Self-focusing of nonlinear ion-acoustic waves and solitons in magnetized plasmas. Part 2. Numerical simulations, two-soliton collisions

1987 ◽  
Vol 37 (1) ◽  
pp. 97-106 ◽  
Author(s):  
E. Infeld ◽  
P. Frycz
Keyword(s):  
Magnetic Field ◽  
Numerical Simulations ◽  
Growth Rates ◽  
Nonlinear Waves ◽  
Acoustic Waves ◽  
Ion Acoustic Waves ◽  
Self Focusing ◽  
Long Wave ◽  
Ion Acoustic ◽  
Soliton Collisions

Nonlinear waves and solitons satisfying the Zakharov-Kuznetsov equation for a dilute plasma immersed in a strong magnetic field are studied numerically. Growth rates of perpendicular instabilities, found theoretically in part 1, are confirmed and extended to arbitrary wavelengths of the perturbations (the calculations of part 1 were limited to long-wave perturbations). The effects of instabilities on nonlinear waves and solitons are illustrated graphically. Pre-vious, approximate results of other authors on the perpendicular growth rates for solitons are improved on. Similar results for perturbed nonlinear waves are presented. The effects of two-soliton collisions on instabilities are investigated. Rather surprisingly, we find that the growth of instabilities can be retarded by collisions. Instabilities can also be transferred from one soliton to another in a collision. This paper can be read independently of part 1.

Self-focusing of nonlinear ion-acoustic waves and solitons in magnetized plasmas

1985 ◽  
Vol 33 (2) ◽  
pp. 171-182 ◽  
Author(s):  
E. Infeld
Keyword(s):  
Magnetic Field ◽  
Nonlinear Waves ◽  
Acoustic Waves ◽  
Solid Angle ◽  
Ion Acoustic Waves ◽  
Weakly Nonlinear ◽  
Self Focusing ◽  
Long Wave ◽  
Weakly Nonlinear Waves ◽  
The Magnetic Field

The Zakharov-Kuznetsov equation describing Korteweg–de Vries waves and solitons in a strong, uniform magnetic field is rederived taking space stretching to be isotropic. This equation is then used to investigate nonlinear waves and solitons for long-wave instabilities. A solid angle of instability develops around the plane perpendicular to the magnetic field. For weakly nonlinear waves this angle is very narrow: widening as the amplitude of the nonlinear wave is increased. The soliton wave is unstable for all directions other than parallel to the field. Previous results of other authors, limited to solitons and perpendicular propagation are recovered. Calculations are illustrated by polar diagrams for the perturbations. Some broader implications are pointed out.

Dynamics of nonlinear ion-acoustic waves in an external magnetic field

1985 ◽  
Vol 44 (8) ◽  
pp. 537-543 ◽  
Author(s):  
E. Infeld ◽  
P. Frycz ◽  
T. Czerwiśka-Lenkowska
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Acoustic Waves ◽  
Ion Acoustic Waves ◽  
Ion Acoustic

scholarly journals Exact Periodic Wave, Bisoliton, and Various Breather Solutions for the Zakharov Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Heng Wang ◽  
Longwei Chen ◽  
Hongjiang Liu ◽  
Shuhua Zheng
Keyword(s):  
Numerical Simulations ◽  
Acoustic Waves ◽  
Periodic Wave ◽  
Ion Acoustic Waves ◽  
Solution Structures ◽  
Ion Acoustic ◽  
Peregrine Breather

The Zakharov equations, which involve the interactions between Langmuir and ion acoustic waves in plasma, are analytically studied. By using the method of Exp-function, the periodic wave, bisoliton, Akhmediev breather, Ma breather, and Peregrine breather of the Zakharov equations are obtained. These results presented in this paper enrich the diversity of solution structures of the Zakharov equations. Furthermore, based on the numerical simulations of these solutions, some physics analysis of bisolitons and various breathers are given.

