Kappa Distributions: Theory and Applications in Plasmas

Kappa Distributions: Theory and Applications in Plasmas presents the theoretical developments of kappa distributions, their applications in plasmas, and how they affect the underpinnings of our understanding of space and plasma physics, astrophysics, and statistical mechanics/thermodynamics. Separated into three major parts, the book covers theoretical methods, analytical methods in plasmas, and applications in space plasmas. The first part of the book focuses on basic aspects of the statistical theory of kappa distributions, beginning with their connection to the solid backgrounds of 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, in other astrophysical plasmas. Kappa Distributions is ideal for space, plasma, and statistical physicists; geophysicists, especially of the upper atmosphere; Earth and planetary scientists; and astrophysicists.

Author Biography: 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.

Part 1. Theory and Formalism 1. Statistical Background of Kappa Distributions: Connection With Nonextensive 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 2. Plasma Physics 5. Basic Plasma Parameters Described by Kappa Distributions - George Livadiotis 6. Superstatistics: Superposition of Maxwell-Boltzmann Distributions - Christian Beck & E.G.D. Cohen 7. Linear Kinetic Waves in Plasmas Described by Kappa Distributions - Adolfo Figueroa-Vinas, Rudi Gaelzer, Pablo S. Moya, R. Mace, J.A. Araneda 8. Nonlinear Wave-Particle Interaction and Electron Kappa Distribution - Peter H. Yoon & George Livadiotis 9. Solitary Waves in Plasmas Described by Kappa Distributions - G.S. Lakhina & Satyavir Singh Part 3. 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. Parnicas, James F. Carbary, M. Kane, Stamatios M. Krimigis, Barry H. Mauk 13. Kappa Distributions and the Solar Spectra: Theory and Observations - Elena Dzifakova & Jaroslav Dudik 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 Kappa Distributions at Quasiperpendicular Shock Waves - Gary Zank 17. Electron Kappa Distributions in Astrophysical Nebulae - D.C. Nicholls, M. A. Dopita, R.S. Sutherland, L.J. Kewley