## 1 Introduction  
Rigorous experimental and theoretical investigations on the unmagnetized collisionless plasmas having pair-ion and electrons are reported by many researchers because of their significant applications in understanding several types of collective processors in diverse environments, especially in Q-machine plasmas [1; 2; 3; 4], neutral beam source [5], semiconductor and material processing [6], and so on. To illustrate it, [PERSON] et al. [7] and [PERSON] et al. [8] have experimentally confirmed the production of negative ions with low temperature. [PERSON] [2] has also confirmed that the negative ions with low temperature (-0.2 eV) are generated in potassium plasma in Q-machine. [PERSON] et al. [9] have detected a beam of pair ions (Cs\({}^{+}\), Cl\({}^{-}\)) in the hot tungsten plate of a Q-machine. Besides, the negative ions exist in space and astrophysical objects [10; 11], e.g., in the D-region altitudes, F-region of the Earth's ionosphere, etc. More notably, negative ions can coexist with electrons in the ionosphere of Earth at D-region altitudes as they are formed primarily by electron attachment to electronegative species [10]. The Cassini spacecraft has confirmed that the heavy negative ions are likely to have occurred in the upper region of Titan's atmosphere [10]. [PERSON] et al. [12] have experimentally reported that ion acoustic (IA) waves with the presence of SF\({}_{6}^{-}\) plasma species. In addition, [PERSON] et al. [13] have already described the IA wave propagation in a Q-machine plasma having pair ions (K\({}^{+}\), SF\({}_{6}^{-}\)and electrons. They have investigated that the phase velocity of IA \"fast\" mode is increased with the increase in the negative to positive ions density ratio. It is noted that negative ion plasma system is mainly formed naturally, and it is composed of electrons, positive ions, and negative ions in space and astrophysical environments [14; 15; 16]. For instance, negative ions are produced in the lower ionosphere (D region) by the attaching of electrons to atoms or molecules with the presence of relatively high pressure [17]. The decrease in electron density allows the night-time reflection of radio waves from the E layer. [PERSON] et al. [18] have also experimentally observed that Landau damping prevented the formation of a shock, and only a \"spreading\" of the pulse with equal electron and negative ion temperatures, that is, \(T_{e}=T_{ni}\). However, they have found that the Landau damping is reduced and the shock structure is formed by increasing electron temperature and cooling the ions via ion-neutral collisions. With the increase in wave phase velocity, the results can be sufficiently reduced by the wave particle resonance due to the involvement of of negative ions when \(T_{e}>T_{ni}\)[12]. Further, the presence of energetic electrons as ubiquitous in a variety of environments and measurements of their distribution functions revealed them to be highly nonthermal or sub-thermal or superthermal [19; 20; 21; 22; 23; 24; 25]. Due to the energetic electrons, the electrons have long range interactions with other plasma species because the plasma species are actually occurred in different phase space [26]. Already, many researchers have examined the IA structures in the plasma system by assuming the plasma species in thermal equilibrium, which is followed the Maxwell-Boltzmann distribution. However, such an ideal thermal equilibrium assumption is no longer valid when some external agents, such as force field present in natural space environments, wave-particle interaction, turbulence, etc., are disturbed in the thermal equilibrium of the plasma systems. The fast ions and electrons mode in plasma environments is also suggested that the particles have a deviated velocity distributions far from Maxwellian distribution. Moreover, the systems with the presence of long-range interactions as well as long-time memory are intractable within the Boltzmann-Gibbs statistics.