Electromagnetics of Time Varying Complex Media: Frequency and Polarization Transformer, Second Edition

Contents......Page 8
Foreword to the First Edition......Page 18
Preface......Page 20
Preface to the First Edition......Page 24
Acknowledgments......Page 26
Acknowledgments to the First Edition......Page 28
Author......Page 30
Overview......Page 32
Part I: Theory: Electromagnetic Wave Transformation in a Time-Varying Magnetoplasma Medium......Page 55
1.2 Basic Field Equations for a Cold Isotropic Plasma......Page 57
1.3 One-Dimensional Equations......Page 59
1.4 Profile Approximations for Simple Solutions......Page 62
1.5 Dispersive Media......Page 64
References......Page 65
2.1 Basic Equations......Page 67
2.2 Dielectric–Dielectric Spatial Boundary......Page 71
2.3 Reflection by a Plasma Half-Space......Page 73
2.4 Reflection by a Plasma Slab......Page 75
2.4.1 Tunneling of Power through a Plasma Slab......Page 81
2.5 Inhomogeneous Slab Problem......Page 83
2.5.1 Periodic Layers of the Plasma......Page 84
2.5.2 Surface Waves......Page 87
References......Page 92
3.1 Basic Equations......Page 95
3.2 Reflection by a Suddenly Created Unbounded Plasma Medium......Page 96
3.3 ω–k Diagram and the Wiggler Magnetic Field......Page 100
3.4 Power and Energy Considerations......Page 101
3.5 Perturbation from Step Profile......Page 103
3.6 Causal Green's Function for Temporally-Unlike Plasma Media......Page 105
3.7 Transmission and Reflection Coefficients for a General Profile......Page 107
3.8 Transmission and Reflection Coefficients for a Linear Profile......Page 109
3.9 Validation of the Perturbation Solution by Comparing with the Exact Solution......Page 110
3.10 Hump Profile......Page 112
3.11 Comparison Identities......Page 115
References......Page 116
4.2 Steady-State Solution......Page 119
4.3.1 Formulation and Solution......Page 125
4.3.2 Steady-State Solution from the Transient Solution......Page 128
References......Page 130
5.1 Introduction......Page 133
5.2 Development of the Problem......Page 134
5.3 Transient Solution......Page 135
5.5 A Component from Steady-State Solution......Page 139
5.6 Numerical Results......Page 141
References......Page 144
6.2 Basic Field Equations for a Cold Anisotropic Plasma Medium......Page 145
6.3 One-Dimensional Equations: Longitudinal Propagation: L and R Waves......Page 147
6.5 One-Dimensional Solution: Transverse Propagation: X Wave......Page 151
6.6 Dielectric Tensor of a Lossy Magnetoplasma Medium......Page 155
References......Page 157
7.2 One-Dimensional Equations: Longitudinal Propagation......Page 159
7.3 Sudden Creation: Longitudinal Propagation......Page 160
7.4 Numerical Results: Longitudinal Propagation......Page 165
7.5 Damping Rates: Longitudinal Propagation......Page 172
7.6 Sudden Creation: Transverse Propagation: X wave......Page 173
7.7 Additional Numerical Results......Page 174
References......Page 179
8.1 Introduction......Page 181
8.2 Perturbation from Step Profile......Page 183
8.3 Causal Green's Function for Temporally-Unlike Magnetized Plasma Media......Page 185
8.4 Scattering Coefficients for a General Profile......Page 189
8.5 Scattering Coefficients for a Linear Profile......Page 190
8.6 Numerical Results......Page 191
8.7 Wiggler Magnetic Field......Page 192
8.9 Summary......Page 194
References......Page 195
9.2 Adiabatic Analysis for R Wave......Page 197
9.4 Modification of the Whistler Wave by a Collapsing Plasma Medium......Page 200
9.5 Alternative Model for a Collapsing Plasma......Page 202
9.6 Modification of the Whistler Wave by a Collapsing Magnetic Field......Page 204
References......Page 205
10.3 Moving Ionization Front......Page 207
10.5 Lorentz Medium......Page 210
10.6 Mode Conversion of X Wave......Page 211
10.8 Chiral Media: R and LWaves......Page 214
10.9 Solitons......Page 215
References......Page 216
