“…In the field of space plasmas, many works about the measurements of plasma velocity distribution indicate that kappa-distributions are more suitable to model the plasma than Maxwellian velocity distributions especially at high energies in various space plasmas, for example, star's corona, 1 the solar wind, 2-4 the planetary exosphere, [5][6][7] the planetary magnetosphere, [8][9][10] and also some other observations, 11,12 etc. Therefore the kappa-distribution, as one of non-Maxwellian distributions, has already been a very interesting research topic in the related studies of astrophysical and space plasmas, such as origin of the kappa-distribution, [13][14][15] physical explanations of the kappa-parameter, 16,17 connections between the kappa-distribution and the nonextensive statistics, 18,19 ion-acoustic waves and dust-acoustic waves in plasmas, [20][21][22][23][24][25][26] and also some other plasma applications, [27][28][29][30] etc.…”