Surface Electron Cyclotron X-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)


In this chapter electron surface cyclotron X-modes (SCX-modes) propagating along an interface perpendicular to the external magnetic field are investigated. Damping of these waves caused by plasma particle collisions both with each other and with the plasma boundary is studied. If there is no dielectric coating and the plasma has direct contact with the metal wall, the propagation of SCX-modes is unidirectional in the direction of electron gyration nearby the plasma–metal interface. The presence of the protective dielectric coating results in removing this unidirectionality and the surface electron cyclotron waves can propagate in both directions across the external magnetic field. The additional mode caused by the presence of the dielectric layer has a longer wavelength than the main mode. Parametric excitation of surface SCX-mode waves with both monochromatic and non-monochromatic pumping RF fields is investigated. An electrodynamic model of plasma sources sustained by SCX-mode waves is proposed. Increase in the magnitude of the external magnetic field results in larger discharge length and volume of the produced plasma. The dimensions of the uniform plasma space, which can be sustained in the gas discharge by the electron SCX-modes, are determined.


  1. 1.
    Bluyssen, H., Maan, J. C., Wyder, P., et al. (1975). Cyclotron resonance in an InAs-GaSb superlattice. Solid State Communications, 31(1), 35–38.ADSCrossRefGoogle Scholar
  2. 2.
    Maan, J. C., Guldner, Y., Vieren, J. P., et al. (1981). Three dimensional character of semimetallic InAs-GaSb superlattices. Solid State Communications, 39(5), 683–686.ADSCrossRefGoogle Scholar
  3. 3.
    Guldner, Y., Vieren, J. P., Voisin, P., et al. (1982). Observation of double cyclotron resonance and interband transitions in InAs-GaSb multi-heterojunctions. Solid State Communications, 41(6), 755–758.ADSCrossRefGoogle Scholar
  4. 4.
    Bass, F. G., Bulgakov, A. A., & Tetervov, A. P. (1989). High-frequency properties of semiconductors with superlattices. Moscow: Nauka. (in Russian).Google Scholar
  5. 5.
    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
  6. 6.
    Stix, T. H. (1990). Waves in plasmas: Highlight from the past and present. Physics of Fluids B, 2(8), 1729–1743.ADSCrossRefGoogle Scholar
  7. 7.
    Kaner, E. A. (1958). Theory of cyclotron resonance. Journal of Experimental and Theoretical Physics, 6(6), 1135–1138.ADSzbMATHGoogle Scholar
  8. 8.
    Kaner, E. A., & Skobov, V. G. (1967). Electromagnetic waves in metals in a magnetic field. Soviet Physics Uspekhi, 9(4), 480–503.ADSCrossRefGoogle Scholar
  9. 9.
    Vedenov, A. A. (1965). Solid state plasma. Physics-Uspekhi, 7(6), 809–822.MathSciNetCrossRefGoogle Scholar
  10. 10.
    Lifshits, I. M., Azbel, M., & Kaganov, M. I. (1973). Electron theory of metals. New York: Consultants Bureau.zbMATHGoogle Scholar
  11. 11.
    Steele, M., & Vural, B. (1969). Wave interactions in solid state plasmas. New York: McGraw Hill.zbMATHGoogle Scholar
  12. 12.
    Vladimirov, V. V., Volkov, A. F., & Meylikhov, Ye. Z. (1979). Plasma of semiconductors. Moscow: Atomizdat. (in Russian).Google Scholar
  13. 13.
    Platzman, P. M., & Wolff, P. A. (1973). Waves and interactions in solid state plasmas. New York: Academic Press.Google Scholar
  14. 14.
    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
  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.
    Damon, R. W., & Eshbach, J. R. (1961). Magnetostatic modes of a ferromagnetic slab. Journal of Physics and Chemistry of Solids, 19(3/4), 308–320.ADSCrossRefGoogle Scholar
  17. 17.
    Kaner, E. A., & Makarov, N. M. (1970). Theory of surface electromagnetic waves in metals located in a weak magnetic fieid. Soviet Physics JETP, 31(6), 1063–1070.ADSGoogle Scholar
  18. 18.
