Modified Korteweg—de Vries ion-acoustic solitons in a plasma

Nakamura, Yoshiharu; Tsukabayashi, Isao

doi:10.1017/s0022377800002968

Cited by 83 publications

(51 citation statements)

References 22 publications

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“…Furthermore, Raychaudhuri et al (1985) and Verheest (1988) have made extensions to observe the interaction of negative ions with the solitons in the general multicomponent plasma. Studies on the soliton's behaviour in plasmas with the ionic species (Ar+, F-), (Ar+, SFij) have been made experimentally (Nakamura and Tsukabayashi 1985;Nakamura 1987) and show 0004-9506/90/030319$03.00 agreement with the earlier theoretical ones, especially the existence of the compressive and rarefactive solitons in the plasma. Very recently, Singh and Das (1989) have studied theoretically the existence of a critical density of negative ions in a generalised multicomponent plasma, with the ionic species (He+, W), (Ar+, F-), (Ar+, SF 6 ), (K+, Cl-) showing a matching relation with solitons observed experimentally.…”

Section: Introductionsupporting

confidence: 59%

Soliton Characteristics at the Critical Density of Negative Ions in Ion-beam Plasmas

Das¹,

Singh²

1990

Aust. J. Phys.

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By using the reductive perturbation technique, ion-acoustic waves are studied in a generalised multicomponent plasma. The multiple ions modify drastically the characteristics of the solitary waves. In particular, the negative ions have a critical density at which the nonlinearity of the Korteweg-deVries (K-dV) equation vanishes and the ion-acoustic solitary wave is seen to be described by a modified K-dV (mK-dV) equation. Using higher order nonlinearities, the non-uniform transition of the K-dV equation to the mK-dV equation along with the conservation of the Sagdeev potential is described. Theoretical observations on the existence of the solitary waves, as expected, could be of interest in laboratory plasmas.

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Section: Introductionsupporting

confidence: 59%

Soliton Characteristics at the Critical Density of Negative Ions in Ion-beam Plasmas

Das¹,

Singh²

1990

Aust. J. Phys.

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“…Nakamura 1982;Ludwig et al 1984;Nakamura and Tsukabayashi 1985;Cooney et al 1991a, b, and references therein). In addition to the electron population and tiny fractions of other components, the positive Ar þ ; SF þ 5 and negative F À ; SF À 5 ions are believed to be the most abundant species in such a plasma (according to Ludwig et al 1984).…”

Section: Supersolitons Detected In Laboratory Experiments With Sf 6 -mentioning

confidence: 99%

“…In this section, the concept of supersolitons is employed for the interpretation of these unusual forms of ion-acoustic solitons shown in Fig. 21, and a theoretical Nakamura and Tsukabayashi 1985). Right: oscilloscope traces showing the electron concentration in the ion-acoustic rarefaction solitons in SF 6 -Arplasma, measured at different distances (shown on the right-hand side) from the initial excitation site.…”

Section: Supersolitons Detected In Laboratory Experiments With Sf 6 -mentioning

confidence: 99%

Above the weak nonlinearity: super-nonlinear waves in astrophysical and laboratory plasmas

Дубинов

Kolotkov

2018

Rev. Mod. Plasma Phys.

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The review summarises recent theoretical achievements and observational manifestations of a new, recently discovered type of nonlinear oscillations in multi-component plasmas, namely super-nonlinear periodic waves and super-nonlinear solitary waves (supersolitons). Both are characterised by a non-trivial topology of their phase portraits, highly anharmonic profile shapes, extremely long periods, and large amplitudes. Based upon multi-fluid magnetohydrodynamic plasma models, examples of ion-acoustic and Alfvén super-nonlinear waves are considered. A multi-component nature of the plasma was revealed to be a crucial condition for the existence of these super-nonlinear waves, with the complexity of the system growing with the number of plasma species accounted for in the model. A minimum number of plasma components which allow for the existence of supernonlinear waves are also discussed. From the observational point of view, typical signatures of periodic super-nonlinear waves are manifested, for example, in the oscillatory processes operating in the magnetised plasma of the solar corona and ground-based plasma machines. Super-nonlinear solitary structures (supersolitons) of an electrostatic origin are recognised in the Earth's magnetosphere, laboratory experiments with chemically active plasmas, and numerical simulations.

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“…When the concentration of negative ions is equal to the critical value, the coefficient at the nonlinear term in the KdV equation is equal to zero, which implies that the cubic non-linearity has to be takes into account. As a result, nonlinear ion-acoustic waves in plasmas with the critical concentration of negative ions are described by the modified Korteweg-de Vries (mKdV) equation [24][25][26][27][28]. The mKdV solutions were also observed in the experiment [29].…”

Section: Gardner Equation For Nonlinear Wavesmentioning

confidence: 99%

Freak waves in laboratory and space plasmas

Рудерман

2010

Eur. Phys. J. Spec. Top.

137

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Abstract. Generation of large-amplitude short-lived wave groups from small-amplitude initial perturbations in plasmas is discussed. Two particular wave modes existing in plasmas are considered. The first one is the ion-sound wave. In a plasmas with negative ions it is described by the Gardner equation when the negative ion concentration is close to critical. The results of numerical solution of the Gardner equation with the modulationally unstable initial condition are presented. These results clearly show the possibility of generation of freak ionacoustic waves due to the modulational instability. The second wave mode is the Alfvén wave. When this wave propagates at a small angle with respect to the equilibrium magnetic field, and its wave length is comparable with the ion inertia length, it is described by the DNLS equation. Studying the evolution of an initial perturbation using the linearized DNLS equation shows that the generation of freak Alfvén waves is possible due to linear dispersive focusing. The numerical solution of the DNLS equation reveals that the nonlinear dispersive focusing can also produce freak Alfvén waves.

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Modified Korteweg—de Vries ion-acoustic solitons in a plasma

Cited by 83 publications

References 22 publications

Soliton Characteristics at the Critical Density of Negative Ions in Ion-beam Plasmas

Soliton Characteristics at the Critical Density of Negative Ions in Ion-beam Plasmas

Above the weak nonlinearity: super-nonlinear waves in astrophysical and laboratory plasmas

Freak waves in laboratory and space plasmas

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