The plasma particle velocity distributions observed in the solar wind generally show enhanced (non-Maxwellian) suprathermal tails, decreasing as a power law of the velocity and well described by the family of Kappa distribution functions. The presence of non-thermal populations at different altitudes in space plasmas suggests a universal mechanism for their creation and important consequences concerning plasma fluctuations, the resonant and nonresonant wave - particle acceleration and plasma heating. These effects are well described by the kinetic approaches where no closure requires the distributions to be nearly Maxwellian. This paper summarizes and analyzes the various theories proposed for the Kappa distributions and their valuable applications in coronal and space plasmas.

Kappa Distributions: Theory and Applications in Space Plasmas

Preface. 1. Plasmas and Dust. 2. Charging Mechanisms and Experiments. 3. Space Observations. 4. Multispecies Formalism and Waves. 5. Electrostatic Modes. 6. Electromagnetic Modes. 7. Fluctuating Dust Charges. 8. Self-Gravitation. 9. Mass and Size Distributions. 10. Other Modes. 11. Conclusions and Outlook. Bibliography. Index.

https://physicstoday.scitation.org/doi/pdf/10.1063/1.1404853

Waves in Dusty Space Plasmas

In this paper we examine the physical foundations and theoretical development of the kappa distribution, which arises naturally from non-extensive Statistical Mechanics. The kappa distribution provides a straightforward replacement for the Maxwell distribution when dealing with systems in stationary states out of thermal equilibrium, commonly found in space and astrophysical plasmas. Prior studies have used a variety of inconsistent, and sometimes incorrect, formulations, which have led to significant confusion about these distributions. Therefore, in this study, we start from the N-particle phase space distribution and develop seven formulations for kappa distributions that range from the most general to several specialized versions that can be directly used with common types of space data. Collectively, these formulations and their guidelines provide a “toolbox” of useful and statistically well-grounded equations for future space physics analyses that seek to apply kappa distributions in data analysis, simulations, modeling, theory, and other work.

/pdf/understanding-kappa-distributions-a-toolbox-for-space-3h0qt94s0k.pdf

Understanding Kappa Distributions: A Toolbox for Space Science and Astrophysics

Ultracold neutral plasmas

Tsallis holographic dark energy

Arbitrary amplitude ion-acoustic solitary waves are addressed in a two-component plasma with a q-nonextensive electron velocity distribution. Our results show that in such a plasma solitary waves, the amplitude and nature of which depend sensitively on the q-nonextensive parameter can exist. Due to the electron nonextensivity, our plasma model can admit compressive as well as rarefactive ion-acoustic solitons. For q>1 (−1<q<1), the lower limit of the allowable Mach numbers is smaller (greater) than its Boltzmannian counterpart, allowing therefore the possibility of the existence of subsonic ion-acoustic solitons. As the nonextensive character of the plasma becomes important, the potential pulse amplitude increases while its width is narrowed. For −1<q<0, our plasma model can admit only rarefactive ion-acoustic solitary waves involving relatively high Mach numbers. Due to the flexibility provided by the nonextensive q-parameter, our results should help in providing a good fit between theoretical and experi...

Ion-acoustic solitary waves in a plasma with a q-nonextensive electron velocity distribution

The seminal paper of Mamun et al. [Phys. Plasmas 3, 702 (1996)] is revisited within the theoretical framework of the Tsallis statistical mechanics. The nonextensivity may originate from the correlation or long-range interactions in the dusty plasma. It is found that depending on whether the nonextensive parameter q is positive or negative, the dust-acoustic (DA) soliton exhibits compression for q 0. The lower limit of the Mach number for the existence of DA solitary waves is greater (smaller) than its Maxwellian counterpart in the case of superextensivity (subextensivity).

Nonextensive dust-acoustic solitary waves

The model of Cairns et al. [Geophys. Res. Lett. 22, 2709 (1995)] is generalized. A physically meaningful nonextensive nonthermal velocity distribution is outlined. As the nonextensive character of the nonthermal electrons increases, the distribution shoulders may become less or more prominent and high-energy states are less or more probable than in the extensive nonthermal case. It is found that our plasma model supports the coexistence of smooth rarefactive and spiky compressive ion-acoustic solitary waves. The rarefactive solitons are more affected by nonextensivity than their compressive counterpart and a slight increase in the nonextensive parameter may destroy this dual nature.

Ion acoustic solitary waves in a plasma with nonthermal electrons featuring Tsallis distribution.

A first theoretical work is presented to study variable charge dust acoustic solitons within the theoretical framework of the Tsallis statistical mechanics. Our results reveal that the spatial patterns of the variable charge solitary wave are significantly modified by electron nonextensive effects. In particular, it may be noted that for −1 1 provides qualitatively opposite results: electron nonextensivity makes the solitary structure more spiky. Our results should help in providing a go...

Variable charge dust acoustic solitary waves in a dusty plasma with a q-nonextensive electron velocity distribution

Electron-acoustic double-layers (EA-DLs) are addressed in a plasma with a q-nonextensive electron velocity distribution. The domain of their allowable Mach numbers depends drastically on the plasma parameters and, in particular, on the electron nonextensivity. As the electrons evolve far away from their thermodynamic equilibrium, the negative EA-DLs shrinks and may develop into compressive EA-DLs. Our results may be relevant to the double-layers observed both in the auroral region and the plasma sheet of Earth’s magnetosphere (during enhanced magnetic activity). These DLs associated parallel electric fields are thought to be responsible for particle (electrons and ions) acceleration. Furthermore, our theoretical analysis brings a possibility to develop more refined theories of nonlinear cosmic DLs that may occur in astrophysical plasmas.

Mouloud Tribeche

Papers

Ion-acoustic solitary waves in a plasma with a q-nonextensive electron velocity distribution

Nonextensive dust-acoustic solitary waves

Ion acoustic solitary waves in a plasma with nonthermal electrons featuring Tsallis distribution.

Variable charge dust acoustic solitary waves in a dusty plasma with a q-nonextensive electron velocity distribution

Electron acoustic double layers in a plasma with a q -nonextensive electron velocity distribution