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El. knyga: Foundations of Plasma Physics for Physicists and Mathematicians

(University of York, UK)
  • Formatas: PDF+DRM
  • Išleidimo metai: 22-Apr-2021
  • Leidėjas: John Wiley & Sons Inc
  • Kalba: eng
  • ISBN-13: 9781119774273
Kitos knygos pagal šią temą:
Foundations of Plasma Physics for Physicists and MathematiciansDidesnis paveikslėlis
  • Formatas: PDF+DRM
  • Išleidimo metai: 22-Apr-2021
  • Leidėjas: John Wiley & Sons Inc
  • Kalba: eng
  • ISBN-13: 9781119774273
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"Plasma physics has a short but complex history. Over the past 100 years the subject has embraced a wide range of separate disciplines. The possibility of controlled fusion power generation and its application to magnetospheric physics and astrophysics has made it an essential element of almost all graduate courses in physics. Its relatively short development is reflected in the large amount of research effort currently expended world-wide."--

A comprehensive textbook on the foundational principles of plasmas, including material on advanced topics and related disciplines such as optics, fluid dynamics, and astrophysics 

Foundations of Plasma Physics for Physicists and Mathematicians covers the basic physics underlying plasmas and describes the methodology and techniques used in both plasma research and other disciplines such as optics and fluid mechanics. Designed to help readers develop physical understanding and mathematical competence in the subject, this rigorous textbook discusses the underlying theoretical foundations of plasma physics as well as a range of specific problems, focused on those principally associated with fusion. 

Reflective of the development of plasma physics, the text first introduces readers to the collective and collisional behaviors of plasma, the single particle model, wave propagation, the kinetic effects of gases and plasma, and other foundational concepts and principles. Subsequent chapters cover topics including the hydrodynamic limit of plasma, ideal magneto-hydrodynamics, waves in MHD plasmas, magnetically confined plasma, and waves in magnetized hot and cold plasma. Written by an acknowledged expert with more than five decades’ active research experience in the field, this authoritative text: 

  • Identifies and emphasizes the similarities and differences between plasmas and fluids 
  • Describes the different types of interparticle forces that influence the collective behavior of plasma 
  • Demonstrates and stresses the importance of coherent and collective effects in plasma 
  • Contains an introduction to interactions between laser beams and plasma 
  • Includes supplementary sections on the basic models of low temperature plasma and the theory of complex variables and Laplace transforms 

Foundations of Plasma Physics for Physicists and Mathematicians is the ideal textbook for advanced undergraduate and graduate students in plasma physics, and a valuable compendium for physicists working in plasma physics and fluid mechanics. 

Preface xvii
1 Fundamental Plasma Parameters - Collective Behaviour 1(12)
1.1 Introduction
1(1)
1.2 Cold Plasma Waves
2(2)