Dynamics of waves and multidimensional solitons of the Zakharov–Kuznetsov equation: II. Higher-order calculation; nonlinear development

2001 ◽  
Vol 66 (4) ◽  
pp. 295-300
Author(s):  
E. INFELD ◽  
A. A. SKORUPSKI
Keyword(s):  
Growth Rates ◽  
Acoustic Waves ◽  
Maximum Amplitude ◽  
Plasma Phys ◽  
Higher Order ◽  
Magnetized Plasma ◽  
Linear Growth Rate ◽  
Ion Acoustic Waves ◽  
Soliton Collisions ◽  
Better Than

The Zakharov–Kuznetsov equation describes the propagation of weak ion acoustic waves in a strongly magnetized plasma. Their dynamics have been studied in a series of papers, one of which gives growth rates of instabilities found numerically, as well as pictures of soliton collisions [J. Plasma Phys.64, 397 (2000) – Part I]. In the present paper, we find good approximate formulas for growth rates of the dominant instability, vastly improving those of Part I. This is done by proceeding to higher order in the expansion, combined with an incorporation of exact values for the boundaries of the unstable region in the formulas. The result is better than we had any right to expect. We next depart from linear stability analysis and look at nonlinear dynamics to obtain a pulse in time. The maximum amplitude of this pulse is seen to be proportional to the linear growth rate, a result that was so far suspected from numerics but not derived theoretically. (This paper can be read independently of Part I.)

scholarly journals Plasma Capacitor with Ion Acoustic Waves

1974 ◽  
Vol 29 (6) ◽  
pp. 851-858 ◽  
Author(s):  
F. Leuterer
Keyword(s):  
Magnetic Field ◽  
Velocity Distribution ◽  
Acoustic Waves ◽  
Radius Of Gyration ◽  
Ion Acoustic Waves ◽  
Homogeneous Plasma ◽  
Ion Acoustic ◽  
Zero Radius ◽  
The Magnetic Field ◽  
Plasma Capacitor

We examine experimentally and theoretically the r. f. potential within a capacitor, filled with a homogeneous plasma in a magnetic field and driven at frequencies ωci <ω<4ωci . We assume the ions to be cold, and the electrons to have a Maxwellian velocity distribution along the magnetic field, but zero radius of gyration. Thus ion acoustic waves are included. The whole kz-spectrum of the exciter is needed to explain the experimental results.

Stability of nonlinear ion sound waves and solitons in plasmas

1979 ◽  
Vol 366 (1727) ◽  
pp. 537-554 ◽  
Keyword(s):  
Nonlinear Waves ◽  
Acoustic Waves ◽  
Three Dimensional ◽  
Soliton Solutions ◽  
One Dimension ◽  
Sound Waves ◽  
Ion Acoustic Waves ◽  
Two Component ◽  
Ion Acoustic ◽  
Nonlinear Solutions

Large amplitude ion acoustic waves and solitons in two component plasmas are investigated for stability. The soliton solutions are found to be stable, while the nonlinear waves are always unstable, though for a significant range of parameters they are only unstable to fully three-dimensional perturbations. The results in one dimension are compared with those obtained from the K. –de V. equation, which gives stability for the nonlinear waves and solitons. Agreement is surprisingly good for Mach numbers less than about 1.5. A three-dimensional generalization of the K. –de V. equation is considered but this leads to stability for all nonlinear solutions and hence is not a good model for nonlinear waves. It is, however, reasonable in the soliton limit.

Long wavelength ion-acoustic waves in a magneto-plasma in a gravitational field

1970 ◽  
Vol 4 (3) ◽  
pp. 617-627 ◽  
Author(s):  
C. H. Liu
Keyword(s):  
Magnetic Field ◽  
Dispersion Relation ◽  
Static Magnetic Field ◽  
Acoustic Waves ◽  
Fluid Dynamic ◽  
Debye Length ◽  
Ion Acoustic Waves ◽  
Long Wavelength ◽  
Special Cases ◽  
Ion Acoustic

Ion-acoustic waves propagating in a collision-free, gravity-supported plasma in a static magnetic field are studied with a linearized Vlasov equation. The dispersion relation is derived in the limit of vanishing electron to ion mass ratio and wavelength much larger than the Debye length. From this dispersion relation it is shown that the well-known fluid dynamic steepening tendency of waves propagating in the direction of decreasing density is competing with the effect of Landau damping. Depending on the ratio of electron and ion temperatures, the direction of propagation and the strength of the static magnetic field, waves of wavelengths of the order of the scale height or even greater are shown to be damped. Several special cases are discussed.

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