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

Abstract

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.

Variable‐size dust grains with generalized (r, q) electrons in a dusty plasma

“…Solving Equations (14) with the aid of Equations (12) and (13) and eliminating the second-order perturbed quantities, we finally obtain the KdV equation as…”

“…The dust size distribution (DSD) can be considered to obey a power-law distribution, [4][5][6][7] a Gaussian (normal) distribution, [8] or a polynomial distribution [9] depending on where we apply our model. [14] In these situations, the velocity distribution functions of the plasma particles show non-Maxwellian superthermal tails, which decrease following a power-law function of the particle velocity. Moreover, the effects of DSD on the dispersion relation for oscillations in an infinite self-gravitating medium and the plasma frequency have also been studied.…”

“…Moreover, the effects of DSD on the dispersion relation for oscillations in an infinite self-gravitating medium and the plasma frequency have also been studied. [14] In the limiting case r = 0 and q = + 1, the generalized (r, q) distribution reduces to the -distribution, while in the case r = 0 and q → ∞ it reduces to the Maxwellian distribution. [4][5][6][7][8][9][10] In real plasma systems, the particle distribution deviates from the thermal distribution.…”

“…ionosphere, solar wind, interstellar medium, planetary magnetosphere, and magnetosheaths. [14] In these situations, the velocity distribution functions of the plasma particles show non-Maxwellian superthermal tails, which decrease following a power-law function of the particle velocity. Vasyliunas was the first to introduce a mathematical function, the so-called kappa or generalized Lorentzian distribution, containing the spectral index to model the velocity distribution of high-energy electrons within the plasmas.…”

“…[15] A more suitable and generalized distribution function, termed "the generalized (r, q) distribution," was introduced by Shah et al, [16,17] which has two spectral indices r (showing the high-energy particles on a broad shoulder of the velocity curve) and q (indicating the superthermality on the tail of the velocity curve). [14] In the limiting case r = 0 and q = + 1, the generalized (r, q) distribution reduces to the -distribution, while in the case r = 0 and q → ∞ it reduces to the Maxwellian distribution. The generalized (r, q) distribution has been employed to study different wave modes.…”