A generalized AZ-non-Maxwellian velocity distribution function for space plasmas

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.