using ordinary-mode polarization. Plasma Sources Science and Technology, 8, 519–529.ADSCrossRefGoogle Scholar
  72. 72.
    Girka, V. O. (2001). Application of electron cyclotron surface modes to solids processing. Physica Scripta, 63, 484–490.ADSCrossRefGoogle Scholar
  73. 73.
    Girka, V. O., & Denysenko, I. B. (2000). Propagation of the surface cyclotron O-modes and their application for sustaining of microwave gas discharges. In Proceedings of the International Congress on Plasma Physics ICPP-2000 (Vol. 1, pp. 9–12), Canada.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Physics and TechnologyV.N. Karazin Kharkiv National UniversityKharkivUkraine
  2. 2.School of Physics and TechnologyV.N. Karazin Kharkiv National UniversityKharkivUkraine
  3. 3.Institute for Pulsed Power and Microwave Technology and Institute of Radio Frequency Engineering and ElectronicsKarlsruhe Institute of TechnologyKarlsruheGermany

Personalised recommendations