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E-raamat: Vlasov Equation 1 - History and General Properties: History and General Properties [Wiley Online]

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  • Formaat: 320 pages
  • Ilmumisaeg: 01-Oct-2019
  • Kirjastus: ISTE Ltd and John Wiley & Sons Inc
  • ISBN-10: 1119476801
  • ISBN-13: 9781119476801
Teised raamatud teemal:
  • Wiley Online
  • Hind: 174,45 €*
  • * hind, mis tagab piiramatu üheaegsete kasutajate arvuga ligipääsu piiramatuks ajaks
Vlasov Equation 1 - History and General Properties: History and General PropertiesSuurem pilt
  • Formaat: 320 pages
  • Ilmumisaeg: 01-Oct-2019
  • Kirjastus: ISTE Ltd and John Wiley & Sons Inc
  • ISBN-10: 1119476801
  • ISBN-13: 9781119476801
Teised raamatud teemal:
Wiley Online e-raamatudRohkem infot Wiley Online kohta
Raamatu kodulehekülg: https://onlinelibrary.wiley.com/doi/book/10.1002/9781119476801

The Vlasov equation is the master equation which provides a statistical description for the collective behavior of large numbers of charged particles in mutual, long-range interaction. In other words, a low collision (or “Vlasov”) plasma. Plasma physics is itself a relatively young discipline, whose “birth” can be ascribed to the 1920s. The origin of the Vlasov model, however, is even more recent, dating back to the late 1940s. This “young age” is due to the rare occurrence of Vlasov plasma on Earth, despite the fact it characterizes most of the visible matter in the universe.

This book – addressed to students, young researchers and to whoever wants a good understanding of Vlasov plasmas – discusses this model with a pedagogical presentation, focusing on the general properties and historical development of the applications of the Vlasov equation. The milestone developments discussed in the first two chapters serve as an introduction to more recent works (characterization of wave propagation and nonlinear properties of the electrostatic limit).

