In this paper, we have investigated the head-on collision of quantum ion acoustic solitons with relativistically degenerate electrons by deriving a set of Korteweg–de Vries equations. Using the refined Poincaré-Lighthill-Kuo method, we have derived the expressions for phase shifts of colliding solitons. It has been found that the system under consideration admits only compressive electrostatic solitary structures. The solitons have also been found to form only for the sub-acoustic velocities of the nonlinear structures. It has been observed that the soliton interaction happens over long spatial and temporal scales in the non-relativistic limit whereas the converse happens in the ultrarelativistic regime. It has been found that the phase shift of the solitons after interaction is more pronounced in the ultra-relativistic limit by comparison with its non-relativistic counterpart. It has also been found that the phase shift settles to a constant value in the nonrelativistic limit. Using the parameters that are customarily found in white dwarf stars, we have given an estimate of the spatial scales over which the nonlinear structures are expected to interact with each other both in the non-relativistic and in the ultra-relativistic regimes.
We present here theoretical investigation of colliding electrostatic shocks in an electron–ion plasma with relativistically degenerate electrons. A set of Korteweg–de Vries Burgers equations has been derived by employing a modified Poincaré–Lighthill–Kuo method for dissipative nonlinear ion acoustic structures. It has been found that relativistically degenerate plasma allows the formation of only compressional shocks. Moreover, the shocks are found to be sub-acoustic for the non-relativistic regime and super-acoustic for ultra-relativistic regime for a certain range of values of the ion kinematic viscosity. We have estimated the spatio–temporal scales, using the parameters generally found in white dwarf stars, for which the shock waves are theoretically anticipated to collide with each other in the relativistically degenerate plasma. The electric field across the shock has also been plotted numerically. The phase shifts of the shock waves resulting from the head-on collision have been estimated. The results may be helpful to understand the collision and dynamics of shock waves in astrophysical objects, such as hydrogen-rich white dwarf stars, and laboratory experiments, such as inertial confinement fusion.
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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