Kappa Distributions

Theory and Applications in Plasmas

1st Edition - April 19, 2017
Author: George Livadiotis
Language: English
Paperback ISBN:
9 7 8 - 0 - 1 2 - 8 0 4 6 3 8 - 8
eBook ISBN:
9 7 8 - 0 - 1 2 - 8 0 4 6 3 9 - 5

Kappa Distributions: Theory and Applications in Plasmas presents the theoretical developments of kappa distributions, their applications in plasmas, and how they affect the under… Read more

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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.

Part 1. Theory and Formalism

Chapter 1. Statistical Background of Kappa Distributions: Connection With Nonextensive Statistical Mechanics

1.1. Summary
1.2. Introduction
1.3. Mathematical Motivation
1.4. Nonextensive Statistical Mechanics, in Brief!
1.5. Entropy Maximization
1.6. Connection of Kappa Distributions With Nonextensive Statistical Mechanics
1.7. Structure of the Kappa Distribution
1.8. The Concept of Temperature
1.9. The Concept of the Kappa (or q) Index
1.10. Concluding Remarks
1.11. Science Questions for Future Research

Chapter 2. Entropy Associated With Kappa Distributions

2.1. Summary
2.2. Introduction
2.3. The Role and Impact of Scale Parameters in the Entropic Formulation
2.4. Derivation of the Entropic Formula for Velocity Kappa Distributions
2.5. Entropy for Isothermal Transitions Between Stationary States
2.6. The Discrete Dynamics of Transitions Between Stationary States
2.7. Concluding Remarks
2.8. Science Questions for Future Research

Chapter 3. Phase Space Kappa Distributions With Potential Energy

3.1. Summary
3.2. Introduction
3.3. The Hamiltonian Distribution
3.4. Normalization of the Phase Space Kappa Distribution
3.5. Marginal Distributions
3.6. Mean Kinetic Energy in the Presence of a Potential Energy
3.7. Degeneration of the Kappa Index in the Presence of a Potential Energy
3.8. Local Kappa Distribution
3.9. Negative Potentials
3.10. Gravitational Potentials
3.11. Potentials with Angular Dependence
3.12. Potentials Forming Anisotropic Distribution of Velocity
3.13. Concluding Remarks
3.14. Science Questions for Future Research

Chapter 4. Formulae of Kappa Distributions: Toolbox

4.1. Summary
4.2. Introduction
4.3. Isotropic Distributions (Without Potential) (Livadiotis and McComas, 2009; 2011b)
4.4. Anisotropic Distributions (Without Potential)
4.5. Distributions With Potential
4.6. Multiparticle Distributions
4.7. Non-Euclidean–Normed Distributions (Livadiotis, 2007, 2008, 2012, 2016b)
4.8. Discrete Distributions (Tsallis et al., 1998)
4.9. Concluding Remarks
4.10. Science Questions for Future Research

Part 2. Plasma Physics

Chapter 5. Basic Plasma Parameters Described by Kappa Distributions

5.1. Summary
5.2. Introduction
5.3. Polytropes
5.4. Correlation Between Particle Energies
5.5. Debye Length in Equilibrium and Nonequilibrium Plasmas
5.6. Electrical Conductivity
5.7. Collision Frequency and Mean Free Path
5.8. Magnetization: The Curie Constant
5.9. Large-Scale Quantization Constant
5.10. Concluding Remarks
5.11. Science Questions for Future Research

Chapter 6. Superstatistics: Superposition of Maxwell–Boltzmann Distributions

6.1. Summary
6.2. Introduction: Dynamical Creation of Kappa Distributions
6.3. Timescale Separation in Nonequilibrium Situations
6.4. Typical Universality Classes for f(β)
6.5. Asymptotic Behavior for Large Energies
6.6. Universality for Not Too Large Energies ε
6.7. From Measured Time Series to Superstatistics
6.8. Some Examples of Applications
6.9. Concluding Remarks
6.10. Science Questions for Future Research

Chapter 7. Linear Kinetic Waves in Plasmas Described by Kappa Distributions

7.1. Summary
7.2. Introduction
7.3. Plasma Dielectric Tensor and the Dispersion Relation
7.4. Kappa Velocity Distribution Plasma Waves at Parallel Propagation (ϑ=0)
7.5. Kappa Velocity Distribution Plasma Waves at Oblique Propagation (ϑ ≠ 0)
7.6. Concluding Remarks
7.7. Science Questions for Future Research