Preface ix
Chapter 1 Introduction to a Universal Model: the Vlasov Equation
1(30)
1.1 A historical point of view
1(4)
1.2 Individual and collective effects in plasmas
5(2)
1.3 Graininess parameter
7(1)
1.4 The collective description of a Coulomb gas: an intuitive approach
8(4)
1.5 From Ar-body to Vlasov
12(4)
1.6 The graininess parameter and 1D, 2D or 3D models
16(3)
1.7 The Vlasov equation at the microscopic fluctuations level
19(2)
1.8 The Wigner equation (Vlasov equation for quantum systems)
21(5)
1.9 The relativistic Vlasov--Maxwell model
26(2)
1.10 References
28(3)
Chapter 2 A Paradigm for a Collective Description of a Plasma: the 1D Vlasov--Poisson Equations
31(44)
2.1 Introduction
31(2)
2.2 The linear Landau problem
33(6)
2.2.1 The Maxwellian case
34(2)
2.2.2 Landau poles and others
36(2)
2.2.3 Unstable plasma: two-stream instability
38(1)
2.3 The 1D cold plasma model: nonlinear oscillations
39(5)
2.3.1 Hydrodynamic description
39(1)
2.3.2 Lagrangian formulation through the Von Mises transformation
40(2)
2.3.3 The wave-breaking phenomenon
42(2)
2.4 The water bag model
44(6)
2.4.1 Basic equations
44(3)
2.4.2 Linearized theory
47(1)
2.4.3 Water bag hydrodynamic description
48(2)
2.5 Connection between the hydrodynamic, water bag and Vlasov models
50(8)
2.5.1 A Vlasov hydrodynamic description
50(2)
2.5.2 Vlasov numerical simulations of Pn-3
52(4)
2.5.3 The fundamental contribution of poles besides Landau
56(2)
2.6 The multiple water bag model
58(8)
2.6.1 A multifluid description
59(4)
2.6.2 Linearized analysis
63(3)
2.7 Further remarks
66(5)
2.8 References
71(4)
Chapter 3 Electromagnetic Fields in Vlasov Plasmas: General Approach to Small Amplitude Perturbations
75(72)
3.1 Introduction and overview of the chapter
75(2)
3.2 Linear analysis of the Vlasov-Maxwell system: general approach
77(16)
3.2.1 Dispersion relation and response matrix
81(2)
3.2.2 The choice of the basis for the response tensor
83(6)
3.2.3 About the number of "waves" in plasmas
89(3)
3.2.4 Real or complex values of k and to: steady state and initial value problems
92(1)
3.3 Polynomial approximations of the dispersion relation: why and how to use them
93(16)
3.3.1 Truncated-Vlasov and fluid-plasma descriptions for the linear analysis
96(3)
3.3.2 Wave dispersion and resonances allowed by inclusion of high-order moments in fluid models
99(4)
3.3.3 An example: fluid moments and Finite--Larmor--Radius effects
103(5)
3.3.4 Key points about approximated normal mode analysis
108(1)
3.4 Vlasov plasmas as collisionless conductors with polarization and finite conductivity: meaning of plasma's "dielectric tensor"
109(17)
3.4.1 Polarization charges and wave equation in dielectric materials
112(3)
3.4.2 The "equivalent" dielectric tensor and its complex components
115(5)
3.4.3 Temporal and spatial dispersion in plasmas
120(2)
3.4.4 Conductivity and collisional resistivity in Vlasov plasmas
122(4)
3.5 Symmetry properties of the complex components of the equivalent dielectric tensor and energy conservation
126(15)
3.5.1 Onsager's relations
126(3)
3.5.2 Poynting's theorem
129(1)
3.5.3 Symmetry of the coefficients of the equivalent dielectric tensor
130(4)
3.5.4 More about Onsager's relations for wave dispersion
134(4)
3.5.5 Energy dissipation versus real and imaginary parts of and σij
138(3)
3.6 References
141(6)
Chapter 4 Electromagnetic Fields in Vlasov Plasmas: Characterization of Linear Modes
147(68)
4.1 Introduction
147(1)
4.2 Characterization of electromagnetic waves and of wave-packets
148(34)
4.2.1 Polarization of electromagnetic waves in plasmas
153(3)
4.2.2 Phase velocity, group velocity and refractive index
156(5)
4.2.3 Example of propagation in unmagnetized plasmas: underdense and overdense regimes
161(5)
4.2.4 Example of propagation in magnetized plasmas: ion-cyclotron resonances and Faraday's rotation effect
166(6)
4.2.5 Wave-particle resonances, Landau damping and wave absorption
172(4)
4.2.6 Resonance and cut-off conditions on the refractive index
176(2)
4.2.7 Graphical representations of the dispersion relation
178(4)
4.3 Instabilities in Vlasov plasmas: some terminology and general features
182(16)
4.3.1 Linear instabilities
184(8)
4.3.2 Absolute and convective instabilities and some other classification criteria
192(6)
4.4 On some complementary interpretations of the collisionless damping mechanism in Vlasov plasmas
198(9)
4.4.1 Landau damping as an inverse Vavilov--Cherenkov radiation
199(4)
4.4.2 Landau damping in N-body "exact" models
203(3)
4.4.3 Some final remarks about interpretative issues of collisionless damping in Vlasov mean field theory
206(1)
4.5 References
207(8)
Chapter 5 Nonlinear Properties of Electrostatic Vlasov Plasmas
215(82)
5.1 The Vlasov--Poisson system
215(1)
5.2 Invariants of the Vlasov--Poisson model
216(1)
5.3 Stationary solutions: Bernstein--Greene--Kruskal equilibria
217(3)
5.4 Some mathematical properties of the Vlasov equation
220(9)
5.5 The Bernstein--Greene--Kruskal solutions
229(13)
5.5.1 The case of (electrostatic) two-stream instability
230(5)
5.5.2 Chain of BGK equilibria
235(1)
5.5.3 Stability of the periodic BGK steady states
236(6)
5.6 Traveling waves of BGK-type solutions
242(3)
5.7 Role of minority population of trapped particles
245(25)
5.7.1 Nonlinear Landau damping and the emergence of the nonlinear Langmuir-type wave
247(7)
5.7.2 Electron acoustic wave in the nonlinear Landau damping regime
254(6)
5.7.3 Kinetic electrostatic electron nonlinear waves
260(8)
5.7.4 Emergent resonance for KEEN waves
268(2)
5.8 Nature of KEEN waves and NMI
270(11)
5.8.1 Adiabatic model for a single linear wave: the (electrostatic) trapped electron mode model
270(4)
5.8.2 The Dodin and Fisch model connected to the emergence of KEEN waves
274(7)
5.9 Electron hole and plasma wave interaction
281(10)
5.10 References
291(6)
Index 297
Pierre Bertrand is Emeritus Professor at the University of Lorraine, France. He has been working for more than 50 years in various fields of theoretical physics, and numerical simulation involving plasma physics, quantum mechanics, signal theory and fluid mechanics.

Daniele Del Sarto is Associate Professor at the Jean Lamour Institute, University of Lorraine, France. Her main research field is fundamental physics of warm plasmas, with applications to astrophysics, magnetic confinement fusion and laser-plasma interactions.

Alain Ghizzo is Professor at the Jean Lamour Institute, University of Lorraine, France. He is active in plasma Vlasov modeling, high performance computing, laser-plasma interactions and gyrokinetic modeling.
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