an introduction to magnetohydrodynamcs by Roberts

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The wave is still a one-dimensional wave propagating in the direction of ζ-coordinate, which can be expressed in terms of x and z: ζ = x sin θ + z cos θ. 7 Arbitrary direction of propagation. where S = sin θ, C = cos θ. 85) We can have two cases of TEM waves, one with the electric field in the plane of incidence and the other with the electric field normal to the plane of incidence. The former is called a p wave and the latter an s wave. The p wave has the magnetic field perpendicular to the plane of incidence.

Appendix 2B gives the theory and application of the Smith chart. The input impedance is reactive, if the load is either short-circuited or open-circuited and the reflection coefficient has a magnitude of 1: ⎧⎪ jZ0 tan β d, ZL = 0, Z(d) = ⎨ ⎪⎩− jZ0 cot β d, ZL = ∞. 72) In the above two cases, the waves are standing waves, there are permanent nulls in voltage at certain points on the transmission line, and the source does not supply any real power to the load but supplies only a reactive power. Transmission line serves as a powerful analog for describing many electromagnetic phenomena since voltage and current variables are easily measurable and electrical engineers have a certain feel for these variables.

S I = 2 EsI 2η1 2 [x sin θ1 + z cos θ1 ]. 11 shows the constant phase planes in medium 2. When the angle of incidence θ1 > θc , then sin θ2 = k1 n sin θ1 = 1 sin θ1 > 1. 109) The equation can be satisfied only if θ2 is complex [2]: θ2 = θR + jθX , θ1 > θc . 113) and the phase velocity of this wave is given by vPe = vP 2 ω ω = . 12 Constant-phase planes and constant-amplitude planes, for θ1 > θc. This wave is a surface wave. The wave propagates in the positive x-direction but attenuates in the positive z-direction.

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