Stable approximate equations for ion-acoustic waves

Broer, L. J. F.; Sluijter, F. W.

doi:10.1063/1.862043

Cited by 11 publications

(7 citation statements)

References 5 publications

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“…The other solutions of (7) give rise to the so-called slow ion-acoustic solitons, but these disappear when the ions are considered as strictly cold. However, as mentioned already in §1, Landau damping can overwhelm the ion-acoustic waves if the ions have a finite temperature (Stix 1962;Broer & Sluijter 1977). Therefore the inclusion of non-zero ion temperatures can only be viewed as a very small correction; in other words, all <r s have to be kept small.…”

Section: Ordinary Ion-acoustic Solitonsmentioning

confidence: 98%

“…Before proceeding, a strong note of caution must be sounded about the inclusion of temperature effects for the ions. Non-zero ion temperatures would seem to indicate the possibility of slow ion-acoustic solitons (Tran 1974), but Landau damping can overwhelm the ion-acoustic waves if the ions really do have a finite temperature (Stix 1962;Broer & Sluijter 1977). The inclusion of ion temperatures is thus done here in the sense of a small correction, and it is obvious that only the fast ion-acoustic solitons merit a deeper study.…”

Section: Introductionmentioning

confidence: 99%

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Ion-acoustic solitons in multi-component plasmas including negative ions at critical densities

Verheest¹

1988

J. Plasma Phys.

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Ion-acoustic solitons in a plasma with different adiabatic ion constituents and isothermal electrons are studied via a reductive perturbation method. The basic fluid equations then give rise to KdV or modified KdV equations, depending upon the relative ion densities. At critical densities, rarefactive and compressive fast ion-acoustic solitons are possible. Explicit stationary solutions are discussed in the special case of cold ions, in a plasma containing two species of negative ions and one of positive ions. The inclusion of heavier ions, even at low densities, increases the amplitudes of the critical solitons.

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Section: Ordinary Ion-acoustic Solitonsmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Ion-acoustic solitons in multi-component plasmas including negative ions at critical densities

Verheest¹

1988

J. Plasma Phys.

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“…-n e -m = At equilibrium, the ion density rii -1, the flow velocity of the ions u -0 and the potential <p -0 (same density of the electrons). For a thorough analysis of the different steps towards a solvable model regarding stability, we refer to Broer and Sluijter (1977).…”

Section: £•«£=-mentioning

confidence: 99%

The theory of nonlinear ion-acoustic waves revisited

Malfliet

Wieërs

1996

J. Plasma Phys.

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The basic set of equations describing nonlinear ion-acoustic waves in a cold collisionless plasma, in the limit of long wavelengths, is reconsidered. First, a travelling-wave solution is found up to third order by means of a straightforward perturbation approach based on the smallness of the wavenumber. As a result, a positive dressed solitary wave shows up, which is larger, taller and faster than the KdV soliton, the first-order result. Furthermore, the accuracy of this approach is tested and compared with previous result. Secondly, the reductive perturbation techique to study higher-order corrections is revised and adapted to the present problem.

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“…Broer and Sluijter[49] have presented a new method to obtain an equation for nonlinear ion waves. This method is based on the use of an approximate Hamiltonian.…”

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confidence: 99%