    Silin, V. P., & Tolkachev, O. M. (1978). Cyclotron resonance on the skipping orbits in an electron liquid. Soviet Physics JETP, 47(6), 1113–1121.ADSGoogle Scholar
  19. 19.
    Silin, V. P., & Tolkachev, O. M. (1980). Quantum theory of cyclotron resonance on sliding orbits near the frequencies of transitions between the levels of surface electrons in the degenerate electronic fluid. Fizika tverdogo tela, 22(2), 374–382. (in Russian).Google Scholar
  20. 20.
    Man’kov, Y. I. (1980). Longitudinal electromagnetic waves in a metal in inclined magnetic field nearby the cyclotron resonance. Fizika tverdogo tela, 22(2), 408–412. (in Russian).Google Scholar
  21. 21.
    Walsh, W. M., Platzman, J., & Platzman, P. M. (1965). Excitation of plasma waves near cyclotron resonance in potassium. Physical Review Letters, 15(20), 784–786.ADSCrossRefGoogle Scholar
  22. 22.
    Platzman, P. M., Walsh, W. M., & Foo, E.-N. (1968). Fermi-liquid effects on high-frequency wave propagation in simple metals. Physical Review, 172(3), 689–698.Google Scholar
  23. 23.
    Foo, E.-N. (1969). Dispersion of ordinary and extraordinary high-frequency waves in metals. Physical Review, 182(3), 674–678.Google Scholar
  24. 24.
    Kondratenko, A. N. (1979). Penetration of a field into plasmas. Moscow: Atomizdat. (in Russian).Google Scholar
  25. 25.
    Akhiezer, A. I., Akhiezer, I. A., Polovin, R. V., Sitenko, A. G., & Stepanov, K. N. (1975). Plasma electrodynamics. Oxford: Pergamon Press.Google Scholar
  26. 26.
    Lominadze, D. G. (1981). Cyclotron waves in plasma. Oxford: Pergamon Press.Google Scholar
  27. 27.
    Aleksandrov, A. F., Bogdankevich, L. S., & Rukhadze, A. A. (1984). Principles of plasma electrodynamics. Berlin: Springer.CrossRefGoogle Scholar
  28. 28.
    Kondratenko, A. N. (1976). Plasma waveguides. Moscow: Atomizdat. (in Russian).Google Scholar
  29. 29.
    Krall, N. A., & Trivelpiece, A. W. (1986). Principles of plasma physics. San Francisco: San Francisco Press.Google Scholar
  30. 30.
    Brambilla, M. (1998). Kinetic theory of plasma waves. Homogeneous plasmas. Oxford: Clarendon Press.Google Scholar
  31. 31.
    Girka, V. O., Kondratenko, A. M., & Pavlenko, I. V. (1993). Surface cyclotron waves in the planar metal waveguide with plasma filling. In Proceedings and Contributed Papers of International Conference “Physics in Ukraine” (pp. 108–110), Ukraine.Google Scholar
  32. 32.
    Girka, V. O., & Pavlenko, I. V. (1993). To the kinetic theory of surface waves at the plasma-metal interface. Ukrainain Journal of Physics, 38(4), 529–533. (in Russian).Google Scholar
  33. 33.
    Kondratenko, A. N. (1985). Surface and bulk waves in bounded plasmas. Moscow: Energoatomizdat. (in Russian).Google Scholar
  34. 34.
    Ginzburg, V. L., & Rukhadze, A. A. (1972). Waves in magnetoplasma. Heidelberg: Springer.Google Scholar
  35. 35.
    Sitenko, O. G., & Mal’nev, V. M. (1994). Principles of plasma theory. Kyiv: Naukova Dumka. (in Ukrainian).Google Scholar
  36. 36.
    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
  37. 37.
    Girka, V. A., Kondratenko, A. N., & Podobinski, V. O. (1981). Extraordinary surface cyclotron waves in semi-bonded plasma under the conditions of weak spatial dispersion. Ukrainain Journal of Physics, 26(4), 681–683. (in Russian).Google Scholar
  38. 38.
    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
  39. 39.
    Azarenkov, N. A., Girka, V. O., & Sporov, A. E. (1997). Surface cyclotron waves in a nonuniform plasma filled metal waveguide with dielectrical coating. Physica Scripta, 55, 339–344.ADSCrossRefGoogle Scholar
  40. 40.
