Wave Propagation in Linear Media | re-examined

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30 30 3Wave propagation in electromagnetic transmission lines 0 20 0 20 10 X 10 X T 10 T 10 20 20 30 1 0.5 0 -0.5 -1 0 30 1 0 -1 -2 0 I/I0 U/U0 Figure 3.15: Evolution of the current (3.82) and voltage (3.83) along a one-dimensional transmission line with a lossless plasma for an input current with high frequency ( = 0:8). Note the high voltage amplitude at the entrance. 56
3.7 Turn-on e ects in a lossless plasma 1 0.8 0.6 0.4 0.2 9.9 9.95 10.05 10.1 1 0.8 0.6 0.4 0.2 99.99 99.995 100.005 100.01 1 0.8 0.6 0.4 0.2 999.999 1000 1000. Figure 3.16: Wave front of the current for = 0:5 depending on the spatial coordinate. 1 0.8 0.6 0.4 0.2 9.9 9.95 10.05 10.1 1 0.8 0.6 0.4 0.2 99.99 99.995 100.005 100.01 1 0.8 0.6 0.4 0.2 999.999 1000 1000. Figure 3.17: Wave front of the voltage for = 0:5 depending on the spatial coordinate. T = X ,1=X, so that an arbitrary initial point (X0;T0) follows a phenomenological trajectory given by X , T X0 , T0 = T0 T : (3.84) This again is due to dispersion. The high frequencies move ahead, the lower ones more and more lag behind, such that the high-pass lter e ect becomes more marked. The behaviour of the wave is therefore locally similar to the output of a high-pass lter whose characteristic frequency is tuned higher and higher, i. e. the needle of the output pulse becomes sharper. As last item of the examination, we discuss the propagation of a rectangular pulse through the plasma. Owing to the linearity of the medium, we already stated in (3.68) that such a pulse can be constructed from two delayed step functions. If the duration of the pulse is an integer multiple n of the signal period, we can use identical step responses for switch-on and switch-o and need not take care of the additional phase shift otherwise introduced by an arbitrary pulse length. In our scaled variables, the pulse duration then becomes T t= = 2n : (3.85) We expect that both the leading and the trailing edge of the pulse cause a sharp wave front travelling at the velocity of light. The contour plots for short pulses with low ( g. 3.18) and high ( g. 3.19) input frequencies con rm this suspicion. They also show how the phase trajectories of the peaks and troughs of the wave asymptotically approach the wave front. Note that if we trace the evolution of such a peak, we nd that it travels always at a velocity 57
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DISSERTATION Wave Propagation in Li
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Kurzfassung Seit der Entdeckung des
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Nullum est iam dictum, quod non sit
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Preface Our popular writers and rep
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the quest for superluminality and t
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Contents Part I Wave propagation ph
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7.3.4 PartitionPoints . . . . . . .
