Skip to main content
    • Aa
    • Aa

Non-linear dispersion of cold plasma waves

  • Christopher K. W. Tam (a1)

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.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

J. H. Adlam & J. E. Allen 1958 Phil. Mag. 3, 448.

T. B. Benjamin & M. J. Lighthill 1954 Proc. Roy. Soc. Lond. A 224, 448.

J. G. Cordey & P. G. Saffman 1967 J. Plasma Phys. 1, 129.

V. C. A. Ferraro 1956 Proc. Roy. Soc. A 233, 310.

M. J. Lighthill 1965 J. Inst. Math. Appl. 1, 269.

J. C. Luke 1966 Proc. Roy. Soc. Lond. A 292, 403.

D. Montgomery 1959 Phys. Fluids 2, 585.

C. K. W. Tam 1969 Phys. Fluids, 12, 1028.

G. B. Whitham 1965 aProc. Roy. Soc. Lond. A 283, 238.

G. B. Whitham 1967 aProc. Roy. Soc. Lond. A 299, 6.

T. Yeh 1968 Phys. Fluids 11, 2406.

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? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 2 *
Loading metrics...

Abstract views

Total abstract views: 36 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 28th May 2017. This data will be updated every 24 hours.