Hostname: page-component-77c89778f8-sh8wx Total loading time: 0 Render date: 2024-07-17T18:27:52.675Z Has data issue: false hasContentIssue false
  • English
  • Français

A weak turbulence analysis of the two-stream instability

Published online by Cambridge University Press:  13 March 2009

D. F. Smith  and
P. C. W Fung
D. F. Smith
Affiliation:
Institute for Plasma Research, Stanford University, Stanford, California
P. C. W Fung
Affiliation:
Institute for Plasma Research, Stanford University, Stanford, California
Get access Rights & Permissions [Opens in a new window]

Abstract

In this investigation, we study the effects of non-linear interaction of plasma waves in the weak turbulence approximation on a stream-plasma system which is subject to the two-stream instability. The momentum distribution of the stream is assumed to be a Gaussian function and the background plasma is assumed to be a Maxwellian with a temperature T. The non-linear wave-particle interaction of induced scattering on the polarization clouds of ions may lead to stabilization of the stream—plasma waves in the resonant cone are scattered into the nonresonant region. The non-linear wave-particle interaction of induced scattering on the polarization clouds of ions may lead to stabilization of the stream; plasma waves in the resonant cone are scattered into the non-resonant region and vice versa, leading to a well-defined average energy density in plasma waves which is much less than the energy density of the stream. Non-linear scattering also causes transformation of plasma waves into electromagnetic radiation near the fundamental of the electron plasma frequency of the background plasma, and combination of two plasma waves leads to electromagnetic radiation near the second harmonic of this frequency. Expressions are given for the latter process for emission and absorption for arbitrary values of the ratio of the wave number of plasma waves to the wave number of the electromagnetic wave. The major features of the whole phenomenon are illustrated with the help of a numerical example, with conditions typical for the solar corona in which case an ion stream would be stabilized, but an electron or neutral stream (with the chosen density) would not.

Type
Articles
Information
Journal of Plasma Physics , Volume 5 , Issue 1 , January 1971 , pp. 1 - 30
Copyright
Copyright © Cambridge University Press 1971

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Akhiezer, A. I., Akhiezer, I. A., Polovin, R. V., Sitenko, A. G. & Stepanov, K. N. 1967 Collective Oscillations in a Plasma. Cambridge, Mass: M.I.T. Press.Google Scholar
Bekefi, G. 1966 Radiation Processes in Plasmas. New York: Wiley.Google Scholar
Ginzburg, V. L. 1961 Propagation of Electromagnetic Waves in Plasma, p. 691. New York: Gordon and Breach.Google Scholar
Gorburg, L.M. & Tumerbulatov, A.M. 1967 ZhETF 53, 1789. [1968 JETP 26, 1023.]Google Scholar
Harris, E. 1967 Phys. Fluids 10, 238.CrossRefGoogle Scholar
Heitler, W. 1954 The Quantum Theory of Radiation, 3rd ed.Oxford University Press.Google Scholar
Kadomstev, B. B. 1965 Plasma Turbulence. New York: Academic Press.Google Scholar
Kaplan, S. A. & Tsytovich, V. N. 1967 Astron. Zh. 44, 194. [1968 Soviet Astron.-AJ 11, 956.]Google Scholar
Kaplan, S. A. & Tsytovich, V. N. 1969 Usp. Fiz. Nauk 97, 77. [1969 Soviet Phy. Uspekhi 12, 42.]CrossRefGoogle Scholar
Kovrizhykh, L. M. 1968 Proceedings of the P. N. Lebedev Institute of Physics 32, 155. Consultants Bureau, New York.Google Scholar
Landau, L. D. & Lifshiftz, E. M. 1958 Statistical Physics, p. 374. Reading, Mass.: Addison-Wesley.Google Scholar
Makhankov, V. G. & Tsytovich, V. N. 1967 ZhETF 53, 1789. [1968 JETP 26, 1023.]Google Scholar
Melrose, D. B. 1968 Ap. and Space Sci. 2, 171.CrossRefGoogle Scholar
Rogister, A. & Oberman, C. 1968 J. Plasma Phys. 2, 33.CrossRefGoogle Scholar
Smith, D. F. 1970 Advances in Astronomy and Astrophysics 7 (in the Press).Google Scholar
Stix, T. H. 1962 Theory of Plasma Waves. New York: McGraw-Hill.Google Scholar
Sturrock, P. A., Ball, R. H. & Baldwin, D. E. 1965 Phys. Fluids 8, 1509.CrossRefGoogle Scholar
Tsytovich, V. N. & Shapiro, V. D. 1965 Nuclear Fusion 5, 228.CrossRefGoogle Scholar
Tsytovich, V. N. 1966 Usp. Fiz. Nauk 90, 435. [Soviet Phys. Uspekhi 9, 805.]CrossRefGoogle Scholar
Tsytovich, V. N. 1970 Nonlinear Process in Plasma. New York: Plenum.CrossRefGoogle Scholar
Wild, J. P., Smerd, J. F. & Weiss, A. A. 1963 Ann. Rev. Astron. and Ap. 1, 291.CrossRefGoogle Scholar
Zheleznyakov, V. V. 1967 Astrophys. J. 148, 849.CrossRefGoogle Scholar