A more generalized form of the non-Maxwellian distribution function, i.e., the AZ-distribution function is presented. Its fundamental properties are numerically observed by the variation of three parameters: α (rate of energetic particles on the shoulder), r (energetic particles on a broad shoulder), and q (superthermality on the tail of the velocity distribution curve of the plasma species). It has been observed that (i) the $AZ-$ distribution function reduces to the $(r,q)-$ distribution for $\alpha \to 0$ ; (ii) the $AZ-$ distribution function reduces to the $q-$ distribution for $\alpha \to 0,$ and $r\to 0;$ (iii) the $\hspace{0.17em}AZ$ -distribution reduces to Cairns-distribution function for $r\to 0,$ and $q\to \infty$ ; (iv) the AZ-distribution reduces to Vasyliunas Cairns distribution for $r\to 0,$ and $q=\kappa +1;$ (v) the AZ-distribution reduces to kappa distribution for $\alpha \to 0$ , $r\to 0$ , and $q=\kappa +1;$ and (vi) finally, the AZ-distribution reduces to Maxwellian distribution $\hspace{0.17em}$ for $\alpha \to 0,r\to 0$ , and $q\to \infty$ . The uses of this more generalized $AZ-$ distribution function in various space plasmas are briefly discussed.

Dust grain charging processes are presented in a non-Maxwellian dusty plasma following the Cairns-Tsallis (q, α)–distribution, whose constituents are the electrons, as well as the positive/negative ions and negatively charged dust grains. For this purpose, we have solved the current balance equation for a negatively charged dust grain to achieve an equilibrium state value (viz., q_d = constant) in the presence of Cairns-Tsallis (q, α)–distribution. In fact, the current balance equation becomes modified due to the Boltzmannian/streaming distributed negative ions. It is numerically found that the relevant plasma parameters, such as the spectral indexes q and α, the positive ion-to-electron temperature ratio, and the negative ion streaming speed (U₀) significantly affect the dust grain surface potential. It is also shown that in the limit q → 1 the Cairns-Tsallis reduces to the Cairns distribution; for α = 0 the Cairns-Tsallis distribution reduces to pure Tsallis distribution and the latter reduces to Maxwellian distribution for q → 1 and α = 0.

Dust charging processes involving the collection of electrons and positive/negative ions in a non-equilibrium dusty plasma are revisited by employing the power-law kappa (κ)-distribution function. In this context, the current balance equation is solved to obtain dust grain surface potential in the presence of negative ions. Numerically, it is found that plasma parameters, such as the κ spectral index, the negative ion-to-electron temperature ratio (γ), the negative–positive ion number density ratio (α), and the negative ion streaming speed (U₀) significantly modify the dust grain potential profiles. In particular, for large kappa values, the dust grain surface potential reduces to the Maxwellian case, and at lower kappa values the magnitude of the negative dust surface potential increases. An increase in γ and U₀ leads to the enhancement of the magnitude of the dust grain surface potential, while α leads to an opposite effect. The relevance of present results to low-temperature laboratory plasmas is discussed.

Electromagnetic ion cyclotron (EMIC) waves have been studied in this manuscript which are triggered by hot proton thermal anisotropy having energy ranging from 7 to 26 keV with a minimum resonant energy of 6.9 keV. However, an opposite effect can be observed for the hot protons for energy less than the minimum resonant energy. When the intensity of EMIC waves is large, the cold protons (ions) having low-energies can be energized by the EMIC waves. The possible reasons for this energization are the phase bunching of low energy ions with EMIC waves and the generation of electric fields at the relaxation time of substorm. As a consequence, these undetectable protons now become detectable, and the number density and temperature anisotropy of the protons also increase within the energy range from 1 to 100 eV. Accordingly, the helium ions are also energized by the EMIC waves.

Dust grain potential variation influence by positive ion streaming as well as negative ion streaming is presented in a complex (dusty) plasma following the Maxwellian/non-Maxwellian (kappa distribution and Cairns distribution) function. The components of complex plasma are the electrons, ions [positive and negative], and dust grains having negative charge. For this purpose, the mathematical statement (equation) of currents is derived for dust grains having negative charge to fulfill the equilibrium state (viz., q_D = constant). It is observed numerically that positive ion streaming speed as well as negative ion streaming speed has a significant influence on the surface potential of dust particles, e.g., by increasing the positive ion and negative ion streaming speed, the magnitude of dust particle surface potential increases. The relevance to low-temperature research center in a non-equilibrium complex (dusty) plasma is precisely discussed by associating oxygen ion (negative and positive) species.

Electrostatic solitary (ES) structures have been frequently observed in the solar wind, Earth’s and other planetary magnetosphere and are the most widely theoretically studied waves in literature. However, there are very few studies in which simulations and theoretical studies have been performed simultaneously. In this paper, we perform 1-D electrostatic Particle-in-Cell (PIC) simulations of electrostatic solitary (ES) waves in a plasma which consists of immobile ions, and cold, beam and hot electrons. It is found that for a small value of electron beam velocity, ES structures are formed due to the steepening of initially quasi monochromatic electron acoustic (EA) waves. We interpret these ES structures as electron acoustic solitary (EAS) structures, which agree with the rarefactive (negative electrostatic potential) electron acoustic solitary structures obtained theoretically as a solution of the Korteweg de-Vries (KdV) equation. We found that polarity of solitary structures depends on the drift velocity of electron beam and formation of electric field spikes are consistent with the ES waves observations from Earth’s magnetosphere.