Dissipative formation of hole-like excitation in ion-acoustic plasma

Chowdhury, Abhishek Dutta; Pakira, G.

doi:10.1007/bf00673933

Cited by 4 publications

(3 citation statements)

References 13 publications

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“…It is worth noticing here that for a conservative plasma (η = 0), the DR (6) reduces to ω 2 = k 2 /(σ 1 + k 2 ) and coincides with equation ( 23) in [53]. Moreover, in the limit κ → ∞, where the distribution function degenerates into Maxwellian, σ 1 → 1 and this brings ( 6) back to the one obtained in [62]. Switching into physical units, DR (6) reads…”

Section: Multiscale Perturbation Analysis: Cgl Equationsupporting

confidence: 66%

“…In our system, the condition T e T i is well satisfied; therefore, our assumption of the minimized Landau damping can be easily applied. Note that the Maxwellian limit of this formalism and these results can be seen in [62]. This paper is arranged in the following manner: the governing equations are introduced in section 2.…”

Section: Introductionmentioning

confidence: 99%

“…Various types of analytical solutions to the CGL equation have been addressed in recent decades [58], including families of localized solutions with a fixed and arbitrary amplitude [59,60], breathing pulses and holes [61]. With regards to IA waves, Chowdhury and Pakira investigated the formation of dissipative excitations in viscous plasmas [62]. They derived, by means of a reductive perturbation theory, a NLS equation with complex coefficient for an IA envelop.…”

Section: Introductionmentioning

confidence: 99%

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Dissipative ion-acoustic solitary and shock waves in a plasma with superthermal electrons

Borhanian

2013

Plasma Phys. Control. Fusion

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The excitation of a nonlinear ion-acoustic (IA) wave packet in a viscous plasma consisting of superthermal electrons and cold ions is investigated. It is assumed that the superthermal components obey the Kappa distribution. The standard reductive perturbation technique is employed to obtain a cubic complex Ginzburg-Landau type equation, which governs the dynamics of the amplitude of IA wave packets in a viscous plasma. In a weakly dissipative regime, by means of a perturbation method adopted from non-integrable dynamical systems theory, explicit soliton solutions are obtained of the dissipative dynamical system, determined as fixed points of a two-dimensional system of evolution equations describing the soliton amplitude and velocity. The stability of bright solitons is addressed using adiabatic perturbation theory in a weakly dissipative case. In a general dissipation regime, a novel type of travelling solitary (dissipative solitons) and shock-type solutions are derived for an envelope equation. Moreover, the dependence of the solitary and shock wave characteristics on relevant physical parameters of the problem is studied. It is shown that dissipative solitons do exist, sustained by a mutual balance between loss and gain terms, in addition to the interplay between dispersion and nonlinearity. The dependence of solitary and shock wave velocities on the parameters of the system are investigated. To feature distinctive characteristics of a dissipative soliton, it is compared with the bright soliton solution of the nonlinear Schrödinger equation.

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Section: Multiscale Perturbation Analysis: Cgl Equationsupporting

confidence: 66%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dissipative ion-acoustic solitary and shock waves in a plasma with superthermal electrons

Borhanian

2013

Plasma Phys. Control. Fusion

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Phase portrait analysis of super solitary waves and flat top solutions

Steffy

Ghosh

2018

Physics of Plasmas

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The phase portrait analysis of super solitary waves has revealed a new kind of intermediate solution which defines the boundary between the two types of super solitary waves, viz., Type I and Type II. A Type I super solitary wave is known to be associated with an intermediate double layer while a Type II solution has no such association. The intermediate solution at the boundary has a flat top structure and is called a flat top solitary wave. Its characteristics resemble an amalgamation of a solitary wave and a double layer. It was found that, mathematically, such kinds of structures may emerge due to the presence of an extra nonlinearity. Although they are relatively unfamiliar in the realm of plasma physics, they have much wider applications in other physical systems.

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Shock pattern solutions for viscous-collisional plasma ion acoustic waves in view of the linear theory of the non-equilibrium thermodynamics

Abourabia

Shahein

2011

Can. J. Phys.

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In the framework of irreversible thermodynamics, we study nonlinear ion-acoustic waves (IAWs) in viscous and collisional plasmas. Electrons, which form the background, are assumed to be nonthermal. On account of ion viscosity and ion-electron collisions, we investigate using ion fluid equations. We study the effects of the nonthermally distributed electrons β and the temperature ratio σ (= Ti/Te) on the stability, where the stability for Burger’s equation is analyzed by two methods: the phase portrait method and irreversible thermodynamics relations at different values of σ and β. We usa a reductive perturbation technique, where the nonlinear evolution of an IAW is governed by the driven Burger equation. This equation is solved exactly by using two methods: the tanh-function method and the Cole–Hopf transformation. Both methods produce shock wave solutions, their results compared, and good agreement exists in most predictions. The analytical calculations show that an IAW propagates as a shock wave with subsonic speed. The flow velocity, pressure, number density, electrostatic potential, and thermodynamic characteristics are estimated and illustrated as functions of time t and the distance x. It is found via the tanh-function method that the amplitudes of the sought-for functions of the system are suppressed and move towards an equilibrium state at the highest value of β. The tanh-function method reveals an advantage over the Cole–Hopf method in the viscous and collisional cases of IAWs, where it satisfies the stability conditions at the highest value of β with the chosen σ values when applied to evaluate the Onsager relation.

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Dissipative formation of hole-like excitation in ion-acoustic plasma

Cited by 4 publications

References 13 publications

Dissipative ion-acoustic solitary and shock waves in a plasma with superthermal electrons

Dissipative ion-acoustic solitary and shock waves in a plasma with superthermal electrons

Phase portrait analysis of super solitary waves and flat top solutions

Shock pattern solutions for viscous-collisional plasma ion acoustic waves in view of the linear theory of the non-equilibrium thermodynamics

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