1.2.1 Wave Breaking
3(1)
1.3 Debye Shielding
4(4)
1.3.1 Weakly and Strongly Coupled Plasmas
6(1)
1.3.2 The Plasma Parameter
7(1)
1.4 Diffusion and Mobility
8(1)
1.4.1 Einstein-Smoluchowski Relation
8(1)
1.4.2 Ambipolar Diffusion
9(1)
1.5 Wall Sheath
9(4)
1.5.1 Positively Biased Wall
10(1)
1.5.2 Free Fall Sheath
10(1)
1.5.2.1 Pre-sheath
11(1)
1.5.3 Mobility Limited Sheath
11(2)
2 Fundamental Plasma Parameters - Collisional Behaviour 13(30)
2.1 Electron Scattering by Ions
13(8)
2.1.1 Binary Collisions - Rutherford Cross Section
13(2)
2.1.2 Momentum Transfer Cross Section
15(1)
2.1.2.1 Dynamical Friction and Diffusion
16(1)
2.1.3 Many Body Collisions - Impulse Approximation
16(4)
2.1.4 Relaxation Times
20(1)
2.2 Collisional Transport Effects
21(9)
2.2.1 Random Walk Model for Transport Effects
22(1)
2.2.2 Maxwell's Mean Free Path Model of Transport Phenomena
23(3)
2.2.2.1 Flux Limitation
25(1)
2.2.3 Drude Model of Electrical Conductivity
26(3)
2.2.3.1 Alternating Electric Field, No Magnetic Field
27(1)
2.2.3.2 Steady Electric Field, Finite Magnetic Field
27(1)
2.2.3.3 Oscillatory Electric Field, Finite Magnetic Field
28(1)
2.2.4 Diffusivity and Mobility in a Uniform Magnetic Field
29(1)
2.3 Plasma Permittivity
30(2)
2.3.1 Poynting's Theorem - Energy Balance in an Electro-magnetic Field
31(1)
2.4 Plasma as a Fluid - Two Fluid Model
32(7)
2.4.1 Waves in Plasma
33(3)
2.4.2 Beam Instabilities
36(1)
2.4.2.1 Plasma Bunching
36(1)
2.4.2.2 Two Stream Instability
36(1)
2.4.3 Kinematics of Growing Waves
37(2)
Appendix 2.A Momentum Transfer Collision Rate
39(2)
Appendix 2.B The Central Limit Theorem
41(2)
3 Single Particle Motion - Guiding Centre Model 43(24)
3.1 Introduction
43(1)
3.2 Motion in Stationary and Uniform Fields
44(1)
3.2.1 Static Uniform Magnetic Field - Cyclotron Motion
44(1)
3.2.2 Uniform Static Electric and Magnetic Fields
45(1)
3.3 The Guiding Centre Approximation
45(6)
3.3.1 The Method of Averaging
46(2)
3.3.2 The Guiding Centre Model for Charged Particles
48(3)
3.4 Particle Kinetic Energy
51(1)
3.5 Motion in a Static Inhomogeneous Magnetic Field
52(4)
3.5.1 Field Gradient Drift
53(1)
3.5.2 Curvature Drift
53(2)
3.5.3 Divergent Field Lines
55(1)
3.5.4 Twisted Field Lines
55(1)
3.6 Motion in a Time Varying Magnetic Field
56(1)
3.7 Motion in a Time Varying Electric Field
56(2)
3.8 Collisional Drift
58(1)
3.9 Plasma Diamagnetism
58(1)
3.10 Particle Trapping and Magnetic Mirrors
59(2)
3.10.1 Fermi Acceleration
61(1)
3.11 Adiabatic Invariance
61(2)
3.12 Adiabatic Invariants of Charged Particle Motions
63(1)
Appendix 3.A Northrop's Expansion Procedure
64(1)
3.A.1 Drift Velocity and Longitudinal Motion along the Field Lines
65(2)
4 Kinetic Theory of Gases 67(22)
4.1 Introduction
67(1)
4.2 Phase Space
68(3)
4.2.1 F Phase Space
68(2)
4.2.1.1 Liouville's Equation
69(1)
4.2.2 µ Space
70(1)
4.3 Relationship Between F Space and µ Space
71(2)
4.3.1 Integrals of the Liouville Equation
72(1)
4.4 The BBGKY (Bogoliubov-Born-Green-Kirkwood-Yvon) Hierarchy
73(1)
4.5 Bogoliubov's Hypothesis for Dilute Gases
74(2)
4.6 Derivation of the Boltzmann Collision Integral from the BBGKY Hierarchy
76(2)
4.7 Boltzmann Collision Operator
78(1)
4.7.1 Summation Invariants
79(1)
4.8 Boltzmann's H Theorem
