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Waves and Oscillations in Plasmas [Kõva köide]

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  • Formaat: Hardback, 575 pages, kõrgus x laius: 254x178 mm, kaal: 1247 g, 6 Tables, black and white; 163 Illustrations, black and white
  • Sari: Series in Plasma Physics
  • Ilmumisaeg: 20-Sep-2012
  • Kirjastus: Taylor & Francis Inc
  • ISBN-10: 143987848X
  • ISBN-13: 9781439878484
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Waves and Oscillations in PlasmasSuurem pilt
  • Formaat: Hardback, 575 pages, kõrgus x laius: 254x178 mm, kaal: 1247 g, 6 Tables, black and white; 163 Illustrations, black and white
  • Sari: Series in Plasma Physics
  • Ilmumisaeg: 20-Sep-2012
  • Kirjastus: Taylor & Francis Inc
  • ISBN-10: 143987848X
  • ISBN-13: 9781439878484
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781439878484.html
Märksõnad:
Winner of an Outstanding Academic Title Award from CHOICE Magazine



 



The result of more than 15 years of lectures in plasma sciences presented at universities in Denmark, Norway, and the United States, Waves and Oscillations in Plasmas addresses central issues in modern plasma sciences. The book covers fluid models as well as kinetic plasma models, including a detailed discussion of, for instance, collisionless Landau damping. Offering a clear separation of linear and nonlinear models, the book can be tailored for readers of varying levels of expertise.









Designed to provide basic training in linear as well as nonlinear plasma dynamics, and practical in areas as diverse as the space sciences, laboratory experiments, plasma processing, and more, this book includes:















Sections on basic experimental methods, facilitating students appreciation of experimental results from laboratory and space plasmas Elements of electromagnetic field theory, fluid mechanics, and wave dynamics, including features of nonlinear wave analysis Basic mathematical tools and other relevant material are summarized in Appendices Exercises as well as short sections that can be used for student presentations A comprehensive reference list reviewing classic papers and notable texts in the field















Waves and Oscillations in Plasmas provides a solid foundation in basic plasma physics and its applications, giving a practical introduction to more advanced methods as well. Including simple physical interpretations where possible, this comprehensive, classroom-tested book places plasma sciences in the logical context of general classical physics.

Arvustused

"The first edition of this book, which covers both plasma physics theory and its applications, has been an excellent resource for many physicists. It is my pleasure to highly recommend this book to plasma physicists at all levels." Lennart Stenflo, Linköping University, Sweden



"This excellent, comprehensive work addresses both the foundations of and advanced methods in the field. Pécseli (Univ. of Oslo, Norway) based the book on lectures he gave over 15-plus years in Norwegian, Danish, and American universities. Distinct sections effectively illustrate the diversity and potential of plasma physics, covering both fluid models and kinetic plasma models and linear and nonlinear processes. The author also explains experimental results from both laboratory and space plasmas. Each of the volume's 24 chapters advances a particular focus, and chapters can be flexibly modified to meet the needs of a wide range of readers, depending on their backgrounds. The book includes exercises at different levels along with short sections suitable as a basis for student presentations. A concise summary of plasma instabilities and common mathematical tools are provided in the appendixes. Statistical aspects of plasmas are limited in the main body of the book, but covered for collision processes within one appendix. This work fills a critical niche in fleshing out the full range of classical physics. Summing Up: Highly recommended. Upper-division undergraduates and above." T. Eastman, formerly, University of Maryland

Preface
1 Introduction
1(4)
1.1 What is a plasma?
1(1)
1.2 Where do we find plasma?
1(1)
1.3 Plasma physics - why bother?
2(1)