    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
  41. 41.
    Silin, V. P. (1973). Parametric effect of high-intensity irradiation on plasmas. Moscow: Nauka. (in Russian).Google Scholar
  42. 42.
    Galeev, A. A., & Sagdeev, R. Z. (1973). Parametric phenomena in a plasma. Nuclear Fusion, 13(4), 603–621.CrossRefGoogle Scholar
  43. 43.
    Aliev, Y. M., Silin, V. P., & Watson, C. (1966). Parametric resonance in a plasma in a magnetic field. Soviet Physics JETP, 23(4), 626–632.ADSGoogle Scholar
  44. 44.
    Silin, V. P. (1967). Ion cyclotron instability of plasma in strong high frequency field. Soviet Physics Technical Physics, 37(5), 991–993. (in Russian).Google Scholar
  45. 45.
    Tzoar, N. (1969). Parametric excitation in plasma in a magnetic field. Physical Review, 178(1), 356–362.ADSCrossRefGoogle Scholar
  46. 46.
    Aliev, Y. M., & Zunder, D. (1970). Parametric excitation of upper and lower hybrid resonances. Soviet Physics JETP, 30(4), 718–720.ADSGoogle Scholar
  47. 47.
    Andreev, N. E., & Kiriy, A. Y. (1971). To the theory of plasma instability in HF electric and stationary magnetic fields. Soviet Physics Technical Physics, 41(6), 1080–1087. (in Russian).Google Scholar
  48. 48.
    Andreev, N. E. (1971). Parametric instability of a plasma in a constant magnetic field and a weak high-frequency electric field. Radiophysics and Quantum Electronics, 14(8), 909–914.ADSCrossRefGoogle Scholar
  49. 49.
    Aliev, Y. M., & Silin, V. P. (1973). Parametric effect on a plasma of high intensity irradiation near electron cyclotron frequencies. Soviet Physics Technical Physics, 17(1), 1752–1767.Google Scholar
  50. 50.
    Kitsenko, A. B., Panchenko, V. I., & Stepanov, K. N. (1973). Electron-acoustic and ion cyclotron parametric instabilities of a plasma in AC electric field. Soviet Physics Technical Physics, 43(7), 1426–1444. (in Russian).Google Scholar
  51. 51.
    Kitsenko, A. B., Lominadze, D. G., & Stepanov, K. N. (1974). The parametric excitation of the electron cyclotron oscillations of a plasma located in an alternating electric field. Soviet Physics JETP, 39(2), 294–298.ADSGoogle Scholar
  52. 52.
    Stepanov, K. N. (1996). Nonlinear parametric phenomena in plasma during radio frequency heating in the ion cyclotron frequency range. Plasma Physics and Controlled Fusion, 38, A13–A29.ADSCrossRefGoogle Scholar
  53. 53.
    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
  54. 54.
    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
  55. 55.
    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
  56. 56.
    Azarenkov, N. A., Kondratenko, A. N., & Ostrikov, K. N. (1990). Parametric excitation of surface waves at the plasma-metal interface. Soviet Physics Technical Physics, 69(1), 31–36. (in Russian).Google Scholar
  57. 57.
    Aliev, Y. M., & Ferlengi, E. (1970). Parametric excitation of surface oscillations of a plasma by an external high frequency field. Soviet Physics JETP, 30(5), 877–879.ADSGoogle Scholar
  58. 58.
    Aliev, Y. M., Gradov, O. M., & Kirii, A. Y. (1973). Kinetic theory of parametric excitation of surface waves in a semi-finite plasma. Soviet Physics JETP, 36(1), 59–63.ADSGoogle Scholar
  59. 59.
    Lovetski, E. E., & Starodub, A. N. (1974). Surface oscillations of magnetoactive plasma in high frequency field. Soviet Physics Technical Physics, 44(3), 508–513. (in Russian).Google Scholar
  60. 60.
    Dragila, R., & Vucovic, S. (1988). Excitation of surface waves by an electromagnetic wave packet. Physical Review Letters, 61(24), 2759–2761.ADSCrossRefGoogle Scholar
  61. 61.
    Aliev, Y. M., & Gradov, O. M. (1972). Parametric excitation of surface waves in nonuniform magnetized plasma. Soviet Physics Technical Physics, 42(11), 2447–2448. (in Russian).Google Scholar
  62. 62.