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Part I Wave propagation phenomena S
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1.1 Phase and group velocity 1.1 Ph
Page 21 and 22: 1.1 Phase and group velocity ! !c v
Page 23 and 24: 1.2 A few notes on dispersion He co
Page 25 and 26: 1.2 A few notes on dispersion v/c 6
Page 27 and 28: 1.3 Signal velocity dipoles with a
Page 29 and 30: 1.3 Signal velocity The arbitrarine
Page 31 and 32: 1.4 Energy velocity For electromagn
Page 33 and 34: 1.5 Other velocity de nitions For n
Page 35 and 36: 1.5 Other velocity de nitions evide
Page 37 and 38: 2.1 Superluminal wave propagation 2
Page 39 and 40: 2.1 Superluminal wave propagation a
Page 41 and 42: 2.1 Superluminal wave propagation t
Page 43 and 44: 2.2 Quantum mechanical tunnelling e
Page 45 and 46: 2.2 Quantum mechanical tunnelling R
Page 47 and 48: Chapter 3 Wave propagation in elect
Page 49 and 50: 3.1 Model of a transmission line th
Page 51 and 52: 3.2 Excursion: a delay line section
Page 53 and 54: 3.3 Re ection due to termination mi
Page 55 and 56: 3.4 A simple thought experiment I0
Page 57 and 58: 3.5 A dispersive system: the lossle
Page 63 and 64: 3.6 Inhomogeneous transmission line
Page 65 and 66: 3.7 Turn-on e ects in a lossless pl
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Page 77 and 78: 3.8 Turn-on e ects in a wave guide
Page 79 and 80: 3.8 Turn-on e ects in a wave guide
Page 81 and 82: 3.9 A Gaussian pulse in plasma Like
Page 83 and 84: 3.9 A Gaussian pulse in plasma 250
Page 85 and 86: 3.9 A Gaussian pulse in plasma 250
Page 87 and 88: 3.9 A Gaussian pulse in plasma Note
Page 89 and 90: 4.1 The potential step 4.1 The pote
Page 91 and 92: 4.1 The potential step Inside the b
Page 93 and 94: 4.2 Initial wave forms -60 -50 -40
Page 95 and 96: 4.2 Initial wave forms -60 -50 -40
Page 97 and 98: 4.3 Examples of scattering processe
Page 109 and 110: 4.4 The square barrier they have va
Page 111 and 112: 4.4 The square barrier 1 0.8 0.6 0.
Page 113 and 114: 4.5 Tunnelling time de nitions for
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Page 117 and 118: 4.6 Examples of tunnelling events P
Page 119 and 120: 4.6 Examples of tunnelling events 2
Page 121 and 122: 4.6 Examples of tunnelling events -
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4.6 Examples of tunnelling events t
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4.6 Examples of tunnelling events P
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4.6 Examples of tunnelling events 8
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4.6 Examples of tunnelling events T
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Interlude Wave functions in graphic
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Wave functions in graphical represe
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Part II Numerical aspects of wave e
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5.1 Univariate numerical quadrature
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5.1 Univariate numerical quadrature
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5.2 Convergence acceleration one, t
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5.2 Convergence acceleration (1) ,1
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6.1 Partitioning the integration in
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6.2 Choosing the rst partition poin
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6.3 How to compute the rst integral
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6.3 How to compute the rst integral
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6.4 Asymptotic partition consuming
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6.4 Asymptotic partition of the int
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6.5 Considerations for a Mathematic
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6.6 Controlling the accuracy of the
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Chapter 7 Mathematica implementatio
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7.1 User interface of the function
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7.3 Implementation of OscInt and re
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7.4 Auxiliary functions While[itera
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7.4 Auxiliary functions Linear appr
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7.4 Auxiliary functions For the sak
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7.4 Auxiliary functions Out[8]= 3 f
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7.5 Test of the quadrature routine
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8.1 Preparation of the wave integra
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8.2 Outline of the program structur
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8.2 Outline of the program structur
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8.3 Implementation of the quadratur
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8.3 Implementation of the quadratur
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8.4 Test of the package 8.4 Test of
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8.4 Test of the package -200 -150 -
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8.4 Test of the package 0.4 0.2 -0.
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8.4 Test of the package 8.4.2 Forma
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8.4 Test of the package Out[24]= 0
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A.1 Numerical quadrature Asymptotic
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A.1 Numerical quadrature WynnDegree
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A.1 Numerical quadrature Which[ft =
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A.2 Solutions for the step potentia
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A.3 Solutions for the square barrie
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A.3 Solutions for the square barrie
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A.4 Electromagnetic waves function
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A.5 Utilities for displaying points
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Bibliography Bibliography [1] James
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Bibliography [29] Kurt Edmund Oughs
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Bibliography [59] Ch. Spielmann, R.
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Bibliography [91] C. R. Leavens and
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Bibliography [123] T. O. Espelid an
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Index Index absorption, 7, 9 accura
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Index saddle point integration, 11,
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Curriculum vitae Dipl.-Ing. Thilo S
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