Chapter 8. Nonlinear Wave–Particle Interaction and Electron Kappa Distribution

8.1. Summary
8.2. Introduction
8.3. Plasma Weak Turbulence Theory
8.4. Turbulent Quasiequilibrium and Kappa Electron Distribution
8.5. Concluding Remarks
8.6. Science Questions for Future Research

Chapter 9. Solitary Waves in Plasmas Described by Kappa Distributions

9.1. Summary
9.2. Introduction: Observations and Origin of Suprathermal Electrons
9.3. Model of Ion-Acoustic Solitons and Double Layers in Plasmas With Suprathermal Electrons
9.4. Model for Electron-Acoustic Solitons in Plasmas With Suprathermal Electrons
9.5. Concluding Remarks
9.6. Science Questions for Future Research

Part 3. Applications in Space Plasmas

Chapter 10. Ion Distributions in Space Plasmas

10.1. Summary
10.2. Introduction
10.3. Formulations of Ion Kappa Distributions
10.4. Toward Antiequilibrium, the Farthest State From Thermal Equilibrium
10.5. Arrangement of the Stationary States
10.6. Interpreting the Observations
10.7. Concluding Remarks
10.8. Science Questions for Future Research

Chapter 11. Electron Distributions in Space Plasmas

11.1. Summary
11.2. Introduction: Observations and Origins of Suprathermal Electrons
11.3. Coronal Heating by Velocity Filtration Due to Suprathermal Electrons
11.4. Heat Flux
11.5. Influence of Suprathermal Electrons on the Acceleration of Escaping Particles
11.6. Concluding Remarks
11.7. Science Questions for Future Research

Chapter 12. The Kappa-Shaped Particle Spectra in Planetary Magnetospheres

12.1. Summary
12.2. Introduction
12.3. Measuring and Interpreting the Kappa Distribution in Space Plasmas
12.4. Kappa Distribution in the Magnetospheres of the Gas Giant Planets
12.5. Kappa Distribution in the Magnetospheres of the Terrestrial Planets
12.6. Are Kappa Distributions Useful for Magnetospheric Research?
12.7. Concluding Remarks
12.8. Science Questions for Future Research

Chapter 13. Kappa Distributions and the Solar Spectra: Theory and Observations

13.1. Summary
13.2. Introduction
13.3. Synthetic Line and Continuum Intensities
13.4. Plasma Diagnostics From Emission Line Spectra
13.5. Differential Emission Measures for Kappa Distributions
13.6. Concluding Remarks
13.7. Science Questions for Future Research

Chapter 14. Importance of Kappa Distributions to Solar Radio Bursts

14.1. Summary
14.2. Introduction
14.3. Qualitative Aspects for the Generation and Damping of Plasma Waves and Radio Emissions
14.4. Type III Bursts, Electron Beams, and Langmuir Waves
14.5. Type II Bursts, Shocks, and Electron Reflections
14.6. Concluding Remarks
14.7. Science Questions for Future Research

Chapter 15. Common Spectrum of Particles Accelerated in the Heliosphere: Observations and a Mechanism

15.1. Summary
15.2. Introduction
15.3. Observations
15.4. Acceleration Mechanism That Yields the Common Spectrum
15.5. Applications of the Pump Acceleration Mechanism
15.6. Concluding Remarks
15.7. Science Questions for Future Research

Chapter 16. Formation of Kappa Distributions at Quasiperpendicular Shock Waves

16.1. Summary
16.2. Introduction
16.3. Upstream Distributions and Their Transmission Through Quasiperpendicular Shocks
16.4. Velocity Distribution Function Downstream of a Quasiperpendicular Shock
16.5. Simulations
16.6. Observational Tests
16.7. Dissipation and Particle Acceleration at Quasiperpendicular Shocks
16.8. Concluding Remarks
16.9. Science Questions for Future Research

Chapter 17. Electron Kappa Distributions in Astrophysical Nebulae

17.1. Summary
17.2. Introduction
17.3. Are Energy Kappa Distributions Present in Astrophysical Nebulae?
17.4. Ionization Structures in an HII Region
17.5. Magnetic Structures in HII Regions
17.6. Nebular Spectral Lines
17.7. Atomic Energy Levels and Kappa Distribution
17.8. Diagnostics for the Kappa Index
17.9. Modeling of Photoionized Nebulae
17.10. Other Applications of Kappa Distributions in Astrophysical Nebulae
17.11. Alternative Explanations of Abundance Discrepancy
17.12. Concluding Remarks
17.13. Science Questions for Future Research

Appendix A: Abbreviations

Appendix B. Main Symbols

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Kappa Distributions

Theory and Applications in Plasmas

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George Livadiotis