1.4 Why study waves in plasmas?
3(2)
1.4.1 Alfven waves
3(1)
1.4.2 Landau damping and instability
4(1)
2 Basics of Continuum Models
5(24)
2.1 Continuity equation
6(1)
2.2 Newton's second law
7(2)
2.3 Equation of state
9(4)
2.3.1 Gas pressure on a surface
10(2)
2.3.2 Heat capacities
12(1)
2.4 Dynamic properties
13(2)
2.4.1 Sound waves
13(2)
2.5 Incompressibility
15(2)
2.6 Molecular viscosity
17(4)
2.6.1 An explicit calculation of the viscosity coefficient
18(3)
2.7 Thermal conductivity in gases
21(1)
2.8 Diffusion in gases
22(1)
2.9 Dimensional analysis
22(4)
2.10 Summation convention
26(3)
3 Linear Wave Dynamics
29(16)
3.1 Dispersion relations
30(12)
3.1.1 Complex notation
31(1)
3.1.2 Characteristic velocities
32(1)
3.1.3 Doppler shifts
33(1)
3.1.4 Wave polarization
34(2)
3.1.5 Method of stationary phase
36(1)
3.1.6 Absolute and convective instabilities
37(1)
3.1.7 Pulse response
38(4)
3.2 Wave propagation in inhomogeneous media
42(3)
3.2.1 Snell's law
42(1)
3.2.2 WKB analysis
42(3)
4 Weakly Nonlinear Waves
45(28)
4.1 Nondispersive waves
46(7)
4.1.1 Simple waves
47(3)
4.1.2 Burgers' equation
50(3)
4.2 Weakly dispersive waves
53(9)
4.2.1 Korteweg-de Vries equation
53(5)
4.2.2 Perturbations of a KdV equation
58(3)
4.2.3 Boussinesq equations
61(1)
4.2.4 Generalization to three dimensions
61(1)
4.3 Strongly dispersive waves
62(11)
4.3.1 Simple oscillators
62(2)
4.3.2 Weakly nonlinear dispersive waves
64(3)
4.3.3 Modulational instability
67(1)
4.3.4 Soliton solutions of the NLS equation
68(1)
4.3.5 Derivation of the nonlinear Schrodinger equation
69(2)
4.3.6 Generalization to three spatial dimensions
71(2)
5 Basics of Electromagnetism
73(36)
5.1 Maxwell's equations in their basic form
73(2)
5.1.1 Boundary conditions
74(1)
5.1.2 Material relations for simple media
75(1)
5.2 Discussions of Maxwell's equations
75(4)
5.3 Potentials
79(1)
5.4 Poynting's identity
79(3)
5.4.1 Poynting's identity for a vacuum
80(2)
5.5 Electromagnetic forces
82(3)
5.5.1 Electromagnetic forces on particles and currents
82(1)
5.5.2 Electromagnetic forces on matter
83(2)
5.6 Waves in simple conducting media (K)
85(2)
5.7 Polarization description
87(3)
5.7.1 Method of images
89(1)
5.8 Lorentz transformations
90(4)
5.9 Dielectric properties
94(4)
5.9.1 Simple media
94(1)
5.9.2 Material relations
95(2)
5.9.3 Definition of the dielectric function
97(1)
5.10 Energy density in dielectrics
98(6)
5.10.1 Simple media
98(1)
5.10.2 Real dielectric functions---dispersive media
99(1)
5.10.2.1 Electrostatic waves
100(1)
5.10.3 Inclusion of spatial dispersion
101(1)
5.10.4 Negative energy waves
102(1)
5.10.5 Complex dielectric functions---dispersive media
102(1)
5.10.6 Damping by dielectric losses---electrostatic waves
103(1)
5.11 Force on a fluid or a gas
104(5)
6 Natural Occurrences of Plasmas
109(10)
6.1 Saha's equation
109(2)
6.2 Coronal equilibrium (K)
111(2)
6.3 Chapman ionosphere (K)
113(6)
7 Single Particle Motion
119(30)
7.1 Single particle orbits
119(22)
7.1.1 E || B
119(2)
7.1.2 E B
121(1)
7.1.3 Fc B
122(3)
7.1.4 Finite Larmor radius corrections for inhomogeneous electric fields
125(2)
7.1.5 Polarization drifts, dE/dt ≠ 0
