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: a (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 thedr; q-distribution for alpha -> 0; (ii) the AZ-distribution function reduces to the q-distribution for alpha -> 0; and r -> 0; (iii) the AZ-distribution reduces to Cairns-distribution function for r -> 0; and q -> infinity; (iv) the AZ-distribution reduces to Vasyliunas Cairns distribution for r -> 0; and q = k + 1; (v) the AZ-distribution reduces to kappa distribution for alpha -> 0, r -> 0, and q = k + 1; and (vi) finally, the AZ-distribution reduces to Maxwellian distribution for alpha -> 0; r -> 0, and q -> infinity. The uses of this more generalized AZ-distribution function in various space plasmas are briefly discussed.