Head-on collision of nonlinear electrostatic shock waves in a relativistically degenerate plasma

Hasan, Usman; Masood, W.; Jahangir, R.; Mirza, Arshad M.

doi:10.1088/1402-4896/ab20e9

Cited by 10 publications

(5 citation statements)

References 43 publications

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“…This phenomenon is opposite to the one observed in the unmagnetized plasma. [36,37] It is due to the fact that phase shifts are directly proportional to the square root of dispersion coefficient as can be seen in 37), which is dominated by effect of external magnetic field, which is much stronger in ultra-relativistic regime as discussed is last paragraph.…”

Section: Resultsmentioning

confidence: 95%

“…This indicates that the system under consideration allows only compressive solitons, which is consistent with the case of unmagnetized plasma. [36,37] Figures 3a-d show the variation of phase shifts for both solitons as a result of their interaction in relativistically degenerate plasma. The variation of the phase shifts as a result of interaction of solitons provides an insight about the change in trajectory of solitary waves.…”

Section: Resultsmentioning

confidence: 99%

“…In the multicomponent plasmas, ion acoustic solitary waves has also been studied. [35] Head-on collisions of nonlinear structures in unmagnetized relativistically degenerate plasma using PLK method have been investigated by Hasan et al [36,37] Recently, the interaction of magnetosonic shock wave structures in degenerate magnetoplasma have been studied. [38] Oblique interaction of propagating ion acoustic waves has been studied in number of systems.…”

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confidence: 99%

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Oblique interaction of electrostatic nonlinear structures in relativistically degenerate dense magnetoplasmas

Hasan

Masood

Jahangir

et al. 2021

Contributions to Plasma Physics

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We have investigated the interaction of obliquely propagating ion acoustic solitary waves in a magnetoplasma with relativistically degenerate electrons. Using the quantum hydrodynamics model and by employing the extended Poincaré-Lighthill-Kuo technique, we have derived a set of Korteweg de Vries equations for two solitons. We have observed that the system under consideration allows the formation of only compressive solitons and their velocities remain in the sub-acoustic limit. Furthermore, phase shifts of solitons as a result of their interaction have been calculated. The phase shifts have been observed to be dependent on the obliqueness and the physical parameters of plasma. It has also been noticed that phase shifts remain negative for the whole range of parameters generally found in white dwarf stars. We have observed that the phase shifts enhance with the enhancement in number density, however, the converse happens when the magnetic field is enhanced. It has also been observed that the phase shift is slightly greater for the solitons that are less oblique as compared to their more oblique counterparts. Furthermore, we have estimated the spatial scales of interaction of solitons using the parameters found in white dwarf stars. K E Y W O R D Snonlinear structures, quantum plasma, solitons INTRODUCTIONRelativistically degenerate plasmas have engendered research interest in the past few decades. Dense plasmas have enormous applications in different situations like nanostructures, white dwarf stars, and other such extreme conditions. [1][2][3][4][5][6][7][8][9][10] At high pressure and low temperature, the electron degeneracy effects become important in order to study the properties of plasma systems. [11] In such conditions, the electron Fermi energy level rises above the thermal energy level. Therefore, electron Fermi energy level becomes dominant in order to investigate different properties of plasma. The coupling of the quantum scale properties with the large-scale astrophysical objects like white dwarf stars creates interesting areas of plasma systems. For instance, the electron degeneracy on the quantum scale can get coupled with the stability of astrophysical objects such as white dwarf stars. A balance is created between degeneracy pressure caused by the Pauli exclusion principle and the gravitational pull of the white dwarf star. The pulsations in the white dwarf stars originate from gravity (g-mode) waves, [12,13] whereas the observation of compressional (p-mode) waves is still awaited. [14] In these dense environments, the electron equation of state changes from P ∼ n 5/3 to P ∼ n 4/3 and in these circumstances the white dwarf star can become gravitationally unstable. [15,16] Such instabilities modify the oscillation spectrum of the core of white dwarf star, which enables us to study the properties of dense plasma. [17]

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Section: Resultsmentioning

confidence: 95%

Section: Resultsmentioning

confidence: 99%

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confidence: 99%

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Oblique interaction of electrostatic nonlinear structures in relativistically degenerate dense magnetoplasmas

Hasan

Masood

Jahangir

et al. 2021

Contributions to Plasma Physics

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“…Hassan et. al., [27] investigated interaction between two counter traveling electrostatic shock waves in a relativistic degenerated plasma. For the different value of the ion kinematic viscosity, for the non relativistic regime the shocks are found to be sub-acoustic while for the ultra-relativistic regime, the super acoustic shocks are found.…”

Section: Introductionmentioning

confidence: 99%

Numerical solution and characteristic study of time-fractional shocks collision

Shakeel¹,

Parveen²,

Islam³

et al. 2021

Phys. Scr.

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In this study, the interaction of counter-propagating ion acoustic shock waves in three-component unmagnetized plasmas with inertial warm ions, superthermal electrons and positrons are examined. By employing the extended Poincare-Lighthill-Kuo (PLK) method, two-sided Korteweg-deVries-Burgers (KdVB) equations and their corresponding phase shifts for the shock wave are also derived. The derived two-sided KdVB equations are converted to two-sided time-fractional KdVB (TFKdVB) equations by semi inverse method, which is then solved numerically by a local meshless method (LMM). The effects of the ratio of electron temperature to positron temperature, the spectral index κ e , κ p and fractional concentration of positron component p on the phase shift are also examined. Figures are given to judge the performance of the LMM. Comparison is made with the exact solution for the classical case (i.e. ρ = 1) and with Petrov-Galerkin method (PGM) in case of fractional derivative. The influence of the fractional parameter on the behaviour of ion acoustic shock wave in e-p-i plasma is investigated.

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“…By solving the next order of ε using the values of n i ) , we finally get the following KdVB equation[23,41] coefficients of the nonlinear, dispersion, and dissipation terms are, respectively, given by If the effect of the ion kinematic viscosity is taken into account, i.e. C 1 ≠ 0, then equation (8) could be reduced to the normal KdV equation y y y y…”

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A new approach for modelling the damped Helmholtz oscillator: applications to plasma physics and electronic circuits

El-Tantawy¹,

Salas²,

Alharthi³

2021

Commun. Theor. Phys.

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In this paper, a new approach is devoted to find novel analytical and approximate solutions to the damped quadratic nonlinear Helmholtz equation (HE) in terms of the Weiersrtrass elliptic function. The exact solution for undamped HE (integrable case) and approximate/semi-analytical solution to the damped HE (non-integrable case) are given for any arbitrary initial conditions. As a special case, the necessary and sufficient condition for the integrability of the damped HE using an elementary approach is reported. In general, a new ansatz is suggested to find a semi-analytical solution to the non-integrable case in the form of Weierstrass elliptic function. In addition, the relation between the Weierstrass and Jacobian elliptic functions solutions to the integrable case will be derived in details. Also, we will make a comparison between the semi-analytical solution and the approximate numerical solutions via using Runge–Kutta fourth-order method, finite difference method, and homotopy perturbation method for the first-two approximations. Furthermore, the maximum distance errors between the approximate/semi-analytical solution and the approximate numerical solutions will be estimated. As real applications, the obtained solutions will be devoted to describe the characteristics behavior of the oscillations in RLC series circuits and in various plasma models such as electronegative complex plasma model.

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Head-on collision of nonlinear electrostatic shock waves in a relativistically degenerate plasma

Cited by 10 publications

References 43 publications

Oblique interaction of electrostatic nonlinear structures in relativistically degenerate dense magnetoplasmas

Oblique interaction of electrostatic nonlinear structures in relativistically degenerate dense magnetoplasmas

Numerical solution and characteristic study of time-fractional shocks collision

A new approach for modelling the damped Helmholtz oscillator: applications to plasma physics and electronic circuits

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