127(1)
7.1.6 B B
128(4)
7.1.7 B || B
132(1)
7.1.8 Magnetic moment
133(4)
7.1.9 Magnetic mirror confinement
137(3)
7.1.10 Larmor's theorem
140(1)
7.2 Adiabatic invariants
141(2)
7.3 Radiation losses
143(2)
7.4 The Dessler-Parker relations (K)
145(4)
8 Basic Plasma Parameters
149(32)
8.1 Plasma frequencies
149(1)
8.2 The Debye length
150(1)
8.3 The plasma parameter
150(1)
8.4 Debye shielding
151(5)
8.4.1 Immobile ions
151(1)
8.4.1.1 Shielding in three spatial dimensions
152(1)
8.4.1.2 Shielding in two spatial dimensions
153(1)
8.4.1.3 Shielding in one spatial dimension
153(1)
8.4.2 Mobile ions
154(1)
8.4.3 Nonlinear Debye shielding in one spatial dimension (K)
155(1)
8.5 Interaction energy (K)
156(2)
8.6 Evacuation of a Debye Sphere (K)
158(1)
8.7 Collisions between charged particles
158(5)
8.7.1 Simple arguments for collisional cross sections
160(1)
8.7.2 Center-of-mass dynamics
161(2)
8.8 Plasma resistivity by electron-ion collisions
163(9)
8.8.1 Collisions in magnetic fields
167(1)
8.8.2 Collisions in electric and magnetic fields
168(1)
8.8.2.1 The approximation E(y)
169(1)
8.8.2.2 The approximation E(y)
170(2)
8.9 Plasma resistivity by neutral collisions (K)
172(4)
8.9.1 Time-varying electric fields
175(1)
8.10 Plasma as a dielectric (K)
176(5)
8.10.1 Plasma as a dielectric at high frequencies
177(1)
8.10.2 A magnetized plasma as a dielectric at low frequencies
177(4)
9 Experimental Devices
181(24)
9.1 The Q-machine (K)
181(6)
9.1.1 Electron emission
182(2)
9.1.2 Ion emission
184(2)
9.1.3 Discussion
186(1)
9.2 Double plasma devices
187(1)
9.3 Langmuir probes
188(13)
9.3.1 A simple example
188(1)
9.3.2 Plane probes (K)
189(4)
9.3.3 Double probes (K)
193(1)
9.3.3.1 Plasma sheaths
194(1)
9.3.4 Orbit theory for thin cylindrical probes (K)
195(3)
9.3.5 The Bohm condition (K)
198(3)
9.4 Ion energy analyzers
201(4)
9.4.1 Space charge limited currents (K)
202(3)
10 Magneto-Hydrodynamics by Brute Force
205(40)
10.1 Ideal magneto-hydrodynamics
205(4)
10.1.1 Faraday's law
206(1)
10.1.2 Ampere's law
206(1)
10.1.3 Ohm's law
207(1)
10.1.4 Equation of state
208(1)
10.2 Compressible MHD
209(8)
10.2.1 Virial theorem (K)
211(1)
10.2.2 Frozen-in field lines
212(4)
10.2.2.1 Other arguments for frozen-in field lines
216(1)
10.3 Dissipative MHD
217(7)
10.3.1 Magnetic pressure
218(1)
10.3.2 Plasma β
219(1)
10.3.3 Plasma pinches
220(1)
10.3.3.1 0-Pinch
220(1)
10.3.3.2 Z-Pinch
220(1)
10.3.3.3 Screw-pinch
221(1)
10.3.3.4 Pinch instabilities
221(1)
10.3.3.5 Kink stability of a long thin pinch
222(1)
10.3.4 Force free fields
223(1)
10.4 Applications of MHD to the Earth's magnetosphere
224(9)
10.4.1 The solar wind (K)
224(3)
10.4.2 The Earth's magnetosphere
227(6)
10.5 Alfven waves
233(4)
10.5.1 Alfven waves in incompressible plasmas
233(3)
10.5.2 Energy density of shear Alfven waves
236(1)
10.6 Compressional Alfven waves
237(3)
10.7 Ideal electron MHD
240(5)
10.7.1 Whistlers (K)
241(4)
11 Plasma as a Mixture of Charged Gases
245(14)
11.1 Multi-component plasmas
245(6)
11.1.1 Plasma diamagnetism
249(2)
11.2 Quasi-neutrality
251(1)
11.3 Collisional diffusion in two component, magnetized plasmas
252(7)
