Relativistic degenerate effects of electrons and positrons on modulational instability of quantum ion acoustic waves in dense plasmas with two polarity ions

Abstract

The nonlinear propagation of quantum ion acoustic wave (QIAW) is investigated in a four-component plasma composed of warm classical positive ions and negative ions, as well as inertialess relativistically degenerate electrons and positrons. A nonlinear Schrödinger equation is derived by using the reductive perturbation method, which governs the dynamics of QIAW packets. The modulation instability analysis of QIAWs is considered based on the typical parameters of the white dwarf. The results exhibit that both in the weakly relativistic limit and in the ultrarelativistic limit, the modulational instability regions are sensitively dependent on the ratios of temperature and number density of negative ions to those of positive ions respectively, and on the relativistically degenerate effect as well.

On a semiclassical model for ion-acoustic solitons in ultrarelativistic pair plasmas and its classical counterpart

“…One area concerns acoustic-type solitons in electron-positron-ion (e-p-i) plasmas as in white dwarfs and magnetars, having ultrarelativistic thermodynamics. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] Pure pair plasmas, with their inherent symmetry in mass and charge between electron and positrons or equivalent descriptions in terms of positive and negative ions, can only support acoustic solitons if there is an imbalance in either thermodynamics or in undisturbed densities. 19 In the latter case, a third charged species is needed to ensure an electrically neutral equilibrium.…”

“…In the modeling of hot species, their inertial effects are often neglected in favor of a balance between pressure and electric forces, on the grounds of their thermal velocities being large compared to wave and/or soliton speeds. However, as a careful discussion shows, 20 in the classical nonrelativistic case, one should use Boltzmann distributions, the adiabatic pressuredensity relations often used 1,4,7,9,[11][12][13] for hot inertialess species being then a poor description. This means that the transition from ultrarelativistic to classical nonrelativistic might be discussed as two opposite limits of the same formulation, c ¼ 4/3 for ultrarelativistic as opposed to c ¼ 1 for classical nonrelativistic hot species, but we prefer to deal with these opposites in separate sections below.…”

“…To the contrary, all nonlinear treatments based on a reductive perturbation method can only deal with weaker amplitudes, a constraint imposed by the use of stretched independent variables and of expansions of the dependent variables. Several authors limit themselves to reductive perturbation methods 1,7,9,11,12 leading to a Korteweg-de Vries (KdV), a nonlinear Schr€ odinger (NLS), or a Zakharov-Kuznetsov (ZK) evolution equation, the latter for magnetized plasmas.…”

“…The semiclassical model discussed here, adopted in a number of works published in the past, 1,4,7,9,[11][12][13] has won its place in the current literature mostly thanks to its analytical tractability and despite, admittedly, a certain lack of realism. It might be argued that its simple analytical structure fails to capture the rich dynamics of ultrarelativistic plasmas in the electrostatic approximation, where a more elaborate description may be required.…”

“…After this introduction, Sec. II describes the ultrarelativistic e-p-i plasma model, in which the pressure-density relations for the electrons and positrons have exponents c e ¼ c p ¼ 4/3, 1,4,[7][8][9]11,12 and recalls the essentials of a Sagdeev pseudopotential analysis for larger-amplitude waves and solitons. Section III is devoted to a numerical evaluation of possible existence ranges in a parametric assessment of where solitons might be encountered, and includes examples of suitable Sagdeev pseudopotentials, soliton profiles, and the associated electric fields.…”