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.

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.

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.

Propagation of dispersive wave solutions for (3 + 1)-dimensional nonlinear modified Zakharov–Kuznetsov equation in plasma physics

2020 ◽  
Vol 34 (25) ◽  
pp. 2050227
Author(s):  
Karmina K. Ali ◽  
Aly R. Seadawy ◽  
Asif Yokus ◽  
Resat Yilmazer ◽  
Hasan Bulut
Keyword(s):  
Magnetic Field ◽  
Acoustic Waves ◽  
Uniform Magnetic Field ◽  
Expansion Method ◽  
Dispersive Wave ◽  
Ion Acoustic Waves ◽  
Weakly Nonlinear ◽  
Wave Solutions ◽  
Proposed Model ◽  
Ion Acoustic

In the current study, we instigate the four-dimensional nonlinear modified Zakharov–Kuznetsov (NLmZK) equation. The NLmZK equation guides the attitude of weakly nonlinear ion-acoustic waves in a plasma comprising cold ions and hot isothermal electrons in the presence of a uniform magnetic field. Two different methods are used, namely the sine-Gordon expansion method (SGEM) and the [Formula: see text]-expansion method to the proposed model. We have successfully constructed some topological, non-topological, and wave solutions. In addition, the 2D, 3D, and contour graphs of the solutions are also plotted under the choice of appropriate values of the parameters.

scholarly journals Stability of ion acoustic nonlinear waves and solitons in magnetized plasmas

2016 ◽  
Vol 82 (6) ◽  
Author(s):  
Piotr Goldstein ◽  
Eryk Infeld
Keyword(s):  
Nonlinear Waves ◽  
Acoustic Waves ◽  
Critical Angle ◽  
Historical Overview ◽  
Ion Acoustic Waves ◽  
Early Results ◽  
Special Cases ◽  
Ion Acoustic ◽  
Field Lines ◽  
The Magnetic Field

Early results concerning the shape and stability of ion acoustic waves are generalized to propagation at an angle to the magnetic field lines. Each wave has a critical angle for stability. Known soliton results are recovered as special cases. A historical overview of the problem concludes the paper.

scholarly journals Ion acoustic waves near a comet nucleus: Rosetta observations at comet 67P/Churyumov–Gerasimenko

2021 ◽  
Vol 39 (1) ◽  
pp. 53-68
Author(s):  
Herbert Gunell ◽  
Charlotte Goetz ◽  
Elias Odelstad ◽  
Arnaud Beth ◽  
Maria Hamrin ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Acoustic Waves ◽  
Magnetic Field Gradient ◽  
Ion Acoustic Waves ◽  
Ion Distributions ◽  
Ion Acoustic ◽  
Low Energies ◽  
The Waves ◽  
Comet 67P ◽  
The Magnetic Field

Abstract. Ion acoustic waves were observed between 15 and 30 km from the centre of comet 67P/Churyumov–Gerasimenko by the Rosetta spacecraft during its close flyby on 28 March 2015. There are two electron populations: one cold at kBTe≈0.2 eV and one warm at kBTe≈2 eV. The ions are dominated by a cold (a few hundredths of electronvolt) distribution of water group ions with a bulk speed of (3–3.7) km s−1. A warm kBTe≈6 eV ion population, which also is present, has no influence on the ion acoustic waves due to its low density of only 0.25 % of the plasma density. Near closest approach the propagation direction was within 50∘ from the direction of the bulk velocity. The waves, which in the plasma frame appear below the ion plasma frequency fpi≈2 kHz, are Doppler-shifted to the spacecraft frame where they cover a frequency range up to approximately 4 kHz. The waves are detected in a region of space where the magnetic field is piled up and draped around the inner part of the ionised coma. Estimates of the current associated with the magnetic field gradient as observed by Rosetta are used as input to calculations of dispersion relations for current-driven ion acoustic waves, using kinetic theory. Agreement between theory and observations is obtained for electron and ion distributions with the properties described above. The wave power decreases over cometocentric distances from 24 to 30 km. The main difference between the plasma at closest approach and in the region where the waves are decaying is the absence of a significant current in the latter. Wave observations and theory combined supplement the particle measurements that are difficult at low energies and complicated by spacecraft charging.

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 Inferring the chromospheric magnetic topology through waves

2007 ◽  
Vol 3 (S247) ◽  
pp. 78-81
Author(s):  
S. S. Hasan ◽  
O. Steiner ◽  
A. van Ballegooijen
Keyword(s):  
Magnetic Field ◽  
Wave Propagation ◽  
Energy Density ◽  
Acoustic Wave ◽  
Acoustic Waves ◽  
Phase Speed ◽  
Time Correlation ◽  
Propagation Time ◽  
Fast Mode ◽  
The Magnetic Field

AbstractThe aim of this work is to examine the hypothesis that the wave propagation time in the solar atmosphere can be used to infer the magnetic topography in the chromosphere as suggested by Finsterle et al. (2004). We do this by using an extension of our earlier 2-D MHD work on the interaction of acoustic waves with a flux sheet. It is well known that these waves undergo mode transformation due to the presence of a magnetic field which is particularly effective at the surface of equipartition between the magnetic and thermal energy density, the β = 1 surface. This transformation depends sensitively on the angle between the wave vector and the local field direction. At the β = 1 interface, the wave that enters the flux sheet, (essentially the fast mode) has a higher phase speed than the incident acoustic wave. A time correlation between wave motions in the non-magnetic and magnetic regions could therefore provide a powerful diagnostic for mapping the magnetic field in the chromospheric network.

scholarly journals Weakly nonlinear waves in magnetized plasma with a slightly non-Maxwellian electron distribution. Part 2. Stability of cnoidal waves

2007 ◽  
Vol 73 (6) ◽  
pp. 933-946
Author(s):  
S. PHIBANCHON ◽  
M. A. ALLEN ◽  
G. ROWLANDS
Keyword(s):  
Growth Rate ◽  
Nonlinear Waves ◽  
Electron Distribution ◽  
Magnetized Plasma ◽  
Weakly Nonlinear ◽  
Long Wavelength ◽  
First Order ◽  
Wave Solutions ◽  
Linear Waves ◽  
Weakly Nonlinear Waves

AbstractWe determine the growth rate of linear instabilities resulting from long-wavelength transverse perturbations applied to periodic nonlinear wave solutions to the Schamel–Korteweg–de Vries–Zakharov–Kuznetsov (SKdVZK) equation which governs weakly nonlinear waves in a strongly magnetized cold-ion plasma whose electron distribution is given by two Maxwellians at slightly different temperatures. To obtain the growth rate it is necessary to evaluate non-trivial integrals whose number is kept to a minimum by using recursion relations. It is shown that a key instance of one such relation cannot be used for classes of solution whose minimum value is zero, and an additional integral must be evaluated explicitly instead. The SKdVZK equation contains two nonlinear terms whose ratio b increases as the electron distribution becomes increasingly flat-topped. As b and hence the deviation from electron isothermality increases, it is found that for cnoidal wave solutions that travel faster than long-wavelength linear waves, there is a more pronounced variation of the growth rate with the angle θ at which the perturbation is applied. Solutions whose minimum values are zero and which travel slower than long-wavelength linear waves are found, at first order, to be stable to perpendicular perturbations and have a relatively narrow range of θ for which the first-order growth rate is not zero.

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