79(1)
4.9 The Equilibrium Maxwell-Boltzmann Distribution
80(1)
4.9.1 Entropy and the H function
81(1)
4.10 Hydrodynamic Limit - Method of Moments
81(3)
4.10.1 Conservation of Mass
83(1)
4.10.2 Conservation of Momentum
83(1)
4.10.3 Conservation of Energy
84(1)
4.11 The Departure from Steady Homogeneous Flow: The Chapman-Enskog Approximation
84(5)
5 Wave Propagation in Inhomogeneous, Dispersive Media 89(22)
5.1 Introduction
89(1)
5.2 Basic Concepts of Wave Propagation - The Geometrical Optics Approximation
90(2)
5.3 The WKB Approximation
92(1)
5.3.1 Oblique Incidence
93(1)
5.4 Singularities in Waves
93(7)
5.4.1 Cut-off or Turning Point
94(2)
5.4.2 Resonance Point
96(3)
5.4.3 Resonance Layer and Collisional Damping
99(1)
5.5 The Propagation of Energy
100(2)
5.5.1 Group Velocity of Waves in Dispersive Media
100(1)
5.5.2 Waves in Dispersive Isotropic Media
101(1)
5.6 Group Velocity of Waves in Anisotropic Dispersive Media
102(5)
5.6.1 Equivalence of Energy Transport Velocity and Group Velocity
106(1)
Appendix 5.A Waves in Anisotropic Inhomogeneous Media
107(4)
6 Kinetic Theory of Plasmas - Collisionless Models 111(10)
6.1 Introduction
111(1)
6.2 Vlasov Equation
111(3)
6.3 Particle Trapping by a Potential Well
114(7)
7 Kinetic Theory of Plasmas 121(28)
7.1 Introduction
121(1)
7.2 The Fokker-Planck Equation - The Stochastic Approach
122(6)
7.2.1 The Scattering Integral for Coulomb Collisions
124(4)
7.3 The Fokker-Planck Equation - The Landau Equation
128(3)
7.3.1 Application to Collisions between Charged Particles
130(1)
7.4 The Fokker-Planck Equation - The Cluster Expansion
131(4)
7.4.1 The Balescu-Lenard Equation
132(3)
7.5 Relaxation of a Distribution to the Equilibrium Form
135(4)
7.5.1 Isotropic Distribution
135(2)
7.5.2 Anisotropic Distribution
137(2)
7.6 Ion-Electron Thermal Equilibration by Coulomb Collisions
139(1)
7.7 Dynamical Friction
140(2)
Appendix 7.A Reduction of the Boltzmann Equation to Fokker-Planck Form in the Weak Collision Limit
142(2)
Appendix 7.B Finite Difference Algorithm for Integrating the Isotropic Fokker-Planck Equation
144(1)
Appendix 7.C Monte Carlo Algorithm for Integrating the Fokker-Planck Equation
145(2)
Appendix 7.D Landau's Calculation of the Electron-Ion Equilibration Rate
147(2)
8 The Hydrodynamic Limit for Plasma 149(38)
8.1 Introduction - Individual Particle Fluid Equations
149(1)
8.2 The Departure from Steady, Homogeneous Flow: The Transport Coefficients
150(1)
8.3 Magneto-hydrodynamic Equations
151(5)
8.3.1 Equation of Mass Conservation
151(1)
8.3.2 Equation of Momentum Conservation
152(2)
8.3.3 Virial Theorem
154(1)
8.3.4 Equation of Current Flow
154(1)
8.3.5 Equation of Energy Conservation
155(1)
8.4 Transport Equations
156(5)
8.4.1 Collision Times
157(1)
8.4.2 Symmetry of the Transport Equations
158(3)
8.5 Two Fluid MHD Equations - Braginskii Equations
161(4)
8.5.1 Magnetic Field Equations
162(3)
8.5.1.1 Energy Balance
164(1)
8.6 Transport Coefficients
165(3)
8.6.1 Collisional Dominated Plasma
165(1)
8.6.1.1 Force Terms F
165(1)
8.6.1.2 Energy Flux Terms
165(1)
8.6.1.3 Viscosity
166(1)
8.6.2 Field-Dominated Plasma
166(4)
8.6.2.1 Force Terms F
166(1)
8.6.2.2 Energy Flux Terms
167(1)
8.6.2.3 Viscosity
168(1)