11.3.1 Diffusion in fully ionized plasmas (K)
253(2)
11.3.2 Diffusion in partially ionized plasmas (K)
255(4)
12 Waves in Cold Plasmas
259(30)
12.1 Unmagnetized plasmas
259(3)
12.1.1 Penetration depth
260(2)
12.2 Magnetized plasmas
262(17)
12.2.1 High frequency waves
263(1)
12.2.1.1 Longitudinal waves
264(1)
12.2.1.2 Transverse waves
265(2)
12.2.2 Wave propagation perpendicular to B0
267(1)
12.2.3 Wave propagation parallel to B0
268(2)
12.2.4 Wave propagation at an arbitrary angle to B0
270(1)
12.2.4.1 Quasi-normal wave propagation
271(1)
12.2.4.2 Quasi-parallel wave propagation
272(1)
12.2.5 Quasi-electrostatic approximation
273(1)
12.2.5.1 Upper-hybrid waves
274(1)
12.2.5.2 Lower-hybrid waves
274(1)
12.2.6 Quasi-transverse approximation
275(1)
12.2.7 Wave propagation in stratified plasmas
275(2)
12.2.8 Electrostatic waves in a strongly magnetized waveguide
277(2)
12.3 Collisional losses
279(2)
12.4 Waves including the ion dynamics
281(4)
12.4.1 Lower-hybrid waves
281(1)
12.4.2 Alfven waves
282(1)
12.4.3 The Hall-MHD model
283(1)
12.4.4 Multi ion species
284(1)
12.5 Instabilities
285(2)
12.5.1 Buneman instability (K)
286(1)
12.6 Conclusions
287(2)
13 Electrostatic Waves in Warm Homogeneous and Isotropic Plasmas
289(10)
13.1 Electron plasma waves
289(7)
13.1.1 Radiation of Langmuir waves from a moving charge
291(5)
13.2 Ion acoustic waves
296(3)
13.2.1 The quasi-neutral limit
298(1)
14 Fluid Models for Nonlinear Electrostatic Waves: Isotropic Case
299(26)
14.1 Weakly nonlinear Langmuir waves
299(19)
14.1.1 Cold electrons with immobile ions
299(4)
14.1.2 Mobile ions
303(2)
14.1.3 The ponderomotive force
305(1)
14.1.3.1 Experimental observations
306(1)
14.1.4 Nonlinear wave equations
307(4)
14.1.5 Langmuir wave decay
311(4)
14.1.6 The nonlinear Schrodinger equation
315(1)
14.1.7 Nonlinear plasma waves in one, two and three spatial dimensions
315(3)
14.2 Weakly nonlinear ion acoustic waves
318(7)
14.2.1 Simple ion acoustic waves
318(1)
14.2.2 Korteweg-deVries model for ion acoustic waves
319(3)
14.2.3 Stationary nonlinear solutions
322(3)
15 Small Amplitude Waves in Anisotropic Warm Plasmas
325(10)
15.1 Warm magnetized plasmas
325(6)
15.1.1 High frequency electrostatic electron waves
325(3)
15.1.2 Electrostatic waves in a strongly magnetized waveguide
328(1)
15.1.3 Low frequency electrostatic ion waves
328(3)
15.1.4 Lower-hybrid waves
331(1)
15.2 Alfven waves in warm plasmas
331(2)
15.3 Ion acoustic waves in gravitational atmospheres (k)
333(2)
16 Fluid Models for Nonlinear Electrostatic Waves: Magnetized Case
335(8)
16.1 Cold electrons with immobile ions
335(1)
16.2 Mobile ions
336(3)
16.3 Simplified special cases
339(1)
16.3.1 B-parallel propagation
339(1)
16.3.2 B-perpendicular propagation
340(1)
16.4 Models for the low frequency response
340(3)
16.4.1 Quasi static response
340(1)
16.4.2 Low frequencies, ω << Ωci
340(1)
16.4.3 Ion cyclotron waves
340(1)
16.4.4 Lower-hybrid response
341(2)
17 Linear Drift Waves
343(44)
17.1 Drift wave basics
343(9)
17.1.1 Spatially varying magnetic fields
345(1)
17.1.2 Physical picture
346(1)
17.1.3 Limitations of the electrostatic assumption
346(1)
