Abstract
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.
Similar content being viewed by others
References
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.
Brevdo, L.: 1988, Geophys. Astrophys. Fluid Dyn. 40, 1.
Briggs, R. J.: 1964, Electron-Stream Interaction with Plasmas, MIT Press, Cambridge, MA.
Brodin, G. and Stenflo, L.: 1988, Physica Scripta 37, 89.
Cramer, N. F., Hertzberg, M. P., and Vladimirov, S. V.: 2003, Pramana ‘ J. Phys. 61, 1171.
Del Zanna, L., Velli, M., and Londrillo, P.: 2001, Astron. Astrophys. 367, 705.
Del Zanna, L., and Velli, M.: 2002, Adv. Space. Res. 30, 471.
Derby, N. F. J.: 1978, Astrophys. J. 224, 1013.
Galeev, A. A., and Oraevskii, V. N.: 1963, Sov. Phys. Dokl., Engl. Transl. 7, 988.
Goldstein, M. L.: 1978, Astrophys. J. 219, 700.
Hertzberg, M. P., Cramer, N. F., and Vladimirov, S. V.: 2003, Phys. Plasmas 10, 3160.
Hertzberg, M. P., Cramer, N. F., and Vladimirov, S. V.: 2004a, Phys. Rev. E 69, art. no. 056402.
Hertzberg, M. P., Cramer, N. F., and Vladimirov, S. V.: 2004b, J. Geophys. Res. 109, art. no. A02103.
Hollweg, J. V., Esser, R., and Jayanti, V.: 1993, J. Geophys. Res. 98, 3491.
Huerre, P., and Monkewitz, P. A.: 1985, J. Fluid Mech. 159, 151.
Jayanti, V., and Hollweg, J. V.: 1993, J. Geophys. Res. 98, 19049.
Jayanti, V., and Hollweg, J. V.: 1994, J. Geophys. Res. 99, 23449.
Kulikovskii, A. G., and Shikina, I. C.: 1977, Izv. Akad. Nauk SSSR Mekh. Zhid. Gaza 5, 46 (English translation:Fluid Dyn. 12, 679).
Longtin, M., and Sonnerup, B. U. ö: 1986, J. Geophys. Res. 91, 6816.
Ruderman, M. S.: 2000, Astrophys. Space Sci. 274, 327.
Ruderman, M. S., and Simpson, D.: 2004a, J. Plasmas Phys. 70, 143.
Ruderman, M. S., and Simpson, D.: 2004b, Phys. Plasmas 11, 4178.
Ruderman, M. S., Brevdo, L., and Erdélyi, R.: 2004Proc. R. Soc. Lond. A 460, 847.
Sagdeev, R. Z., and Galeev, A. A.: 1969, Non-Linear Plasma Theory, Benjamin, New York.
Sakai, J. I., and Sonnerup, B. U. ö: 1983, J. Geophys. Res. 88, 9069.
Simpson, D., and Ruderman, M. S.: 2005, Phys. Plasmas 12, art. no. 062103.
Spangler, S. R.: 1997, Hada, T., and Matsumoto, H. (eds.), Nonlinear Waves and Chaos in Space Plasmas, Terrapub, Tokyo, p. 171.
Terra-Homem, M. T., and Erdélyi, R.: 2003, Astron. Astrophys. 403, 425.
Terra-Homem, M. T., and Erdélyi, R.: 2004, Astron. Astrophys. 413, 7.
Turkman, R., and Torkelsson, U.: 2003, Astron. Astrophys. 409, 813.
Turkman, R., and Torkelsson, U.: 2004, Astron. Astrophys. 428, 227.
Wong, H. K., and Goldstein, M. L.: 1986, J. Geophys. Res. 91, 5617.
Wright, A. N., Mills, K. J., Ruderman, M. S., and Brevdo, L.: 2000, J. Geophys. Res. 105, 385.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ruderman, M.S., Simpson, D. Absolute and Convective Instabilities of Circularly Polarized Alfvén Waves. Space Sci Rev 121, 287–297 (2005). https://doi.org/10.1007/s11214-006-2510-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11214-006-2510-4