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Ray Tracing and Beyond: Phase Space Methods in Plasma Wave Theory [Kietas viršelis]

(College of William and Mary, Virginia), (University of California, Berkeley), , (Saint Michael's College, Vermont)
  • Formatas: Hardback, 541 pages, aukštis x plotis x storis: 253x177x27 mm, weight: 1200 g, 2 Tables, black and white; 101 Line drawings, unspecified
  • Išleidimo metai: 27-Feb-2014
  • Leidėjas: Cambridge University Press
  • ISBN-10: 0521768063
  • ISBN-13: 9780521768061
Kitos knygos pagal šią temą:
Ray Tracing and Beyond: Phase Space Methods in Plasma Wave TheoryDidesnis paveikslėlis
  • Formatas: Hardback, 541 pages, aukštis x plotis x storis: 253x177x27 mm, weight: 1200 g, 2 Tables, black and white; 101 Line drawings, unspecified
  • Išleidimo metai: 27-Feb-2014
  • Leidėjas: Cambridge University Press
  • ISBN-10: 0521768063
  • ISBN-13: 9780521768061
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9780521768061.html
Raktažodžiai:
This complete introduction to the use of modern ray tracing techniques in plasma physics describes the powerful mathematical methods generally applicable to vector wave equations in non-uniform media, and clearly demonstrates the application of these methods to simplify and solve important problems in plasma wave theory. Key analytical concepts are carefully introduced as needed, encouraging the development of a visual intuition for the underlying methodology, with more advanced mathematical concepts succinctly explained in the appendices, and supporting Matlab and Raycon code available online. Covering variational principles, covariant formulations, caustics, tunnelling, mode conversion, weak dissipation, wave emission from coherent sources, incoherent wave fields, and collective wave absorption and emission, all within an accessible framework using standard plasma physics notation, this is an invaluable resource for graduate students and researchers in plasma physics.

Daugiau informacijos

A complete introduction to the use of modern ray tracing techniques in plasma physics.
Preface xiii
Acknowledgements xix
1 Introduction
1(61)
1.1 Fermat's principle of stationary time
2(9)
1.1.1 General comments
2(1)
1.1.2 Uniform media
3(1)
1.1.3 Snell's Law
4(1)
1.1.4 Distributed sources
5(1)
1.1.5 Stationarity vs. minimization: the law of reflection
6(3)
1.1.6 Smoothly varying media
9(2)
1.2 Hamilton's principle of stationary phase
11(7)
1.2.1 Phase speed
12(2)
1.2.2 Phase integrals and rays
14(4)
1.3 Modern developments
18(9)
1.3.1 Quantum mechanics and symbol calculus
18(4)
1.3.2 Ray phase space and plasma wave theory
22(5)
1.4 One-dimensional uniform plasma: Fourier methods
27(11)
1.4.1 General linear wave equation: D(---i∂x, i∂t)ψ = 0
28(1)
1.4.2 Dispersion function: D(k, ω)
29(2)
1.4.3 Modulated wave trains: group velocity and dispersion
31(3)
1.4.4 Weak dissipation
34(1)
1.4.5 Far field of dispersive wave equations
35(3)
1.5 Multidimensional uniform plasma
38(2)
1.6 One-dimensional nonuniform plasma: ray tracing
40(7)
1.6.1 Eikonal equation for an EM wave
40(2)
1.6.2 Wave-action conservation
42(1)
1.6.3 Eikonal phase θ(x)
43(1)
1.6.4 Amplitude A(x)
44(1)
1.6.5 Hamilton's equations for rays
45(1)
1.6.6 Example: reflection of an EM wave near the plasma edge
46(1)
1.7 Two-dimensional nonuniform plasma: multidimensional ray tracing
47(15)
1.7.1 Eikonal equation for an EM wave
48(1)
1.7.2 Wave-action conservation
48(1)
1.7.3 Eikonal phase θ(x,y) and Lagrange manifolds
49(1)
1.7.4 Hamilton's equations for rays
49(2)
Problems