17.1.4 Simplified linear theory with cold ions
347(1)
17.1.5 Dispersion relation
348(2)
17.1.6 Physical picture
350(1)
17.1.7 The electron velocity
350(2)
17.1.8 Divergence-free currents
352(1)
17.2 Drift wave instability
352(1)
17.3 Resistive drift waves with Ti = 0
353(2)
17.3.1 Assumptions
353(1)
17.3.2 Basic equations
354(1)
17.3.3 Equilibrium
354(1)
17.4 Perturbation
355(8)
17.4.1 Dispersion relation
358(2)
17.4.2 Amplitude and phase relations
360(1)
17.4.3 Physical picture
360(2)
17.4.4 Model consistency
362(1)
17.5 Resistive drift waves with Ti > 0
363(10)
17.5.1 Basic equations
363(1)
17.5.2 Equilibrium
364(1)
17.5.3 Perturbation
365(2)
17.5.3.1 Comments on the cancellation of terms in the viscosity tensor
367(1)
17.5.4 Dispersion relation
367(1)
17.5.4.1 Pure drift wave
368(1)
17.5.4.2 Resistive-g mode
368(4)
17.5.5 FLR stabilization of flute modes
372(1)
17.6 Drift waves with ion viscosity
373(4)
17.6.1 Dispersion relation
374(1)
17.6.2 Long-λ|| limit
374(1)
17.6.3 Amplitude and phase relations
375(1)
17.6.4 Short-λ|| limit
376(1)
17.6.4.1 Long-λ|| and short-λ|| stabilization points
376(1)
17.6.5 An apparent paradox
376(1)
17.7 Experimental observations of drift waves
377(3)
17.8 Velocity shear driven instabilities
380(4)
17.8.1 Shear instabilities with electron shielding
383(1)
17.9 List of symbols
384(3)
18 Weakly Nonlinear Electrostatic Drift Waves
387(16)
18.1 Hasegawa-Mima equation
387(10)
18.1.1 Linearized Hasegawa-Mima equation
389(1)
18.1.2 Conservation laws
389(1)
18.1.3 Wave interactions
390(3)
18.1.4 Coherent three wave interactions
393(1)
18.1.5 Stationary solutions
394(3)
18.2 Hasegawa-Wakatani equations
397(6)
18.2.1 Linearized Hasegawa-Wakatani equations
398(1)
18.2.2 Conservation laws for the Hasegawa-Wakatani equations
399(2)
18.2.3 Comments on the Hasegawa-Wakatani equations
401(2)
19 Kinetic Plasma Theory
403(10)
19.1 The Vlasov equation
403(3)
19.1.1 Collisions
405(1)
19.2 Relation between kinetic and fluid models
406(4)
19.3 Water-bag models
410(1)
19.4 Drift kinetic equation
411(2)
20 Kinetic Description of Electron Plasma Waves
413(30)
20.1 Linearized equations
414(1)
20.2 Kinetic dispersion relation
415(17)
20.2.1 Landau damping the easy way
419(2)
20.2.2 Physical arguments for Landau damping
421(2)
20.2.3 Landau damping the hard way
423(1)
20.2.3.1 Solution by Laplace transform
424(5)
20.2.4 Normal-mode solution
429(3)
20.3 The Penrose criterion for plasma stability
432(5)
20.3.1 Two counter streaming cold electron beams
435(2)
20.4 Small amplitude power theorem
437(1)
20.5 Experimental investigations
438(5)
21 Kinetic Plasma Sound Waves
443(22)
21.1 Kinetic dispersion relation for ion sound waves
444(2)
21.1.1 Unstable ion acoustic waves
446(1)
21.2 Basic nonlinear dynamic equation for low frequency kinetic plasma waves
446(4)
21.2.1 Energy conservation
448(1)
21.2.2 Energy density of an ion sound wave
449(1)
21.3 Sound radiation from a moving charge
450(8)
21.3.1 Calculations in one spatial dimension
450(4)
21.3.2 Calculations in three spatial dimensions
454(2)
21.3.2.1 Numerical results
456(2)
21.4 A boundary value problem for wave excitation
458(2)
