By E. Krause
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This complex point textbook is dedicated to the outline of structures which express ordered magnetic stages. a big variety of issues is roofed, together with an in depth therapy of the mean-field approximation because the major paradigm for the phenomenological description of section transitions. The publication discusses the houses of low-dimensional platforms and makes use of Green's capabilities greatly after an invaluable mathematical creation.
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91) where C is an arbitrary constant. 92), we see that the extraordinary wave traveling perpendicular to B0 is a transverse magnetic (TM) wave with its magnetic vector parallel to B0 . Overall, the cases y ¼ 0 and y ¼ 90 , which correspond to longitudinal and transverse propagations, generate two uncoupled waves which are known as principal waves. 5 Cut-off and Resonance Conditions The term cut-off for any type of the wave occurs when k ¼ 0 or the phase velocity, vp ¼ ok ¼ 1 infinite, and the term resonance is used when k ¼ 1 or the phase velocity vp ¼ ok ¼ 0 .
58) have always real values. 97) is positive, it is equal to b2 ; when it is negative it is equal to À a2 . 36). 36). 6 Dispersion Curves and Propagation Characteristics 47 where op ¼ N0 e2 me0 1=2 ; ob ¼ À eB0 m So in our analysis, we will use X and Y to describe the dispersion curves in a gyroelectric medium such as cold plasma for three different cases, namely, the isotropic case, the longitudinal propagation and the transverse propagation. 1 Isotropic Case, No Magnetic Field, Y ¼ 0 It is conventional to represent the dispersion of electromagnetic waves by a plot of the propagation constant k against o as shown in Fig.
Then, repeating the same procedure in Chap. 12) where k02 ¼ o2 m0 e0 . 10), we obtain H. 18), W E M are obtained matrix, respectively. 20) are the dispersion relations for general anisotropic medium. It is interesting to note the duality between the electric wave matrix and magnetic wave matrix. If one of the wave matrix is known, the other one can be simply obtained by using the following duality relations e ! 1 m ! 23) Please note that we are using double over bar to represent dyadics. p^ shows the direction of the optic axis exist in the uniaxially anisotropic medium and equals p^ ¼ ^ z.