51(4)
References
55(7)
2 Some preliminaries
62(18)
2.1 Variational formulations of wave equations
62(1)
2.2 Reduced variational principle for a scalar wave equation
63(3)
2.2.1 Eikonal equation for the phase
64(1)
2.2.2 Noether symmetry and wave-action conservation
64(2)
2.3 Weyl symbol calculus
66(14)
2.3.1 Symbols in one spatial dimension
66(6)
2.3.2 Symbols in multiple dimensions
72(2)
2.3.3 Symbols for multicomponent linear wave equations
74(1)
2.3.4 Symbols for operator products: the Moyal series
74(2)
Problems
76(2)
References
78(2)
3 Eikonal approximation
80(74)
3.1 Eikonal approximation: x-space viewpoint
81(3)
3.2 Eikonal approximation: phase space viewpoint
84(27)
3.2.1 Lifts and projections
89(3)
3.2.2 Matching to boundary conditions
92(2)
3.2.3 Higher-order phase corrections
94(1)
3.2.4 Action transport using the focusing tensor
95(2)
3.2.5 Pulling it all together
97(5)
3.2.6 Frequency-modulated waves
102(2)
3.2.7 Eikonal waves in a time-dependent background plasma
104(1)
3.2.8 Symmetries
105(3)
3.2.9 Curvilinear coordinates
108(3)
3.3 Covariant formulations
111(10)
3.3.1 Lorentz-covariant eikonal theory
111(8)
3.3.2 Energy-momentum conservation laws
119(2)
3.4 Fully covariant ray theory in phase space
121(7)
3.5 Special topics
128(26)
3.5.1 Weak dissipation
129(3)
3.5.2 Waveguides
132(2)
3.5.3 Boundaries
134(5)
3.5.4 Wave emission from a coherent source
139(3)
3.5.5 Incoherent waves and the wave kinetic equation
142(4)
Problems
146(5)
References
151(3)
4 Visualization and wave-field construction
154(29)
4.1 Visualization in higher dimensions
155(15)
4.1.1 Poincare surface of section
155(2)
4.1.2 Global visualization methods
157(13)
4.2 Construction of wave fields using ray-tracing results
170(13)
4.2.1 Example: electron dynamics in parallel electric and magnetic fields
173(1)
4.2.2 Example: lower hybrid cutoff model
173(9)
References
182(1)
5 Phase space theory of caustics
183(45)
5.1 Conceptual discussion
187(6)
5.1.1 Caustics in one dimension: the fold
187(4)
5.1.2 Caustics in multiple dimensions
191(2)
5.2 Mathematical details
193(5)
5.2.1 Fourier transform of an eikonal wave field
194(2)
5.2.2 Eikonal theory in k-space
196(2)
5.3 One-dimensional case
198(14)
5.3.1 Summary of eikonal results in x and k
198(2)
5.3.2 The caustic region in x: Airy's equation
200(5)
5.3.3 The normal form for a generic fold caustic
205(5)
5.3.4 Caustics in vector wave equations
210(2)
5.4 Caustics in n dimensions
212(16)
Problems
218(8)
References
226(2)
6 Mode conversion and tunneling
228(99)
6.1 Introduction
228(14)
6.2 Tunneling
242(5)
6.3 Mode conversion in one spatial dimension
247(11)
6.3.1 Derivation of the 2 × 2 local wave equation
247(5)
6.3.2 Solution of the 2 × 2 local wave equation
252(6)
6.4 Examples
258(18)
6.4.1 Budden model as a double conversion
259(2)
6.4.2 Modular conversion in magnetohelioseismology
261(2)
6.4.3 Mode conversion in the Gulf of Guinea
263(6)
6.4.4 Modular approach to iterated mode conversion
269(4)
6.4.5 Higher-order effects in one-dimensional conversion models
273(3)
6.5 Mode conversion in multiple dimensions
276(7)
6.5.1 Derivation of the 2 × 2 local wave equation
276(3)
6.5.2 The 2 × 2 normal form
279(4)
6.6 Mode conversion in a numerical ray-tracing algorithm: RAYCON
283(12)
6.7 Example: Ray splitting in rf heating of tokamak plasma
295(6)
6.8 Iterated conversion in a cavity
301(2)
6.9 Wave emission as a resonance crossing
303(24)
6.9.1 Coherent sources
304(4)
6.9.2 Incoherent sources
308(2)
Problems
310(12)
Suggested further reading
322(1)
References
323(4)
