Space plasmas are often characterized by the presence of energetic particles in the background, due to various electron acceleration mechanisms [1]. This phenomenon is associated with a power-law dependence at high (superthermal) velocity values, modeled by a kappa-type distribution function, which reproduces observed data more efficiently that the standard Maxwellian distribution approach
[2]. It has been shown from first principles that this ubiquitous superthermal feature of plasmas may alter the propagation characteristics of plasma modes, and modify the plasma screening properties [3].

We review, from first principles, of the effect of excess superthermality on the characteristics of electrostatic nonlinear plasma modes. We employ a kappa distribution function [1] to model the deviation of a plasma constituent (electrons, in general) from Maxwellian equlibrium. An excess in superthermal propulation modifies the charge screening mechanism, affecting the dispersion laws of both low- and higher frequency modes substantially. Various observations may thus be interpreted as manifestations of excess electron superthermality [2]. Focusing on the features of nonlinear excitations (shocks, solitary waves), we investigate the role of superthermality in their propagation dynamics (existence laws, stability profile) and dynamical profile [3]. The relation to other nonthermal plasma theories is briefly discussed.

[1] See V.M. Vasyliunas, J. Geophys. Res. 73, 2839 (1968), for a historical reference; also, V.Pierrard and M. Lazar, Solar Phys. 267, 153 (2010), for a more recent review.

[2] M. Hellberg et al, J. Plasma Physics 64, 433 (2000).

[3] S. Sultana, I. Kourakis, N.S. Saini, M.A. Hellberg, Phys. Plasmas 17, 032310 (2010); S. Sultana and I. Kourakis, Plasma Phys. Cont. Fus. 53, 045003 (2011);
S. Sultana, G. Sarri and I. Kourakis, Phys. Plasmas 19, 012310 (2012);
I. Kourakis, S. Sultana and M.A. Hellberg, Plasma Phys. Cont. Fusion, 54, 124001 (2012); G. Williams and I. Kourakis, Plasma Physics and Controlled Fusion 55, 055005/1-13 (2013).