Electrostatic Solitary Waves in Relativistic Degenerate Electron–Positron–Ion Plasma

Abstract

The linear and nonlinear properties of ion acoustic excitations propagating in warm dense electron-positron-ion plasma are investigated. Electrons and positrons are assumed relativistic and degenerate, following the Fermi-Dirac statistics, whereas the warm ions are described by a set of classical fluid equations. A linear dispersion relation is derived in the linear approximation. Adopting a reductive perturbation method, the Korteweg-de Vries equation is derived, which admits a localized wave solution in the form of a small-amplitude weakly super-acoustic pulse-shaped soliton. The analysis is extended to account for arbitrary amplitude solitary waves, by deriving a pseudoenergy-balance like equation, involving a Sagdeev-type pseudopotential. It is shown that the two approaches agree exactly in the small-amplitude weakly super-acoustic limit. The range of allowed values of the pulse soliton speed (Mach number), wherein solitary waves may exist, is determined. The effects of the key plasma configuration parameters, namely, the electron relativistic degeneracy parameter, the ion (thermal)-to-the electron (Fermi) temperature ratio, and the positron-to-electron density ratio, on the soliton characteristics and existence domain, are studied in detail. Our results aim at elucidating the characteristics of ion acoustic excitations in relativistic degenerate plasmas, e.g., in dense astrophysical objects, where degenerate electrons and positrons may occur.

Modelling of relativistic ion-acoustic waves in ultra-degenerate plasmas

“…which can be used to show the complete equivalence between (18) and the kinetic longitudinal dielectric function (9). Therefore, the proposed fluid model satisfies the necessary condition, of agreement with the microscopic (kinetic) theory.…”

“…Recently, there has been a lot of interest on relativistic waves in degenerate plasmas, described by hydrodynamic equations (Haas & Kourakis 2010; Esfandyari-Kalejahi, Akbari-Moghanjoughi & Saberian 2011; Masood & Eliasson 2011; Ali & Ur Rahman 2014; Hussain, Mahmood & Ur Rehman 2014; McKerr, Haas & Kourakis 2014, 2016; Rahman, Kourakis & Qamar 2015; Irfan, Ali & Mizra 2016). The examination of the literature shows sometimes the use of questionable options, namely: choosing to work with the proper number density (which is the number density in a local reference frame where the fluid is at rest) in the equation of state, while using the laboratory number density in the continuity equation, with the same symbol for both objects; the use of relativistic equations of state inside otherwise non-relativistic fluid equations; the use of non-relativistic equations of state inside otherwise relativistic fluid equations; covariant or non-covariant form of the pressure term, including or not the respective time derivative; taking into account or not, the relativistic mass increase due to thermal effects.…”

Magnetoacoustic solitons and shocks in dense astrophysical plasmas with relativistic degenerate electrons

“…, . Thus, the Chandrasekhar equation of state is applicable to describing the dynamics of degenerate species in astrophysical plasmas (Rahman, Kourakis & Qamar 2015 b ). Moreover, these highly dense stars (i.e.…”

“…contain a superdense plasma, where the number density could be found (Shaikh & Shukla 2007;Salimullah et al 2009;Mahmood, Sadiq & Haque 2013) in the range 10 30 -10 34 cm −3 . It is worth mentioning here that for density N (0) ∼ 10 30 cm −3 , the Fermi temperature comes out as ∼10 9 K, which is much greater than the plasma temperature, viz., T Fe > T. Thus, the Chandrasekhar equation of state is applicable to describing the dynamics of degenerate species in astrophysical plasmas (Rahman, Kourakis & Qamar 2015b). Moreover, these highly dense stars (i.e.…”

Overtaking collisions of oblique isothermal ion‐acoustic multisolitons in ultra‐relativistic degenerate dense magnetoplasmas

“…Therefore, T Fe ≅ 6.4 × (10 6 − 10 8 ) K, and T Fp ≅ 6 × (10 6 − 10 8 ) K. Furthermore, B 0 ≅ 10 9 − 10 11 G and T e, p ≅ 6 × 10 6 K. It is demonstrated here that the electron/positron Fermi temperature is of the same order as that of T e, p (i.e., the system temperature), but T Fe, p > T e, p . On the other hand, the ion temperature is T i ≅ 0.2 × (10 4 − 10 6 ) K. [52] Figures 1 and 2 present position/time graphs. The positions are recorded for the discrete different times t = −12, −6, −3, −1, 0, 1, 6, 3, and 12.…”