7 Gyroresonant wave conversion
327(67)
7.1 Introduction
327(8)
7.1.1 General comments
329(2)
7.1.2 Example: Gyroballistic waves in one spatial dimension
331(2)
7.1.3 Minority gyroresonance and mode conversion
333(2)
7.2 Resonance crossing in one spatial dimension: cold-plasma model
335(13)
7.3 Finite-temperature effects in minority gyroresonance
348(46)
7.3.1 Local solutions near resonance crossing for finite temperature
359(14)
7.3.2 Solving for the Bernstein wave
373(6)
7.3.3 Bateman--Kruskal methods
379(6)
Problems
385(7)
References
392(2)
Appendix A Cold-plasma models for the plasma dielectric tensor
394(12)
A.1 Multifluid cold-plasma models
395(2)
A.2 Unmagnetized plasma
397(2)
A.3 Magnetized plasma
399(4)
A.3.1 k || B0
400(1)
A.3.2 k || B0
401(2)
A.4 Dissipation and the Kramers--Kronig relations
403(3)
Problems
404(1)
References
405(1)
Appendix B Review of variational principles
406(6)
B.1 Functional derivatives
406(2)
B.2 Conservation laws of energy, momentum, and action for wave equations
408(4)
B.2.1 Energy-momentum conservation laws
408(1)
B.2.2 Wave-action conservation
409(2)
References
411(1)
Appendix C Potpourri of other useful mathematical ideas
412(14)
C.1 Stationary phase methods
412(14)
C.1.1 The one-dimensional case
412(4)
C.1.2 Stationary phase methods in multidimensions
416(5)
C.2 Some useful facts about operators and bilinear forms
421(3)
Problem
424(1)
References
424(2)
Appendix D Heisenberg--Weyl group and the theory of operator symbols
426(27)
D.1 Introductory comments
426(1)
D.2 Groups, group algebras, and convolutions on groups
427(3)
D.3 Linear representations of groups
430(6)
D.3.1 Lie groups and Lie algebras
434(2)
D.4 Finite representations of Heisenberg--Weyl
436(6)
D.4.1 The translation group on n points
436(3)
D.4.2 The finite Heisenberg--Weyl group
439(3)
D.5 Continuous representations
442(3)
D.6 The regular representation
445(1)
D.7 The primary representation
445(1)
D.8 Reduction to the Schrodinger representation
446(1)
D.8.1 Reduction via a projection operator
446(1)
D.8.2 Reduction via restriction to an invariant subspace
446(1)
D.9 The Weyl symbol calculus
447(6)
References
452(1)
Appendix E Canonical transformations and metaplectic transforms
453(26)
E.1 Examples
453(4)
E.2 Two-dimensional phase spaces
457(9)
E.2.1 General canonical transformations
457(2)
E.2.2 Metaplectic transforms
459(7)
E.3 Multiple dimensions
466(5)
E.3.1 Canonical transformations
466(1)
E.3.2 Lagrange manifolds
467(2)
E.3.3 Metaplectic transforms
469(2)
E.4 Canonical coordinates for the 2 × 2 normal form
471(8)
References
476(3)
Appendix F Normal forms
479(21)
F.1 The normal form concept
479(3)
F.2 The normal form for quadratic ray Hamiltonians
482(6)
F.3 The normal form for 2 × 2 vector wave equations
488(12)
F.3.1 The Braam--Duistermaat normal forms
497(1)
F.3.2 The general case
497(2)
References
499(1)
Appendix G General solutions for multidimensional conversion
500(11)
G.1 Introductory comments
500(1)
G.2 Summary of the basis functions used
500(4)
G.3 General solutions
504(2)
G.4 Matching to incoming and outgoing fields
506(5)
Reference
510(1)
Glossary of mathematical symbols 511(3)
Author index 514(3)
Subject index 517
E. R. Tracy is the Chancellor Professor of Physics at the College of William and Mary, Virginia. A. J. Brizard is a Professor of Physics at Saint Michael's College, Vermont. A. S. Richardson is a Research Scientist in the Plasma Physics Division of the U. S. Naval Research Laboratory (NRL). A. N. Kaufman is an Emeritus Professor of Physics at the University of California, Berkeley.