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  • Cited by 6
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    1982. Handbook on Plasma Instabilities.

    Gribben, R. J. and Parkes, E. J. 1977. Slowly varying nonlinear waves in a cold plasma stream. Journal of Plasma Physics, Vol. 18, Issue. 03, p. 495.

    Mjølhus, Einar 1976. On the modulational instability of hydromagnetic waves parallel to the magnetic field. Journal of Plasma Physics, Vol. 16, Issue. 03, p. 321.

    Dewar, R. L. 1972. A Lagrangian theory for nonlinear wave packets in a collisionless plasma. Journal of Plasma Physics, Vol. 7, Issue. 02, p. 267.

    Kako, Masashi 1972. Nonlinear Wave Modulation in Cold Magnetized Plasmas. Journal of the Physical Society of Japan, Vol. 33, Issue. 6, p. 1678.

    1972. Methods in Nonlinear Plasma Theory.


Non-linear dispersion of cold plasma waves

  • Christopher K. W. Tam (a1)
  • DOI:
  • Published online: 01 February 1970

The propagation of a packet of weakly non-linear dispersive cold plasma waves is studied by means of a two-time scale expansion. The effects of amplitude dispersion and the coupling to the mean plasma motion are taken into account. The governing equations are put into a conservation form. It is found that this system of equations is elliptic or hyperbolic depending on the wave-number of the dispersive waves. In the elliptic case modulations in the wave train grow exponentially in time and a periodic wave train will be unstable in this sense. In the hyperbolic case, slow variations in the wave train propagate and the characteristic velocities give a non-linear generalization of the linear group velocity. It is shown that except for waves which have their wave vectors nearly at right angle to the unperturbed magnetic field only fast waves with wave-number less than 0.585 (Ωi Ωe)½/Vα are stable; where Va is the Alfvén velocity and Ωι Ωε, are the ion and electron cyclotron frequencies respectively. A process of steepening of these waves into shocks with dissipation due to wave turbulence at the head of the wave packet is suggested.

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Journal of Plasma Physics
  • ISSN: 0022-3778
  • EISSN: 1469-7807
  • URL: /core/journals/journal-of-plasma-physics
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