8.7 Calculation of the Transport Coefficients
168(2)
8.8 Lorentz Approximation
170(7)
8.8.1 Electron-Electron Collisions
173(1)
8.8.2 Electron Runaway
174(3)
8.9 Deficiencies in the Spitzer/Braginskii Model of Transport Coefficients
177(1)
Appendix 8.A BGK Model for the Calculation of Transport Coefficients
178(3)
8.A.1 BGK Conductivity Model
178(2)
8.A.2 BGK Viscosity Model
180(1)
Appendix 8.B The Relationship Between the Flux Equations Given By Shkarofsky and Braginskii
181(1)
Appendix 8.C Electrical Conductivity in a Weakly Ionised Gas and the Druyvesteyn Distribution
182(5)
9 Ideal Magnetohydrodynamics 187(10)
9.1 Infinite Conductivity MHD Flow
188(4)
9.1.1 Frozen Field Condition
189(1)
9.1.2 Adiabatic Equation of State
190(1)
9.1.3 Pressure Balance
191(1)
9.1.3.1 Virial Theorem
191(1)
9.2 Incompressible Approximation
192(5)
9.2.1 Bernoulli's Equation - Steady Flow
192(1)
9.2.2 Kelvin's Theorem - Circulation
193(1)
9.2.3 Alfven Waves
193(4)
10 Waves in MHD Fluids 197(26)
10.1 Introduction
197(1)
10.2 Magneto-sonic Waves
198(5)
10.3 Discontinuities in Fluid Mechanics
203(2)
10.3.1 Classical Fluids
203(1)
10.3.2 Discontinuities in Magneto-hydrodynamic Fluids
204(1)
10.4 The Rankine-Hugoniot Relations for MHD Flows
205(1)
10.5 Discontinuities in MHD Flows
206(1)
10.6 MHD Shock Waves
207(1)
10.6.1 Simplifying Frame Transformations
207(1)
10.7 Properties of MHD Shocks
208(4)
10.7.1 Shock Hugoniot
208(1)
10.7.2 Shock Adiabat - General Solution for a Polytropic Gas
209(3)
10.8 Evolutionary Shocks
212(4)
10.8.1 Evolutionary MHD Shock Waves
213(1)
10.8.2 Parallel Shock - Magnetic Field Normal to the Shock Plane
214(2)
10.9 Switch-on and Switch-off Shocks
216(1)
10.10 Perpendicular Shock - Magnetic Field Lying in the Shock Plane
217(1)
10.11 Shock Structure and Stability
218(1)
Appendix 10.A Group Velocity of Magneto-sonic Waves
218(2)
Appendix 10.B Solution in de Hoffman-Teller Frame
220(3)
10.B.1 Parallel Shocks
222(1)
11 Waves in Cold Magnetised Plasma 223(14)
11.1 Introduction
223(1)
11.2 Waves in Cold Plasma
223(4)
11.2.1 Cut-off and Resonance
226(1)
11.2.2 Polarisation
227(1)
11.3 Cold Plasma Waves
227(10)
11.3.1 Zero Applied Magnetic Field
227(1)
11.3.2 Low Frequency Velocity Waves
228(1)
11.3.3 Propagation of Waves Parallel to the Magnetic Field
229(3)
11.3.4 Propagation of Waves Perpendicular to the Magnetic Field
232(2)
11.3.5 Resonance in Plasma Waves
234(3)
12 Waves in Magnetised Warm Plasma 237(44)
12.1 The Dielectric Properties of Unmagnetised Warm Dilute Plasma
237(6)
12.1.1 Plasma Dispersion Relation
238(1)
12.1.1.1 Dispersion Relation for Transverse Waves
239(1)
12.1.1.2 Dispersion Relation for Longitudinal Waves
239(1)
12.1.2 Dielectric Constant of a Plasma
239(6)
12.1.2.1 The Landau Contour Integration Around the Singularity
241(2)
12.2 Transverse Waves
243(1)
12.3 Longitudinal Waves
244(1)
12.4 Linear Landau Damping
245(3)
12.4.1 Resonant Energy Absorption
245(3)
12.5 Non-linear Landau Damping
248(4)
12.5.1 Particle Trapping
248(2)
12.5.2 Plasma Wave Breaking
250(2)
12.6 The Plasma Dispersion Function
252(4)
12.7 Positive Ion Waves
256(2)
12.7.1 Transverse Waves
256(1)
12.7.2 Longitudinal Waves
256(2)
12.7.2.1 Plasma Waves, ζe > 1
257(1)
12.7.2.2 Ion Waves ζe < 1
257(1)