Additional References......Page 218
Appendix A: Constitutive Relation for a Time-Varying Plasma Medium......Page 219
B.1 Introduction......Page 223
B.2 Frequencies and Velocities of the New Waves......Page 224
B.3 Damping Rates of the New Waves......Page 226
B.4 Numerical Results......Page 229
B.6 Conclusions......Page 231
References......Page 232
C.1 Introduction......Page 233
C.2 Frequencies and Power Content of the New Waves......Page 234
C.3 Damping Rates for the New Waves......Page 239
C.4 Magnetoplasma Half-Space: Steady-State Solution......Page 242
C.5 Magnetoplasma Half-Space: Transient Solution......Page 244
C.6 Numerical Results and Discussion......Page 247
References......Page 251
D.1 Introduction......Page 253
D.2 Wave Propagation in a Switched Unbounded Magnetoplasma Medium......Page 254
D.3 Land R Waves......Page 255
D.4 X Waves......Page 257
D.5 Frequency-Shifting Characteristics of Various Waves......Page 258
References......Page 265
E.2 Sudden Collapse......Page 267
E.2.1 Frequencies of the New Waves......Page 268
E.2.3 Choice of the Parameters......Page 269
E.2.4 Eckersley Approximation......Page 270
E.2.5 Experimental Feasibility......Page 271
E.3 Slow Decay......Page 272
E.4 An Illustrative Example......Page 273
E.5 Conclusion......Page 275
References......Page 276
F.1 Introduction......Page 277
F.2 Formulation......Page 278
F.3 Sudden Switching Off of the Static Magnetic Field......Page 279
F.3.1 Frequencies and the Fields of the New Waves......Page 280
F.3.3 Eckersley Approximation......Page 281
F.4 Slow Decay of Bs......Page 282
F.5 An Illustrative Example......Page 285
F.6 Conclusion......Page 287
References......Page 288
G.2 Effect on a Monochromatic Wave: Review......Page 289
G.3 Effect on the Duration of a Monochromatic Pulse......Page 292
G.4 Numerical Results and Discussion......Page 297
References......Page 299
H.2.1 Development of the Problem......Page 301
H.2.3 Higher-Order Differential Equation......Page 303
H.2.4 Riccati Equation......Page 304
H.2.5 Frequencies of the New Waves......Page 305
H.2.7 Complete Solution......Page 306
H.2.8 Explicit Expressions for the Amplitudes of the Fields......Page 307
H.2.9 Adiabatic Analysis of the MSW......Page 308
H.3 Graphical Illustrations and Results......Page 309
References......Page 313
Part II: Numerical Simulation: FDTD for Time-Varying Medium......Page 315
11.1 Air-Transmission Line......Page 317
11.2 FDTD Solution......Page 318
11.3 Numerical Dispersion......Page 322
11.4 Stability Limit and Courant Condition......Page 325
11.5 Open Boundaries......Page 326
11.6 Source Excitation......Page 327
11.7 Frequency Response......Page 328
11.8 Waves in Inhomogeneous, Nondispersive Media: FDTD Solution......Page 329
11.9 Waves in Inhomogeneous, Dispersive Media......Page 332
11.10 Waves in Debye Material: FDTD Solution......Page 335
11.13 Exponential Time Stepping......Page 336
11.14 FDTD for a Magnetoplasma......Page 337
References......Page 338
I.1 Introduction......Page 339
I.2 Development of FDTD Equations......Page 340
I.2.1 Total-Field and Scattered-Field Formulation......Page 341
I.2.2 Lattice Truncation: PML......Page 343
I.2.3 FDTD Formulation for an R Wave in a Switched Plasma Slab......Page 344
I.3 Interaction of a Continuous Wave with a Switched Plasma Slab......Page 345
I.4 Interaction of a Pulsed Wave with a Switched Plasma Slab......Page 346
References......Page 351
J.1 Introduction......Page 353
J.2.1 One-Dimensional Equations......Page 354
J.2.2 FDTD Formulation......Page 355
J.3.1 Time-Varying Unbounded Plasma with an Arbitrary Profile......Page 356
J.3.2 Validation of FDTD......Page 357
J.3.3 Characteristics of Plasma Transition Time Behaviors......Page 358
J.3.4 FDTD Analysis of a Magnetized Plasma Creation......Page 364
J.3.5 Periodic Magnetoplasma Layers: Sudden Switching......Page 367
J.3.6 Periodic Plasma Layers: Finite Rise Time......Page 372
