Until fairly recently, the customary approach to wave and instability studies in space plasmas relied on the Maxwellian distribution or one of its variants. This approach prevailed despite a body of evidence indicating that the plasmas being considered were effectively collisionless and in dynamical states far from equilibrium. Modelling the widely observed superthermal power law tails on nonthermal particle velocity distributions by sums of Maxwellians was a well established tradition among the community of space plasma researchers despite some early recognition [1] that the less well known kappa distribution provided a better fit. The kinetic theory of waves and instabilities in space plasmas based on the kappa distribution or variant is now more widely adopted by researchers. A barrier to its widespread acceptance, the perception that the kappa distribution had no physical theory underpinning its existence, began to fall with the emergence in statistical mechanics of non-extensive Tsallis statistics. The primary advantage of kinetic theory based on the kappa distribution is that it more accurately represents the velocity distributions measured in space plasmas, especially those having power law tails. Use of a kappa distribution model does not change any microphysical processes, but it does alter their probabilities of occurrence, which in turn affects important average quantities such as instability growth and wave damping rates. Dispersion relations also often show features distinguishable from their Maxwellian equivalents, providing valuable signatures for out of equilibrium plasma behaviour. After briefly reviewing the theoretical framework for kinetic studies of plasma waves, this talk presents results from some of the investigations of waves and instabilities in plasmas modelled with kappa distributions carried out by the authors and collaborators. Amongst others, the whistler [2] and EMIC [3] instabilities driven by thermal anisotropy will be discussed, as well as perpendicularly propagating electron and ion Bernstein waves. In addition, some recent results of 1D and 2D simulations of oblique waves in plasmas having a kappa distribution, will be presented.

Using a kinetic theory approach, dust ion acoustic (DIA) waves are investigated in an unmagnetized collisionless plasma with kappa-distributed electrons and ions, and Maxwellian dust grains of constant charge. Both analytical and numerical results, the latter following from the full solution of the associated dispersion relation, are presented, and a comparison is made. The effects of the ion and electron spectral indices, as well as the species' density ( ne/ni) and temperature ( Te/Ti) ratios, on the dispersion and damping of the waves are considered. In the long wavelength regime, increases in both the electron spectral index (κe) and the dust density fraction (reduced f=ne/ni) lead to an increase in phase velocity. The range in wavelength over which modes are weakly damped increases with an increase in Te/Ti. However, the ion spectral index, κi, does not have a significant effect on the dispersion or damping of DIA waves.

Using both the Sagdeev and Korteweg-de Vries (KdV) methods, ion thermal effects on slow mode ion acoustic solitons and double layers are investigated in a plasma with two adiabatic positive ion species. It is found that reducing the gap between the two ion thermal speeds by increasing the relative temperature of the cool ions increases the typical soliton/double layer speeds for all values of the ion-ion density ratio and reduces the range in the density ratio that supports double layers. The effect of increasing the relative cool ion temperature on the soliton/double layer amplitudes depends on the relative densities. For lower values of the ion density ratio, an increase in cool ion temperature leads to a significant decrease in soliton/double layer amplitude, so one may find that solitons of all permissible speeds lie within the range of KdV theory.

Electrostatic dust-acoustic shock waves are investigated in a viscous, complex plasma consisting of dust particles, electrons, and ions. The system is modelled using the generalized hydrodynamic equations, with strong coupling between the dust particles being accounted for by employing the effective electrostatic temperature approach. Using a reductive perturbation method, it is demonstrated that this model predicts the existence of weakly nonlinear dust-acoustic shock waves, arising as solutions to Burgers's equation, in which the nonlinear forces are balanced by dissipative forces, in this case, associated with viscosity. The evolution and stability of dust-acoustic shocks is investigated via a series of numerical simulations, which confirms our analytical predictions on the shock characteristics.