    Girka, V. A., & Lapshin, V. I. (1987). Parametric surface-wave excitation at the second harmonics of ion and electron cyclotron frequencies. Radiophysics and Quantum Electronics, 30(6), 544–547.ADSCrossRefGoogle Scholar
  63. 63.
    Girka, V. O., Girka, I. O., Kondratenko, A. M., et al. (1996). Surface electron cyclotron waves in the metallic waveguide structures with two component filling. Contributions to Plasma Physics, 36(6), 679–686.ADSCrossRefGoogle Scholar
  64. 64.
    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
  65. 65.
    Puzirkov, S. Y., Girka, V. O., & Lapshin, V. I. (1998). Parametric excitation of the surface cyclotron waves by nonmonochromatic electric field. In Proceedings of the 1998 International Conference on Mathematical Methods in Electromagnet. Theory (pp. 697–699), Ukraine.Google Scholar
  66. 66.
    Girka, V. O., Lapshin, V. I., & Puzirkov, S. Y. (1999). Parametric instability of surface type X-modes immersed into a nonmonochromatic pumping electric field. Contributions to Plasma Physics, 39(6), 487–494.ADSCrossRefGoogle Scholar
  67. 67.
    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.), Radiative processes in discharge plasmas. NATO ASI, Series B (Vol. 149, pp. 381–430).Google Scholar
  68. 68.
    Zhelyazkov, I., Atanasov, V., & Benova, E. (1986). In S. Vucovic (Ed.), Surface waves in plasmas and solids. Singapore: World Scientific.Google Scholar
  69. 69.
    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
  70. 70.
    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
  71. 71.
    Margot, J., & Moisan, M. (1991). Electromagnetic surface waves for a new approach to the investigation of plasmas produced at electron cyclotron resonance. Journal of Physics D: Applied Physics, 24(9), 1765–1788.Google Scholar
  72. 72.
    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
  73. 73.
    Girka, V. O. (1998). Theoretical model of a stationary low-pressure plasma source based on surface type X-mode. Physica Scripta, 58(4), 387–391.ADSCrossRefGoogle Scholar
  74. 74.
    Kortshagen, U., Schluter, H., & Shivarova, A. (1991). Determination of electron energy distribution functions in surface waves produced plasma: I. Modelling. Journal of Physics D: Applied Physics, 24, 6063–6078.Google Scholar
  75. 75.
    Shaing, K. C. (1996). Electron heating in inductively coupled discharges. Physics of Plasmas, 3(9), 3300–3303.ADSCrossRefGoogle Scholar
  76. 76.
    Turner, M. M. (1993). Collisionless electron heating in an inductively coupled discharge. Physical Review Letters, 71(12), 1844–1847.ADSCrossRefGoogle Scholar
  77. 77.
    Turner, M. M. (1995). Pressure heating of electrons in capacitively coupled RF discharges. Physical Review Letters, 75(7), 1312–1315.ADSCrossRefGoogle Scholar
  78. 78.
    Kortsgahen, U., Busch, C., & Tsendin, L. D. (1996). On simplifying approaches to the solution of the Boltzmann equation in spatially inhomogeneous plasma. Plasma Source Science and Technology, 5, 1–17.ADSCrossRefGoogle Scholar
  79. 79.
    Kolobov, V. I., & Godyak, V. A. (1995). Nonlocal electron kinetics in collisional gas discharge plasmas. IEEE Transactions on Plasma Science, 23(33), 503–531.ADSCrossRefGoogle Scholar
  80. 80.
    Tatarova, E., Dias, F. M., Ferreira, C. M., et al. (1997). Self-consistent kinetic model of a surface wave sustained discharge in nitrogen. Journal of Physics D: Applied Physics, 30(19), 2663–2676.Google Scholar
  81. 81.
    Chen, F. F. (1995). Industrial application of low-temperature plasma physics. Physics of Plasmas, 2(6), 2164–2175.ADSCrossRefGoogle Scholar
  82. 82.
    Chen, F. F. (1996). Physics of helicon discharges. Physics of Plasmas, 3(5), 1783–1790.ADSMathSciNetCrossRefGoogle Scholar

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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

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