12.8 Microscopic Plasma Instability
258(4)
12.8.1 Nyquist Plot
259(3)
12.8.1.1 Penrose's Criterion
260(2)
12.9 The Dielectric Properties of Warm Dilute Plasma in a Magnetic Field
262(12)
12.9.1 Propagation Parallel to the Magnetic Field
269(1)
12.9.2 Propagation Perpendicular to the Magnetic Field
270(4)
Appendix 12.A Landau's Solution of the Vlasov Equation
274(2)
Appendix 12.B Electrostatic Waves
276(5)
13 Properties of Electro-magnetic Waves in Plasma 281(32)
13.1 Plasma Permittivity and the Dielectric Constant
281(5)
13.1.1 The Properties of the Permittivity Matrix
284(2)
13.2 Plane Waves in Homogeneous Plasma
286(4)
13.2.1 Waves in Collisional Cold Plasma
287(3)
13.2.1.1 Isotropic Unmagnetised Plasma
287(2)
13.2.1.2 Anisotropic Magnetised Plasma
289(1)
13.3 Plane Waves Incident Obliquely on a Refractive Index Gradient
290(5)
13.3.1 Oblique Incidence at a Cut-off Point - Resonance Absorption
293(2)
13.3.1.1 s Polarisation
293(1)
13.3.1.2 p Polarisation
293(2)
13.4 Single Particle Model of Electrons in an Electro-magnetic Field
295(10)
13.4.1 Quiver Motion
295(2)
13.4.2 Ponderomotive Force
297(1)
13.4.3 The Impact Model for Collisional Absorption
298(3)
13.4.3.1 Electron-Electron Collisions
301(1)
13.4.4 Distribution Function of Electrons Subject to Inverse Bremsstrahlung Heating
301(4)
13.5 Parametric Instabilities
305(5)
13.5.1 Coupled Wave Interactions
305(3)
13.5.1.1 Manley-Rowe Relations
306(1)
13.5.1.2 Parametric Instability
307(1)
13.5.2 Non-linear Laser-Plasma Absorption
308(6)
13.5.2.1 Absorption Instabilities
309(1)
13.5.2.2 Reflection Instabilities
310(1)
Appendix 13.A Ponderomotive Force
310(3)
14 Laser-Plasma Interaction 313(24)
14.1 Introduction
313(1)
14.2 The Classical Hydrodynamic Model of Laser-Solid Breakdown
314(11)
14.2.1 Basic Parameters of Laser Breakdown
315(1)
14.2.2 The General Theory of the Interaction of Lasers with Solid Targets
316(2)
14.2.3 Distributed Heating - Low Intensity, Self-regulating Flow
318(3)
14.2.3.1 Early Time Self-similar Solution
319(1)
14.2.3.2 Late Time Steady-State Solution
319(2)
14.2.4 Local Heating - High Intensity, Deflagration Flow
321(3)
14.2.4.1 Early Time Thermal Front
321(2)
14.2.4.2 Late Time Steady-State Flow
323(1)
14.2.5 Additional Simple Analytic Models
324(16)
14.2.5.1 Short Pulse Heating
324(1)
14.2.5.2 Heating of Small Pellets - Homogeneous Self-similar Model
325(1)
14.3 Simulation of Laser-Solid Target Interaction
325(2)
Appendix 14.A Non-linear Diffusion
327(2)
Appendix 14.B Self-similar Flows with Uniform Velocity Gradient
329(8)
15 Magnetically Confined Plasma 337(34)
15.1 Introduction
337(1)
15.2 Equilibrium Plasma Configurations
337(1)
15.3 Linear Devices
338(2)
15.4 Toroidal Devices
340(4)
15.4.1 Pressure Balance
341(2)
15.4.1.1 Pressure Imbalance Mitigation
342(1)
15.4.2 Guiding Centre Drift
343(1)
15.5 The General Problem: The Grad-Shafranov Equation
344(1)
15.6 Boundary Conditions
345(2)
15.7 Equilibrium Plasma Configurations
347(4)
15.7.1 Perturbation Methods
348(1)
15.7.2 Analytical Solutions of the Grad-Shafranov Equation
349(1)
15.7.3 Numerical Solutions of the Grad-Shafranov Equation
350(1)
15.8 Classical Magnetic Cross Field Diffusion
351(1)
15.9 Trapped Particles and Banana Orbits
352(7)