J.A.1 Spectrum Analysis Using FFT......Page 374
J.A.2 Algorithm of the SRM......Page 376
References......Page 378
K.1 Introduction......Page 381
K.2.1 Maxwell's Equation......Page 382
K.2.2 FDTD Equation......Page 383
K.2.3 PEC Boundary Conditions......Page 386
K.3 Validation of the Algorithm......Page 387
K.4 Illustrative Examples of the New FDTD Method for a Dynamic Medium......Page 390
K.5 Conclusion......Page 391
References......Page 392
Part III: Application: Frequency and Polarization Transformer—Switched Medium in a Cavity......Page 395
12.2.1 Fields before Switching......Page 397
12.2.2 Sudden Creation and Results......Page 399
12.4 Switching a Magnetoplasma: Longitudinal Modes......Page 400
12.5 Switching a Magnetoplasma Medium: X Wave......Page 401
12.6 Switching Off the Magnetoplasma by Collapse of the Ionization: Whistler Source Wave......Page 404
12.7 Switching Off the Magnetoplasma by Collapse of the Background Magnetic Field: Whistler Source Wave......Page 405
References......Page 409
L.2 Sudden Creation in a Cavity......Page 411
L.2.1 Fields before Switching......Page 412
L.2.2 Step Plasma Profile......Page 413
L.2.3 Fields after Switching......Page 414
L.2.5 Results and Observations......Page 419
L.3 Conclusion and Future Work......Page 423
References......Page 424
M.2 Algorithm......Page 425
M.2.1 Initial Conditions......Page 426
M.2.2 FDTD Equations......Page 427
M.3.1 Effect of Time-Varying Profile......Page 430
M.3.2 Effect of Space-Varying Profile......Page 432
M.3.3 Effect of Space-Varying Profile: Comparison of Signal Spectrum at a Cavity Point in Free Space with the One in Plasma......Page 435
M.3.4 Effect of Collisions......Page 436
M.3.5 Simultaneous Effect of Space Profile, Time Profile, and Collision......Page 439
M.4 Conclusion......Page 441
References......Page 442
N.1 Introduction......Page 443
N.2.1 Fields before Switching......Page 444
N.2.3 Fields after Switching......Page 446
N.2.4 Reduction of Field Equation for E+x (z, t) When the External Magnetic Field is Zero (Isotropic Case)......Page 448
N.3.1 Analysis of a Typical Transformation......Page 449
N.3.2 Total E and H Field Variations with Time......Page 452
N.3.3 Variation of the Modes with the Strength of the External Magnetic Field......Page 454
N.4.1 FDTD Equations......Page 457
N.4.4 Effect of Space-Varying Profile......Page 459
N.4.5 Effect of Space-Varying Profile: Comparison of a Signal Spectrum at a Cavity Point in Free Space with the One in Magnetoplasma......Page 461
N.4.6 Lossy Plasma......Page 463
References......Page 464
O.1 Introduction......Page 465
O.2.1 Fields before Switching......Page 466
O.2.3 Fields after Switching......Page 468
O.3 Illustrative Results......Page 470
O.4 Longitudinal Modes versus Transverse Modes......Page 476
O.5 Conclusion......Page 478
O.A.1 Fields' Equations......Page 479
References......Page 481
P.1 Introduction......Page 483
P.2.1 Fields before Switching......Page 485
P.2.2 Equations for the Evolving Fields in the Time-Varying Medium......Page 486
P.2.3 FDTD Computation......Page 487
P.3 Illustrative Results......Page 488
P.4 Conclusion......Page 491
References......Page 493
Q.1 Introduction......Page 495
Q.2 Formulation of the Problem......Page 498
Q.3 FDTD Solution......Page 499
Q.4 Results......Page 500
Q.5 Higher Frequency-Upshift Ratio......Page 506
Q.6.1 Three Waves......Page 508
Q.6.3 Cavity, Plasma Decay Model, and Collision Frequency......Page 509
Q.6.4 FDTD Solution for the Time-Varying Medium......Page 510
Q.6.5 Space-Varying Plasma Profile......Page 511
Q.7 Concluding Remarks......Page 512
Q.A Appendix......Page 513
References......Page 514
Part IV: Experiments......Page 517
13.1 Mark Rader: 1......Page 519
13.2 Mark Rader: 2......Page 521
13.3 Spencer Kuo......Page 526
References......Page 527
14. Problems......Page 529