Space plasmas are often characterized by the presence of energetic particles, due to various electron acceleration mechanisms [1], leading to a power-law dependence at high (superthermal) velocity values. Various theories have been proposed to model this phenomenon; the most promising scenario seems to be the kappa-type (family of) distribution function(s), which reproduces observed data more efficiently that the standard Maxwell-Boltzmann approach [2]. Electrostatic Solitary Waves (ESWs) [3] and shock structures [4] are ubiquitous in Space observations, and also in the laboratory experiments on beam-plasma interactions [5]. It has been shown from first principles that excess electron superthermality may alter the dynamical properties of electrostatic nonlinear modes, and does in particular modify the propagation characteristics of solitary waves [6]. Recent studies have also indicated that the dynamical characteristics of expanding plasma fronts are affected by excess electron superthermality [7]. In this presentation I will review, from first principles, the effects of a non-Maxwellian electron distribution on the characteristics of electrostatic plasma modes. A kappa distribution function [1] is employed to model the deviation of a plasma component (e.g. electrons) from Maxwellian equlibrium. It will be shown that the excess in superthermal propulation modifies the charge screening mechanism, affecting the dispersion laws of both low-frequency (ion-acoustic) and high frequency (Langmuir) modes. Various experimental observations may thus be interpreted as manifestations of excess superthermality [2, 5]. Focusing on the features of nonlinear excitations (shocks, solitons), we investigate the role of superthermality in their propagation dynamics (existence laws, stability profile) and dynamical profile [6]. The relation to other nonthermal plasma theories [8] may also be briefly discussed.

An investigation of the propagation of ion acoustic waves in nonthermal plasmas in the presence of trapped electrons has been undertaken. This has been motivated by space and laboratory plasma observations of plasmas containing energetic particles, resulting in long-tailed distributions, in combination with trapped particles, whereby some of the plasma particles are confined to a finite region of phase space. An unmagnetized collisionless electron-ion plasma is considered, featuring a non-Maxwellian-trapped electron distribution, which is modelled by a kappa distribution function combined with a Schamel distribution. The effect of particle trapping has been considered, resulting in an expression for the electron density. Reductive perturbation theory has been used to construct a KdV-like Schamel equation, and examine its behaviour. The relevant configurational parameters in our study include the superthermality index κ and the characteristic trapping parameter β. A pulse-shaped family of solutions is proposed, also depending on the weak soliton speed increment u0. The main modification due to an increase in particle trapping is an increase in the amplitude of solitary waves, yet leaving their spatial width practically unaffected. With enhanced superthermality, there is a decrease in both amplitude and width of solitary waves, for any given values of the trapping parameter and of the incremental soliton speed. Only positive polarity excitations were observed in our parametric investigation.

Interaction of a stream of high-energy electrons with the background plasma plays an important role in the astrophysical phenomena such as interplanetary and stellar bow shock and Earth's foreshock emission. It is not yet fully understood how electrostatic solitary waves are produced at the bow shock. Interestingly, a population of energetic suprathermal electrons were also found to exist in those environments. Previously, we have studied the properties of negative electrostatic potential solitary structures exist in such a plasma with excess suprathermal electrons. In the present study, we investigate the existence conditions and propagation properties of electron-acoustic solitary waves in a plasma consisting of an electron beam fluid, a cold electron fluid, and hot suprathermal electrons modeled by a kappa-distribution function. The Sagdeev pseudopotential method was used to investigate the occurrence of stationary-profile solitary waves. We have determined how the electron-acoustic soliton characteristics depend on the electron beam parameters. It is found that the existence domain for solitons becomes narrower with an increase in the suprathermality of hot electrons, increasing the beam speed, decreasing the beam-to-cold electron population ratio. These results lead to a better understanding of the formation of electron-acoustic solitary waves observed in those space plasma systems characterized by kappa-distributed electrons and inertial drifting (beam) electrons.

A fully nonlinear Sagdeev pseudopotential approach is used to study the existence domain of fast mode ion-acoustic solitons in a three-species plasma composed of cold and warm adiabatic positive ion species and Boltzmann electrons. It is shown that for appropriate values of the cold-to-warm ion charge-to-mass ratio, μ, and the effective warm ion-to-electron temperature ratio, τ, there is a range in cold to warm ion charge density ratio, f, over which a stopband in soliton speed exists. Solitons do not propagate in the stopband, although they can occur for both higher and lower speeds. The stopbands are associated with a limiting curve of the existence domain that is double-valued in speed for a range of values of f. Analytical estimates of the upper and lower limits of τ and μ that support stopbands are found. It is suggested that, inter alia, the analysis should be applicable to the solar wind plasma.

