Skip to main content
×
×
Home

Parametric instabilities of circularly polarized large-amplitude dispersive Alfvén waves: excitation of parallel-propagating electromagnetic daughter waves

  • Adolfo F. Viñas (a1) and Melvyn L. Goldstein (a1)
Abstract

We investigate the parametric decay and modulational instabilities of a large-amplitude circularly polarized dispersive Alfvén wave. Our treatment is more general than that of previous derivations based on the two-fluid equations in that we allow for propagation of the unstable daughter waves at arbitrary angles to the background magnetic field, although our main concern in this paper is the exploration of new aspects of propagation parallel to the DC magnetic field. In addition to the well-known coupling of pump waves to electrostatic daughter waves, we find a new parametric channel where the pump wave couples directly to electromagnetic daughter waves. Excitation of the electromagnetic instability occurs only for modulation (k/k0 ≤ 1) and not for decay (k/k0 < 1). In contrast with the modulational instability excited by the electrostatic coupling, the electromagnetic modulational instability exists for both left-hand (K > 0) and right-hand (K < 0) polarization. For large k/k0, the electromagnetic channel dominates, while at lower values the electrostatic channel has a larger growth rate for modest values of dispersion, pump-wave amplitude and plasma β. Unlike the electrostatic modulational instability, the growth rate of the electromagnetic instability increases monotonically with increasing pump wave amplitude. This analysis confirms that, for decay, the dominant process is coupling to electrostatic daughter waves, at least for parallel propagation. For modulation, the coupling to electromagnetic daughter waves usually dominates, suggesting that the parametric modulational instability is really an electromagnetic phenomenon.

Copyright
References
Hide All
Abraham-Shrauner, B. & Feldman, W. C. 1977 J. Geophys. Res. 82, 618.
Armstrong, J. W., Cordes, J. M. & Rickett, B. J. 1981 Nature, 291, 561.
Boyd, T. J. M. & Sanderson, J. J. 1969 Plasma Dynamics. Barnes and Noble.
Bragtnskii, S. I. 1957 Soviet Phys. Dokl. 2, 345.
Cohen, R. 1975 J. Geophys. Res. 80, 3678.
Cohen, R. H. & Dewar, R. L. 1974 J. Geophys. Res. 79, 4174.
Derby, N. F. 1978 Astrophys. J. 224, 1013.
Ferraro, V. C. A. 1955 Proc. R. Soc. Lond. A 223, 310.
Flå, T., Mjølhus, E. & Wyller, J. 1989 Physica Scripta, 40, 219.
Formisano, V. & Kennel, C. F. 1969 J. Plasma Phys. 3, 55.
Galeev, A. A. & Oraevskii, V. N. 1963 Soviet Phys. Dokl. 7, 988.
Goldstein, M. L. 1978 Astrophys. J. 219, 700.
Goldstein, M. L., Klimas, A. J. & Barish, F. D. 1974 Solar Wind Three (ed. Russell, C. T.), p. 385. University of California Press.
Goldstein, M. L., Wong, H. K., Viñas, A. F. & Smith, C. W. 1985 J. Geophys. Res. 90, 302.
Hoshino, M. & Goldstein, M. L. 1989 Phys. Fluids B 1, 1405.
Inhester, B. 1990 J. Geophys. Res. 95, 10525.
Ionson, J. A. & Ong, R. S. B. 1976 Plasma Phys. 18, 809.
Kruer, W. L. 1988 The Physics of Laser Plasma Interactions. Addison-Wesley.
Lashmore-Davies, C. N. 1976 Phys. Fluids, 19, 587.
Longtin, M. & Sonnerup, B. U. Ö 1986 J. Geophys. Res. 91, 6816.
Mjølhus, E. 1976 J. Plasma Phys. 16, 321.
Mjølhus, E. & Wyller, J. 1986 Physica Scripta, 33, 442.
Mjølhus, E. & Wyller, J. 1988 J. Plasma Phys. 40, 299.
Ovenden, C. R., Shah, H. A. & Schwartz, S. J. 1983 J. Geophys. Res. 88, 6095.
Roberts, A. D. & Goldstein, M. L. 1991 In Contributions in Solar Planetary Relationships, U.S. National Report 1987–1990 (ed. Shea, M. A.), p. 932. American Geophysical Union.
Robinson, D. C. & Rusbridge, M. G. 1971 Phys. Fluids, 14, 2499.
Sagdeev, R. Z. & Galeev, A. A. 1969 Nonlinear Plasma Theory (ed. O'Neil, T. & Book, D.). Benjamin.
Sakai, J.-I. & Sonnerup, B. U. Ö. 1983 J. Geophys. Res. 88, 9069.
Spangler, S. R. 1985 Astrophys. J. 299, 122.
Spangler, S. R. & Sheerin, J. P. 1982 J. Plasma Phys. 27, 193.
Stringer, T. E. 1963 Plasma Phys. 5, 89.
Terasawa, T., Hoshino, M., Sakai, J.-I. & Hada, T. 1986 J. Geophys. Res. 91, 4171.
Viñas, A. F. & Goldstein, M. L. 1991 J. Plasma Phys. 46, 129.
Viñas, A. F., Goldstein, M. L. & Acuña, M. H. 1984 J. Geophys. Res. 89, 6813.
Wong, H. K. & Goldstein, M. L. 1986 J. Geophys. Res. 91, 5617.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Plasma Physics
  • ISSN: 0022-3778
  • EISSN: 1469-7807
  • URL: /core/journals/journal-of-plasma-physics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed