Oblique interaction of electrostatic nonlinear structures in relativistically degenerate dense magnetoplasmas

Abstract

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]

Acoustic stability of a self-gravitating cylinder leading to astrostructure formation

“…The values for the classical regime in the manuscript are also in good agreement with the specified values of the previous study 43 . The parameters of the study about the non-linear structures in dense magnetoplasmas 44 is purely for white dwarfs, whereas, the values considered herein are generalized values for quantum and classical regimes. Hence, minor disparities are found between input values of the proposed manuscript and the referred study 44 .…”

“…The parameters of the study about the non-linear structures in dense magnetoplasmas 44 is purely for white dwarfs, whereas, the values considered herein are generalized values for quantum and classical regimes. Hence, minor disparities are found between input values of the proposed manuscript and the referred study 44 . The comprehensive review about the fluid description of quantum plasma mostly deals with the pros and cons of the fluid approach of plasma 45 .…”