Using a Vlasov-Poisson model, a numerical investigation of the dispersion relation for ion Bernstein waves in a kappa-distributed plasma has been carried out. The dispersion relation is found to depend significantly on the spectral index of the ions, κi, the parameter whose smallness is a measure of the departure from thermal equilibrium of the distribution function. Over all cyclotron harmonics, the typical Bernstein wave curves are shifted to higher wavenumbers (k) if κi is reduced. For waves whose frequency lies above the lower hybrid frequency, ωLH, an increasing excess of superthermal particles (decreasing κi) reduces the frequency, ωpeak, of the characteristic peak at which the group velocity vanishes, while the associated kpeak is increased. As the ratio of ion plasma to cyclotron frequency (ωpi/ωci) is increased, the fall-off of ω at large k is smaller for lower κi and curves are shifted towards larger wavenumbers. In the lower hybrid frequency band and harmonic bands above it, the frequency in a low-κi plasma spans only a part of the intraharmonic space, unlike the Maxwellian case, thus exhibiting considerably less coupling between adjacent bands for low κi. It is suggested that the presence of the ensuing stopbands may be a useful diagnostic for the velocity distribution characteristics. The model is applied to the Earth's plasma sheet boundary layer in which waves propagating perpendicularly to the ambient magnetic field at frequencies between harmonics of the ion cyclotron frequency are frequently observed.

Supersolitons are a form of soliton characterised, inter alia , by additional local extrema superimposed on the usual bipolar electric field signature. Previous studies of supersolitons supported by three-component plasmas have dealt with ion-acoustic structures. An analogous problem is now considered, namely, dust-acoustic supersolitons in a plasma composed of fluid negative dust grains and two kappa-distributed positive ion species. Calculations illustrating some supersoliton characteristics are presented.

Recently, a hybrid distribution function [Tribeche et al., Phys. Rev. E 85, 037401 (2012)] was proposed to describe a plasma species with an enhanced superthermal component. This combines a Cairns-type "nonthermal" form with the Tsallis theory for nonextensive thermodynamics. Using this alternative model, the propagation of arbitrary amplitude ion acoustic solitary waves in a two-component plasma is investigated. From a careful study of the distribution function it is found that the model itself is valid only for a very restricted range in the q-nonextensive parameter and the nonthermality parameter, α. Solitary waves, the amplitude and nature of which depend sensitively on both q and α, can exist within a narrow range of allowable Mach numbers. Both positive and negative potential structures are found, and coexistence may occur.

Space plasmas provide abundant evidence of highly energetic particle population, resulting in a long-tailed non-Maxwellian distribution. Furthermore, the first stages in the evolution of plasmas produced during laser-matter interaction are dominated by nonthermal electrons, as confirmed by experimental observation and computer simulations. This phenomenon is efficiently modelled via a kappa-type distribution. We present an overview, from first principles, of the effect of superthermality on the characteristics of electrostatic plasma waves. We rely on a fluid model for ion-acoustic excitations, employing a kappa distribution function to model excess superthermality of the electron distribution. Focusing on nonlinear excitations (solitons), in the form of solitary waves (pulses), shocks and envelope solitons, and employing standard methodological tools of nonlinear plasmadynamical analysis, we discuss the role of excess superthermality in their propagation dynamics (existence laws, stability profile), geometric characteristics and stability. Numerical simulations are employed to confirm theoretical predictions, namely in terms of the stability of electrostatic pulses, as well as the modulational stability profile of bright- and dark-type envelope solitons.

