Relativistic degeneracy effect on propagation of arbitrary amplitude ion-acoustic solitons in Thomas-Fermi plasmas

Of the nonlinear excitations, ion-acoustic solitary waves (IASWs) are of the most important and well-understood characteristics of plasma environments. Theoretical studies of main properties of these solitary structures date back to 1961 using Sagdeev pseud-potentials method [1]. Another method which is widely used to investigate the collective wave phenomenon in plasma is the so-called multi-scales perturbation method [2][3][4][5][6][7][8]. However, the latter method, which is based on approximation, is used only for the small-amplitude treatment of plasma in a state away from thermodynamic equilibrium. Therefore to obtain a good agreement with experiments, in this method, one needs to take higher-orders in perturbation amplitudes. In recent years there have been many investigations on solitary IASWs as well as solitary electrostatic waves (ESWs) in diverse plasma environments using Sagdeev pseudo-potential approach [9][10][11][12][13]. The small amplitude propagation and interaction of IASWs with relativistic degeneracy pressure effects have been recently considered in Ref. [14].

Among different kinds, pair-plasmas have attracted special attention in recent years, a special cases of which can be electron-positron (EP) and electron-positron-ion (EPI) [15][16][17][18][19] plasmas. Electron-positron-ion plasma exists in places such as active galactic nuclei [20],

pulsar magnetospheres [21] and in many dense astronomical environments, namely, neutron stars and white dwarfs [22] and may play a key role in understanding the beginning and evolution of our entire universe [23]. This kind of plasma may also be practically produced in laboratories [24][25][26][27]. More specifically when positrons, due to their significant lifetimes, are used to probe particle transport in Tokamaks, two component electron-ion (e-i) plasma behaves as three component (e-p-i) plasma [28]. Furthermore, the wave properties such as stabilities of a two component electron-ion (EI) plasma solitary excitations may be radically altered by inclusion of low amounts of positrons.

Owing to their wide applicabilities in micro-and nano-electronic miniaturization, denseplasmas is becoming one of the interesting fields of theoretical as well as experimental fields of plasma research [29][30][31][32][33][34][35]. Dense plasma or the so-called quantum plasma are characterized by high densities and low temperatures, however, a dense plasma may be realized in such hot places as planet interiors and white dwarfs [36]. More recently, quantum hydrodynamics model has been applied to study the electron-hole dynamics in semiconductors [37,38].

The quantum effects in collective behavior of a plasma system becomes important when the inter-particle distances are comparable or less than the de Broglie thermal wavelength λ B = h/(2πm e k B T ) 1/2 or equivalently when the thermal energies of plasma species are less than Fermi-energies [39]. In such cases the plasma becomes degenerate, in which the plasma ingredients are under effective influence of Pauli exclusion principle and classical statistical assumptions break down. Quantum effects also play important role in the nonlinear processes of white-dwarfs [40]. For instance, for a cold neutron star the densities can be as high as 10 15 gm/cm -3 in the core, which is several times the density of an atomic nuclei. In extreme conditions such as the middle of a supernova or the core of a massive white dwarf the densities can be even catastrophically higher. At these very high densities the electrons and positrons may become ultra-relativistic giving rise to the collapse of star under its giant gravitational force [41,42].

The present study is devoted to investigation of propagation of IASWs in an unmagnetized EPI plasma using Sagdeev pseudo-potential method in such extreme condition, taking into account the relativistic degeneracy effects for electrons and positrons. The basic normalized plasma equations are introduced in section II. Nonlinear arbitrary-amplitude solution is derived in section III. Section IV devotes to short argument about small amplitude IASWs.

Numerical analysis and discussion is given in section V and final remarks are presented in section VI.

Consider a dense plasma consisting of electrons, positrons and positive-ions. Also, suppose that the electrons and positrons follow the zero-temperature Fermi-gas statistics, while, ions behave as classical fluid. In such plasma electrons and positrons may be considered collision-less due to Fermi-blocking process caused by pauli exclusion principle. Therefore, the semi-classical description of nonlinear dynamics and interaction of waves in such plasma can be studied in the framework of conventional hydrodynamics model. The basic normalized equations describing plasma dynamical state may be written as

where, electrons and positrons are of Thomas-Fermi type

In obtaining the normalized set of equations following scalings are used

where, (

Therefore

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