Influence of finite temperature degeneracy and superthermal ions on dust acoustic solitary structures

TL;DR

The paper analyzes dust-acoustic solitary waves in an unmagnetized, collisionless dusty electron–positron–ion plasma, where electrons and positrons are partially degenerate under Fermi–Dirac statistics and ions follow a kappa distribution. Using a normalized fluid–Poisson model and the Sagdeev pseudopotential method, the authors derive a linear dispersion relation that incorporates finite-temperature degeneracy and ion superthermality, and they map the existence domain for arbitrary-amplitude solitary waves. They show that only negative-potential, rarefactive DASWs exist, confined to a subsonic Mach-number interval with a critical Mach number $M_c$ and a numerically determined upper limit $M_u$, and that the wave amplitude and width are highly sensitive to degeneracy strength, ion spectral index, and composition. A small-amplitude expansion yields a Korteweg–de Vries limit that provides closed-form soliton characteristics, consistent with the Sagdeev results, thereby linking the nonlinear dynamics across regimes and clarifying how finite-temperature degeneracy and superthermal ions shape nonlinear dust–acoustic activity in dense space and astrophysical plasmas.

Abstract

We examine dust acoustic (DA) solitary structures in an unmagnetized, collisionless dusty electron positron ion (epi) plasma in which electrons and positrons are described by finite temperature Fermi Dirac statistics and ions obey a superthermal kappa distribution. A normalized fluid Poisson model is formulated using polylogarithm based expressions for the partially degenerate electrons positrons, while cold negatively charged dust grains provide the inertial response. Linear dispersion analysis yields a modified DA phase speed. Nonlinear solitary structures are investigated using the Sagdeev pseudopotential method. The system is found to support only negative potential (rarefactive) DA solitary waves within a bounded subsonic Mach number interval. The critical Mach number, consequently, the corresponding linear DA speed show an explicit dependence on the degeneracy parameters and the ion spectral index. The amplitude and width of the solitary structures are shown to be highly sensitive to the electron (positron) degeneracy strength, the ion positron concentration ratios, the ion temperature ratio, and the superthermality of the ions. A small amplitude approximation of the pseudopotential reduces the system to the Korteweg de Vries limit, providing closed form expressions for the soliton characteristics, in agreement with the Sagdeev predictions. The results clarify the combined roles of finite temperature degeneracy and superthermal ions in shaping nonlinear DA dynamics in space and astrophysical dusty plasmas.

Figures (7)

• Figure 1: Plots of dispersion curves showing the variation of wave frequency $\omega$ with the wave number $k$ for different values of $\delta_i$, $\delta_p$ and $\sigma_i$. Here, $\tau_e=0.5$, $\kappa_i=5$ and $\sigma_p=1$.
• Figure 2: Plots of dispersion curves showing the variation of wave frequency $\omega$ with the wave number $k$ for different values of $\tau_e$ and $\kappa_i$. Here, $\delta_i=0.4$, $\delta_p=0.8$, $\sigma_i=0.4$ and $\sigma_p=1$.
• Figure 3: Domain of existence of negative potential solitary waves in terms of the true Mach number $M/M_c$ and $\tau_e$ for different values of (a) $\delta_i$, $\delta_p$ where $\kappa_i=3$, $\sigma_i=0.4$ and (b) $\kappa_i$, $\sigma_i$ where $\delta_i=0.4$, $\delta_p=0.8$. Here, $\sigma_p=1$.
• Figure 4: (a) The Sagdeev pseudopotential $V(\phi)$ and (b) the corresponding solitary-wave potential profiles $\phi$ are shown for different values of the true Mach number $M/M_c$. The parameters used are $\kappa_i=3$, $\sigma_i=0.4$, $\delta_i=0.4$, $\delta_p=0.8$, $\sigma_p=1$ and $\tau_e=0.2$.
• Figure 5: (a) The Sagdeev pseudopotential $V(\phi)$ and (b) the corresponding solitary-wave potential profiles $\phi$ are shown for different values of $\sigma_i$, $\delta_i$ and $\delta_p$. The other parameters used are $\kappa_i=3$, $\tau_e=0.2$, $\sigma_p=1$ and $M/M_c=1.2$.