The linear and nonlinear properties of large-amplitude electron-acoustic waves are investigated in a magnetized plasma comprising two distinct electron populations (hot and cold) and immobile ions. The hot electrons are assumed to be in a non-Maxwellian state, characterized by an excess of superthermal particles, here modeled by a kappa-type long-tailed distribution function. Waves are assumed to propagate obliquely to the ambient magnetic field. Two types of electrostatic modes are shown to exist in the linear regime, and their properties are briefly analyzed. A nonlinear pseudopotential-type analysis reveals the existence of large-amplitude electrostatic solitary waves and allows for an investigation of their propagation characteristics and existence domain, in terms of the soliton speed (Mach number). The effects of the key plasma configuration parameters, namely the superthermality index and the cold electron density, on the soliton characteristics and existence domain, are studied. The role of obliqueness and magnetic field is discussed.

Existence domains and characteristics of ion acoustic solitons are studied in a two-temperature electron plasma with both electron components being kappa-distributed, as found in Saturn’s magnetosphere. As is the case for double-Boltzmann electrons, solitons of both polarities can exist over restricted ranges of fractional hot electron density ratio for this plasma model. Low κ values, which indicate increased suprathermal particles in the tail of the distribution, yield a smaller domain in the parameter space of hot density fraction and normalized soliton velocity (f, M), over which both soliton polarities are supported for a given plasma composition (the coexistence region). For some density ratios that support coexistence, solitons occur even at the lowest (critical) Mach number (i.e., at the acoustic speed), as found recently for a number of other plasma models. Like Maxwellians, low-κ distributions also support positive potential double layers over a narrow range of low fractional cool electron density (<10%).

The existence of large-amplitude electron-acoustic solitary structures is investigated in an unmagnetized and collisionless two-temperature dusty plasma penetrated by an electron beam. A nonlinear pseudopotential technique is used to investigate the occurrence of stationary-profile solitary waves, and their parametric dependence on the electron beam and dust perturbation is discussed.

The Sagdeev pseudopotential method is used to investigate the occurrence and the dynamics of fully nonlinear electrostatic solitary structures in a plasma containing suprathermal hot electrons, in the presence of massive charged dust particles in the background. The soliton existence domain is delineated, and its parametric dependence on different physical parameters is clarified.

Using the Sagdeev potential approach, arbitrary amplitude modified ion acoustic solitons and double layers have been studied in an electron-positron-ion (e-p-i) plasma composed of Cairns-distributed electrons, Boltzmann positrons and cold ions. Existence domains are presented in different slices of parameter space, and care is taken to differentiate between behaviour at a fixed soliton speed, and at the Mach number normalized with respect to the true acoustic speed for the three-component plasma. Negative solitons, limited in Mach number by double layers, have been found over small ranges in beta, relative positron density and Mach number. These have not previously been reported in an e-p-i plasma. A region of 'coexistence' in parameter space has been identified, in which solitons of both polarities are supported. In this region, one polarity behaves in a 'Korteweg-de Vries (KdV)-like' fashion, vanishing at the acoustic speed, while solitons of the other polarity have finite amplitude at the acoustic speed ('non-KdV-like'), as has been reported recently in a number of other plasma models. This work extends considerably and also corrects some errors in a recent publication (Pakzad 2009 Phys. Lett. A 373 847-50).

Using a kinetic theoretical approach, the characteristics of electron acoustic waves (EAWs) are investigated in plasmas whose electron velocity distributions are modeled by a combination of two kappa distributions, with distinct densities, temperatures, and kappa values. The model is applied to Saturn's magnetosphere, where the electrons are well fitted by such a double-kappa distribution. The results of this model suggest that EAWs will be weakly damped in regions where the hot and cool electron densities are approximately equal, the hot to cool temperature ratio is about 100, and the kappa indices are roughly constant, with kappa(c) similar or equal to 2 and kappa(h) similar or equal to 4, as found in Saturn's outer magnetosphere (R similar to 13-18 R-S, where R-S is the radius of Saturn). In the inner magnetosphere (R < 9 R-S), the model predicts strong damping of EAWs. In the intermediate region (9-13 R-S), the EAWs couple to the electron plasma waves and are weakly damped.