15.9.1 Collisionless Banana Regime (v 1)
354(2)
15.9.1.1 Diffusion in the Banana Regime
355(1)
15.9.1.2 Bootstrap Current (v 1)
355(1)
15.9.2 Resistive Plasma Diffusion - Collisional Pfirsch-Schluter Regime
356(1)
15.9.2.1 Pfirsch-Schluter Current (v 1)
357(1)
15.9.2.2 Diffusion in the Pfirsch-Scluter Regime
357(1)
15.9.3 Plateau Regime
357(1)
15.9.4 Diffusion in Tokamak Plasmas
358(1)
Appendix 15.A Equilibrium Maintaining 'Vertical' Field
359(1)
Appendix 15.B Perturbation Solution of the Grad-Shafranov Equation
360(3)
Appendix 15.C Analytic Solutions of the Homogeneous Grad-Shafranov Equation
363(1)
Appendix 15.D Guiding Centre Motion in a Twisted Circular Toroidal Plasma
364(4)
Appendix 15.E The Pfirsch-Schluter Regime
368(3)
15.E.1 Diffusion in the Pfirsch-Schluter Regime
369(2)
16 Instability of an Equilibrium Confined Plasma 371(16)
16.1 Introduction
371(1)
16.2 Ideal MHD Instability
371(10)
16.2.1 Linearised Stability Equations
371(4)
16.2.2 Normal Mode Analysis - The Stability of a Cylindrical Plasma Column
375(4)
16.2.3 m = 0 Sausage Instability
379(1)
16.2.4 m = 1 Kink Instability
380(1)
16.3 Potential Energy
381(1)
16.4 Interchange Instabilities
382(5)
Supplementary Material 387(26)
M.1 Breakdown and Discharges in d.c. Electric Fields
387(6)
M.1.1 Gas Breakdown and Paschen's Law
387(1)
M.1.2 Similarity and Proper Variables
388(1)
M.1.3 Townsend's First Coefficient
388(1)
M.1.4 Townsend's Breakdown Criterion
389(1)
M.1.5 Paschen Curve and Paschen Minimum
389(1)
M.1.6 Radial Profile of Glow Discharge
390(1)
M.1.7 Collisional Ionisation Rate for Low Temperature Electrons
391(1)
M.1.8 Radio Frequency and Microwave Discharges
392(1)
M.2 Key Facts Governing Nuclear Fusion
393(7)
M.2.1 Fusion Rate
393(3)
M.2.2 Lawson's Criterion
396(2)
M.2.3 Triple Product
398(2)
M.3 A Short Introduction to Functions of a Complex Variable
400(10)
M.3.1 Cauchy-Riemann Relations
401(1)
M.3.2 Harmonic Functions
402(1)
M.3.3 Area Rule
402(1)
M.3.4 Cauchy Integral Theorem
402(1)
M.3.5 Morera's Theorem
403(1)
M.3.6 Analytic Continuation
403(1)
M.3.7 Extension or Contraction of a Contour
404(1)
M.3.8 Inclusion of Isolated Singularities
404(1)
M.3.9 Cauchy Formula
404(1)
M.3.9.1 Interior Domain
404(1)
M.3.9.2 Exterior Domain
405(1)
M.3.10 Treatment of Improper Integrals
405(1)
M.3.11 Sokhotski-Plemelj Theorem
406(1)
M.3.12 Improper Integral Along a Real Line
407(1)
M.3.13 Taylor and Laurent Series
407(1)
M.3.14 The Argument Principle
408(1)
M.3.15 Estimation Lemma
408(1)
M.3.16 Jordan's Lemma
409(1)
M.3.17 Conformal Mapping
409(1)
M.4 Laplace Transform
410(3)
M.4.1 Bromwich Contour
410(3)
Problems 413(14)
Bibliography 427(10)
Index 437
Geoffrey J. Pert is Emeritus Professor, Department of Physics, University of York, UK. He has continuously been involved in research in plasma physics, primarily the interaction of high-power lasers with materials, since first studying the subject as a research student in the 1960s. Professor Pert is a Fellow of the Royal Society and has published more than 200 papers in scientific research journals. He is the author of Introduction to Fluid Mechanics and the co-author of An Introduction to Computer Simulation.
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