Vasyliunas–Cairns distribution function for space plasma species

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.