Finite amplitude waves in ion-beam plasma systems

1994 ◽  
Vol 190 (5-6) ◽  
pp. 460-464 ◽  
Author(s):  
S.I. Popel ◽  
Klaus Elsässer
Keyword(s):  
Ion Beam ◽  
Finite Amplitude ◽  
Beam Plasma ◽  
Finite Amplitude Waves

Solitons in an ion-beam plasma

1988 ◽  
Vol 39 (2) ◽  
pp. 183-191 ◽  
Author(s):  
G. P. Zank ◽  
J. F. McKenzie
Keyword(s):  
Ion Beam ◽  
Finite Amplitude ◽  
Total Momentum ◽  
Plasma System ◽  
Weakly Nonlinear ◽  
Classical Energy ◽  
Convective Instabilities ◽  
Beam Plasma ◽  
Solitary Pulse ◽  
Wave Profiles

It is shown that the conservation law for total momentum of an ion-beam plasma system can be cast in the form of a classical energy integral of a particle in a potential well. By using boundary conditions appropriate to a solitary pulse, we derive conditions for the existence of finite-amplitude solitons propagating in the system. Under suitable conditions, as many as three forward-propagating solitary waves can exist. It is interesting to note that the criterion for their existence is intimately related to the absence of convective instabilities in an ion-beam plasma. Exact ‘sech2’ type solutions are available in the weakly nonlinear regime. Solitary-wave profiles for the general case are obtained numerically.

Solitons in an ion-beam plasma

1990 ◽  
Vol 44 (1) ◽  
pp. 151-165 ◽  
Author(s):  
Lan Huibin ◽  
Wang Kelin
Keyword(s):  
Exact Solution ◽  
Solitary Wave ◽  
General Condition ◽  
Upper Bound ◽  
Ion Beam ◽  
Finite Amplitude ◽  
Plasma Model ◽  
Function Series ◽  
Series Form ◽  
Beam Plasma

In this paper the exact solution in a function-series form is given of the multi-fluid ion-beam plasma model proposed by Zank & McKenzie. The general condition necessary for the existence of finite-amplitude solitons propagating in the system is obtained and the upper bound on the velocity of solitary wave is found.

scholarly journals Finite-amplitude steady waves in plane viscous shear flows

1985 ◽  
Vol 160 ◽  
pp. 281-295 ◽  
Author(s):  
F. A. Milinazzo ◽  
P. G. Saffman
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Finite Amplitude ◽  
Linear Instability ◽  
Navier Stokes ◽  
Unidirectional Flow ◽  
Viscous Shear ◽  
Finite Amplitude Waves

Computations of two-dimensional solutions of the Navier–Stokes equations are carried out for finite-amplitude waves on steady unidirectional flow. Several cases are considered. The numerical method employs pseudospectral techniques in the streamwise direction and finite differences on a stretched grid in the transverse direction, with matching to asymptotic solutions when unbounded. Earlier results for Poiseuille flow in a channel are re-obtained, except that attention is drawn to the dependence of the minimum Reynolds number on the physical constraint of constant flux or constant pressure gradient. Attempts to calculate waves in Couette flow by continuation in the velocity of a channel wall fail. The asymptotic suction boundary layer is shown to possess finite-amplitude waves at Reynolds numbers orders of magnitude less than the critical Reynolds number for linear instability. Waves in the Blasius boundary layer and unsteady Rayleigh profile are calculated by employing the artifice of adding a body force to cancel the spatial or temporal growth. The results are verified by comparison with perturbation analysis in the vicinity of the linear-instability critical Reynolds numbers.

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