Kappa Distributions - 1st Edition - ISBN: 9780128046388

Kappa Distributions

1st Edition

Theory and Applications in Plasmas

Authors: George Livadiotis
Paperback ISBN: 9780128046388
Imprint: Elsevier
Published Date: 13th April 2017
Page Count: 720
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Kappa Distributions: Theory and Applications in Plasmas presents the theoretical developments of kappa distributions, their applications in space plasmas, and how they affect the underpinnings of our understanding of space and plasma physics, astrophysics, and statistical mechanics--thermodynamics. As such, this book is ideal for geophysicists, especially those interested in space and planetary science, particularly space plasma and upper earth atmosphere.

The book is separated into three major parts, theoretical methods, analytical methods in plasmas, and applications in space plasmas. The first part of the book focuses on basic aspects of the theory of kappa distributions, beginning with the connection of kappa distributions with solid statistical backgrounds, hence the non-extensive statistical mechanics.

The book then moves on to plasma physics, and is devoted to analytical methods related to kappa distributions on various basic plasma topics, spanning linear/nonlinear plasma waves, solitons, shockwaves, and dusty plasmas. The final part of the book deals with applications in space plasmas, focusing on applications of theoretical and analytical developments in space plasmas from the heliosphere and beyond.

Key Features

  • Answers important questions, such as how plasma waves are affected by kappa distributions and how solar wind, and planetary/cometary magnetospheres can be modeled using kappa distributions
  • Presents the features of kappa distributions in the context of space plasmas, including how kappa indices, temperatures, and densities vary among the various species populations in different space plasmas
  • Provides readers with the information they need to decide which specific formula of kappa distribution should be used for a certain occasion and system


Kappa Distributions is ideal for space, plasma, and statistical physicists; geophysicists especially of the upper atmosphere, Earth and planetary scientists, and astrophysicists

Table of Contents

PART A: Theory and Formalism
1. Statistical background of kappa distributions: Connection with non-extensive statistical mechanics - George Livadiotis
2. Entropy associated with kappa distributions - George Livadiotis
3. Phase space kappa distributions with potential energy - George Livadiotis
4. Formulae of kappa distributions: Toolbox - George Livadiotis

PART B: Plasma Physics
5. Basic parameters in plasmas described by kappa distributions - George Livadiotis
6. Superstatistics: Superposition of Maxwell-Boltzmann distributions - Christian Beck & E.G.D. Cohen
7. Linear kinetic plasma waves in plasmas described by kappa distributions - Adolfo Figueroa-Viñas, Rudi Gaelzer, Pablo S. Moya,  R. Mace, J.A. Araneda
8. Nonlinear wave-particle interaction and electron kappa distributions - Peter H. Yoon, George Livadiotis
9. Solitary waves in plasmas described by kappa distributions - G.S. Lakhina & Satyavir Singh

PART C: Applications in Space Plasmas
10. Ion distributions in space plasmas - George Livadiotis & David J. McComas
11. Electron distributions in space plasmas - Viviane Pierrard & Nicole Meyer-Vernet
12. The "kappa-shaped" particle spectra in planetary magnetospheres - Konstantinos Dialynas, Chris P. Paranicas, James F. Carbary, M. Kane, Stamatios M. Krimigis, Barry H. Mauk
13. Kappa-distributions and the solar spectra – theory and observations - Elena Dzifčáková & Jaroslav Dudík
14. Importance of kappa distributions to solar radio bursts - Iver H. Cairns, Bo Li, Joachi Schmidt
15. Common spectrum of particles accelerated in the heliosphere: Observations and a mechanism - Lennard Fisk & George Gloeckler
16. Formation of a kappa distribution at quasi-perpendicular shock waves - Gary Zank
17. Electron kappa distributions in astrophysical nebulae - D. C. Nicholls, M. A. Dopita, R. S. Sutherland, L. J. Kewley


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About the Author

George Livadiotis

Dr. George Livadiotis is a Senior Research Scientist in Southwest Research Institute. He is a leading expert on the field of kappa distributions and its statistical background, the framework of non-extensive statistical mechanics. Among other theoretical achievements, he developed (i) the connection of kappa distributions with non-extensive statistical mechanics, (ii) the formula of entropy that is related to the kappa distributions, (iii) the generalization of kappa distribution to describe the whole Hamiltonian of particles, the kinetic and potential energy, (iv) the different types of consistent formulae of kappa distributions, (v) the shock Rankine–Hugoniot conditions for kappa distributions. Among other applications, he used kappa distributions to describe the proton populations in many space plasmas in the heliosphere and the heliosheath.

Affiliations and Expertise

Senior Research Scientist, Southwest Research Institute, USA