A more generalized form of non-Maxwellian distribution function (that can be named as Vasyliunas–Cairns distribution function) is introduced. Its basic properties are numerically analyzed by the variation of two important parameters, namely, α (which shows the amount of energetic particles present in the plasma system) and κ (which shows the superthermality of the plasma species). It has been observed that (i) for α→0 (κ→∞), the Vasyliunas–Cairns distribution function reduces to the Vasyliunas or κ (Cairns or nonthermal) distribution function; (ii) for α→0 and κ→∞, it reduces to the Maxwellian distribution function; and (iii) the effect of the parameter α (κ) significantly modifies the basic properties of the Vasyliunas (Cairns) distribution function. The applications of this generalized non-Maxwellian distribution function (Vasyliunas–Cairns distribution function) in different space plasma situations are briefly discussed.

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 α→0; (ii) the AZ- distribution function reduces to the q- distribution for α→0, and r→0; (iii) the  AZ-distribution reduces to Cairns-distribution function for r→0, and q→∞; (iv) the AZ-distribution reduces to Vasyliunas Cairns distribution for r→0, and q=κ+1; (v) the AZ-distribution reduces to kappa distribution for α→0, r→0, and q=κ+1; and (vi) finally, the AZ-distribution reduces to Maxwellian distribution   for α→0,r→0, and q→∞. 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, a)-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 ¼ constant) in the presence of Cairns-Tsallis (q, a)-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 a, the positive ion-toelectron temperature ratio, and the negative ion streaming speed (U 0) 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 a ¼ 0 the Cairns-Tsallis distribution reduces to pure Tsallis distribution and the latter reduces to Maxwellian distribution for q ! 1 and a ¼ 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 (U 0 ) 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 U 0 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.