Shock waves and double layers in electron degenerate dense plasma with viscous ion fluids

Mamun, A. A.; Zobaer, M. S.

doi:10.1063/1.4863848

Cited by 20 publications

(11 citation statements)

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“…It is well known that in a nonlinear dispersive media shock waves are formed due to an interplay between the nonlinearity (causing wave steepening) and dissipation (e.g., caused by viscosity, collisions, wave particle interaction, etc.) [19][20][21][22]. However, when a medium exhibits both dispersive and dissipative properties, the propagation characteristics of small-amplitude perturbations can be adequately described by KdVB (in one-dimension) or KPB (in two or three dimensios) equations.…”

Section: Introductionmentioning

confidence: 99%

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Kadomtsev—Petviashvili (KP) Burgers Equation in Dusty Negative Ion Plasmas: Evolution of Dust-Ion Acoustic Shocks

Dev¹,

Sarma²,

Deka³

et al. 2014

Commun. Theor. Phys.

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Abstract:We study the nonlinear propagation of dust-ion acoustic (DIA) solitary waves in an unmagnetized dusty plasma which consists of electrons, both positive and negative ions and negatively charged immobile dust grains. Starting from a set of hydrodynamic equations with the ion thermal pressures and ion kinematic viscosities included, and using a standard reductive perturbation method, the Kadomtsev-Petviashivili Burgers (KPB) equation is derived, which governs the evolution of DIA shocks. A stationary solution of the KPB equation is obtained and its properties are analysed with different plasma number densities, ion temperatures and masses. It is shown that a transition from shocks with negative potential to positive one occurs depending on the negative ion concentration in the plasma and the obliqueness of propagation of DIA waves.PACS Numbers: 52.27.Lw, 52.35.Fp, 52.35.Tc IntroductionIn the last few decades, numerous investigations have been made on the study of nonlinear waves and structures in low-temperature dusty plasmas as the presence of extremely massive charged dust particles plays a vital role in understanding the electrostatic disturbances in space plasma environments [1][2][3] as well as laboratory plasma devices [4,5]. It has been pointed out that the static charged dust grains can drastically modify the existing response of electrostatic wave spectra in dusty plasmas [4][5][6][7][8][9][10][11]. On the other hand, depending upon whether the dust grains are static or mobile, there appear new types of electrostatic waves including solitary or shock waves in plasmas. Shukla and Silin first theoretically [12] investigated the existence of low-frequency dust-ion acoustic (DIA) waves (with phase speed much smaller than the electron thermal speed and larger than the ion thermal speed) in a three-component dusty plasma. Later, this DIA wave was experimentally observed by Barkan et al using a dusty plasma device [13].The Korteweg-de Vries (KdV) equation, which governs the evolution of solitary waves, was first derived by Washimi and Tanuiti in a normal two-component plasma [14] using a reductive perturbation technique. It has been reported that multi-component plasmas in presence of sufficient amount of negative ions can support both compressive and rarefactive KdV solitons [15]. Furthermore, the properties of DIA solitary waves and shocks as observed in laboratory dusty plasmas are well explained by the modified KdV and KdV-Burgers (KdVB) equations [5,11,16,17].

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Section: Introductionmentioning

confidence: 99%

“…[19][20][21][22]. However, when a medium exhibits both dispersive and dissipative properties, the propagation characteristics of small-amplitude perturbations can be adequately described by KdVB (in one-dimension) or KPB (in two or three dimensios) equations.…”

Section: Introductionmentioning

confidence: 99%

Kadomtsev—Petviashvili (KP) Burgers Equation in Dusty Negative Ion Plasmas: Evolution of Dust-Ion Acoustic Shocks

Dev¹,

Sarma²,

Deka³

et al. 2014

Commun. Theor. Phys.

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“…To do so, we employ a reductive perturbation technique to examine the electrostatic perturbation propagating in a dense electronpositron degenerate plasma system due to the effect of dissipation. Now, we first introduce the stretched coordinates [15] …”

Section: Derivation Of Modified Burgers Equationmentioning

confidence: 99%

“…For describing and analyzing the different astrophysical environments [14][15][16] (where particle velocities are close to the speed of light), relativistic degeneracy of plasmas has received a great attention and relativistic effects [17][18][19][20][21] play an important role in understanding the different electrostatic nonlinear phenomena. Plasmas in different astrophysical compact objects such as white dwarfs, neutron stars, and so on are examples where relativistic degeneracy is a dominant phenomenon.…”

Section: Introductionmentioning

confidence: 99%

Modified Ion-Acoustic Shock Waves and Double Layers in a Degenerate Electron-Positron-Ion Plasma in Presence of Heavy Negative Ions

Hossen

Mamun

2014

Braz J Phys

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A general theory for nonlinear propagation of one dimensional modified ion-acoustic waves in an unmagnetized electron-positron-ion (e-p-i) degenerate plasma is investigated. This plasma system is assumed to contain relativistic electron and positron fluids, non-degenerate viscous positive ions, and negatively charged static heavy ions. The modified Burgers and Gardner equations have been derived by employing the reductive perturbation method and analyzed in order to identify the basic features (polarity, width, speed, etc.) of shock and double layer (DL) structures. It is observed that the basic features of these shock and DL structures obtained from this analysis are significantly different from those obtained from the analysis of standard Gardner or Burgers equations. The implications of these results in space and interstellar compact objects (viz. nonrotating white dwarfs, neutron stars, etc.) are also briefly mentioned.

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“…So, a purely one-dimensional model can account for none of all observed features since the wave structure and many properties of the solitary waves are modified by these transverse perturbations. [46,47] Motivated by these observations, Zobaer et al [48] and Mamun and Zobaer [49] derived first a modified Burgers equations in the planar case with adiabatic pressure; however, very few investigations have been done on the derivations of a two-dimensional Burgers equations. [50] Furthermore to the best of our knowledge, no observation has been reported on three-dimensional (3D) Burgers equations except a few observations by this author.…”

Section: Introductionmentioning

confidence: 99%

Lower order three-dimensional Burgers equation having non-Maxwellian ions in dusty plasmas

Dev¹

2017

Chinese Phys. B

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The dust acoustic (DA) shock wave with dust charge fluctuations, non-Maxwellian ions, and non-isothermal electrons is studied theoretically. The perturbation technique is employed to derive the lower order three-dimensional (3D) Burgers equation, and shock wave solution is explored by the tan-hyperbolic method. The effects of flat trapped and trapped electron distributions in the presence of Maxwellian and non-Maxwellian ions on characteristics shock waves are observed. The temperature ratio of non-Maxwellian ion temperature and non-isothermal electron temperature is found to play an important role in forming the shock-like structure.

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Shock waves and double layers in electron degenerate dense plasma with viscous ion fluids

Cited by 20 publications

References 55 publications

Kadomtsev—Petviashvili (KP) Burgers Equation in Dusty Negative Ion Plasmas: Evolution of Dust-Ion Acoustic Shocks

Kadomtsev—Petviashvili (KP) Burgers Equation in Dusty Negative Ion Plasmas: Evolution of Dust-Ion Acoustic Shocks

Modified Ion-Acoustic Shock Waves and Double Layers in a Degenerate Electron-Positron-Ion Plasma in Presence of Heavy Negative Ions

Lower order three-dimensional Burgers equation having non-Maxwellian ions in dusty plasmas

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