Space Science Reviews

, Volume 121, Issue 1–4, pp 287–297 | Cite as

Absolute and Convective Instabilities of Circularly Polarized Alfvén Waves

Session IV: Basic Processes in Astrophysical and Space Plasmas


We discuss the recent progress in studying the absolute and convective instabilities of circularly polarized Alfvén waves (pump waves) propagating along an ambient magnetic field in the approximation of ideal magnetohydrodynamics (MHD). We present analytical results obtained for pump waves with small dimensionless amplitude a, and compare them with numerical results valid for arbitrary a. The type of instability, absolute or convective, depends on the velocity U of the reference frame where the pump wave is observed with respect to the rest plasma. One of the main results of our analysis is that the instability is absolute when U l < U < U r and convective otherwise. We study the dependences of U l and U r on a and the ratio of the sound speed to the Alfvén speed b. We also present the results of calculation of the increment of the absolute instability on U for different values of a and b. When the instability is convective (U < U l or U > U r) we consider the signalling problem, and show that spatially amplifying waves exist only when the signalling frequency is in two symmetric frequency bands. Then, we write down the analytical expressions determining the boundaries of these frequency bands and discuss how they agree with numerically calculated values. We also present the dependences of the maximum spatial amplification rate on U calculated both analytically and numerically. The implication of the obtained results on the interpretation of observational data from space missions is discussed. In particular, it is shown that circularly polarized Alfvén waves propagating in the solar wind are convectively unstable in a reference frame of any realistic spacecraft.


MHD plasma solar wind stability waves 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bers, A.: 1973, in: Auer, G. and Cap, F. (eds.), Survey Lectures, Proc. Int. Congr. Waves and Instabilities in Plasmas, Institute for Theoretical Physics, Insbruck, Austria, p. B1.Google Scholar
  2. Brevdo, L.: 1988, Geophys. Astrophys. Fluid Dyn. 40, 1.MATHMathSciNetCrossRefADSGoogle Scholar
  3. Briggs, R. J.: 1964, Electron-Stream Interaction with Plasmas, MIT Press, Cambridge, MA.Google Scholar
  4. Brodin, G. and Stenflo, L.: 1988, Physica Scripta 37, 89.ADSCrossRefGoogle Scholar
  5. Cramer, N. F., Hertzberg, M. P., and Vladimirov, S. V.: 2003, Pramana ‘ J. Phys. 61, 1171.CrossRefADSGoogle Scholar
  6. Del Zanna, L., Velli, M., and Londrillo, P.: 2001, Astron. Astrophys. 367, 705.CrossRefADSGoogle Scholar
  7. Del Zanna, L., and Velli, M.: 2002, Adv. Space. Res. 30, 471.CrossRefADSGoogle Scholar
  8. Derby, N. F. J.: 1978, Astrophys. J. 224, 1013.CrossRefADSGoogle Scholar
  9. Galeev, A. A., and Oraevskii, V. N.: 1963, Sov. Phys. Dokl., Engl. Transl. 7, 988.ADSGoogle Scholar
  10. Goldstein, M. L.: 1978, Astrophys. J. 219, 700.MathSciNetCrossRefADSGoogle Scholar
  11. Hertzberg, M. P., Cramer, N. F., and Vladimirov, S. V.: 2003, Phys. Plasmas 10, 3160.CrossRefADSGoogle Scholar
  12. Hertzberg, M. P., Cramer, N. F., and Vladimirov, S. V.: 2004a, Phys. Rev. E 69, art. no. 056402.CrossRefADSGoogle Scholar
  13. Hertzberg, M. P., Cramer, N. F., and Vladimirov, S. V.: 2004b, J. Geophys. Res. 109, art. no. A02103.Google Scholar
  14. Hollweg, J. V., Esser, R., and Jayanti, V.: 1993, J. Geophys. Res. 98, 3491.ADSCrossRefGoogle Scholar
  15. Huerre, P., and Monkewitz, P. A.: 1985, J. Fluid Mech. 159, 151.MATHMathSciNetCrossRefADSGoogle Scholar
  16. Jayanti, V., and Hollweg, J. V.: 1993, J. Geophys. Res. 98, 19049.ADSCrossRefGoogle Scholar
  17. Jayanti, V., and Hollweg, J. V.: 1994, J. Geophys. Res. 99, 23449.CrossRefADSGoogle Scholar
  18. Kulikovskii, A. G., and Shikina, I. C.: 1977, Izv. Akad. Nauk SSSR Mekh. Zhid. Gaza 5, 46 (English translation:Fluid Dyn. 12, 679).MATHGoogle Scholar
  19. Longtin, M., and Sonnerup, B. U. ö: 1986, J. Geophys. Res. 91, 6816.ADSCrossRefGoogle Scholar
  20. Ruderman, M. S.: 2000, Astrophys. Space Sci. 274, 327.MATHCrossRefADSGoogle Scholar
  21. Ruderman, M. S., and Simpson, D.: 2004a, J. Plasmas Phys. 70, 143.CrossRefADSGoogle Scholar
  22. Ruderman, M. S., and Simpson, D.: 2004b, Phys. Plasmas 11, 4178.MathSciNetCrossRefADSGoogle Scholar
  23. Ruderman, M. S., Brevdo, L., and Erdélyi, R.: 2004Proc. R. Soc. Lond. A 460, 847.MATHADSCrossRefGoogle Scholar
  24. Sagdeev, R. Z., and Galeev, A. A.: 1969, Non-Linear Plasma Theory, Benjamin, New York.Google Scholar
  25. Sakai, J. I., and Sonnerup, B. U. ö: 1983, J. Geophys. Res. 88, 9069.ADSCrossRefGoogle Scholar
  26. Simpson, D., and Ruderman, M. S.: 2005, Phys. Plasmas 12, art. no. 062103.Google Scholar
  27. Spangler, S. R.: 1997, Hada, T., and Matsumoto, H. (eds.), Nonlinear Waves and Chaos in Space Plasmas, Terrapub, Tokyo, p. 171.Google Scholar
  28. Terra-Homem, M. T., and Erdélyi, R.: 2003, Astron. Astrophys. 403, 425.MATHCrossRefADSGoogle Scholar
  29. Terra-Homem, M. T., and Erdélyi, R.: 2004, Astron. Astrophys. 413, 7.CrossRefADSGoogle Scholar
  30. Turkman, R., and Torkelsson, U.: 2003, Astron. Astrophys. 409, 813.CrossRefADSGoogle Scholar
  31. Turkman, R., and Torkelsson, U.: 2004, Astron. Astrophys. 428, 227.CrossRefADSGoogle Scholar
  32. Wong, H. K., and Goldstein, M. L.: 1986, J. Geophys. Res. 91, 5617.ADSCrossRefGoogle Scholar
  33. Wright, A. N., Mills, K. J., Ruderman, M. S., and Brevdo, L.: 2000, J. Geophys. Res. 105, 385.CrossRefADSGoogle Scholar

Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Department of Applied MathematicsUniversity of SheffieldSheffieldU.K.

Personalised recommendations