21.5 A realizable initial value problem
460(5)
21.5.1 Experimental results
461(4)
22 Nonlinear Kinetic Equilibria
465(8)
22.1 Equilibria
465(8)
22.1.1 Experimental results
469(2)
22.1.2 Ion equilibria
471(2)
23 Nonlinear Landau Damping
473(10)
23.1 Nonlinear Landau damping
473(4)
23.1.1 Fluid limit
476(1)
23.2 Damping of Korteweg-deVries ion acoustic solitons by reflected particles
477(6)
24 Quasi-linear Theory
483(12)
24.1 Conservation of energy and momentum
487(1)
24.2 Discussions of the asymptotic stage
487(2)
24.3 Experimental results
489(6)
A A Short Tour of Plasma Instabilities
495(10)
A.1 Fluid-like instabilities
495(6)
A.1.1 Electrostatic Rayleigh-Taylor instability
495(1)
A.1.2 Kelvin-Helmholtz electrostatic mode, B-parallel case
496(1)
A.1.3 Kelvin-Helmholtz electrostatic mode, B-perpendicular case
496(1)
A.1.4 Kelvin-Helmholtz electromagnetic mode
496(1)
A.1.5 Electrostatic drift dissipative instability
496(1)
A.1.6 Electrostatic drift cyclotron instability
496(1)
A.1.7 Drift Alfven instability
496(1)
A.1.8 Farley-Buneman, or "type I" electrojet instability
497(1)
A.1.9 Gradient, or "type II" electrojet instability
497(1)
A.1.10 Recombination instability
497(1)
A.1.11 Ballooning instability
497(1)
A.1.12 Mirror instability in magnetized plasmas
498(1)
A.1.13 Buneman instability
498(1)
A.1.14 Electron-electron beam instability
498(1)
A.1.15 Parametric decay instability
498(1)
A.1.16 Explosive instability
499(1)
A.1.17 Oscillating two stream instability
500(1)
A.1.18 Modulational instability
500(1)
A.1.19 Pierce instability
500(1)
A.1.20 Sausage instability of a linear pinch
500(1)
A.1.21 Kink instability of a linear pinch
500(1)
A.1.22 Fire-hose instability
501(1)
A.1.23 Weibel instability
501(1)
A.1.24 Discharge plasmas
501(1)
A.2 Kinetic instabilities
501(4)
A.2.1 Bump-on-tail instability
501(1)
A.2.2 Kinetic ion-acoustic instability
501(1)
A.2.3 Loss-cone instability
502(1)
A.2.4 Current driven ion cyclotron waves
502(1)
A.2.5 Beam driven ion cyclotron waves
502(1)
A.2.6 Kinetic electrostatic drift instability
502(1)
A.2.7 Kinetic drift Alfven instability
503(2)
B Collisional Cross Sections
505(8)
B.1 Cross sections in general
505(2)
B.2 Mean free path
507(2)
B.3 A statistical model for collisions
509(4)
B.3.1 Analytical collision model
511(1)
B.3.2 Ohm's law
511(2)
C The Plasma Dispersion Function
513(4)
C.1 The plasma dispersion function
513(3)
C.2 Approximations to the plasma dispersion function
516(1)
D Mathematical Theorems
517(4)
D.1 Gauss' theorem
517(1)
D.2 Stokes' theorem
517(1)
D.3 Green's relations
517(1)
D.4 Solenoidal fields
518(1)
D.5 Summary
518(1)
D.6 The Jacobian determinant
519(2)
D.6.1 Cylindrical coordinates
519(1)
D.6.2 Spherical coordinates
519(2)
E Useful Vector Relations
521(4)
E.1 Some basic vector relations
521(1)
E.2 Some basic differential expressions
521(4)
E.2.1 Differential operators in spherical geometry
522(1)
E.2.2 Differential operators in cylindrical geometry
523(2)
F Numbers to Remember
525(4)
F.1 Physical constants
525(1)
F.2 Selected data of geophysical and astrophysical importance
526(1)
F.3 Approximate expressions
527(2)
Bibliography 529(20)
Index 549