Scattering Matrices for Ionosphere

Cover Scattering Matrices for Ionosphere
Scattering Matrices for Ionosphere
A Russek
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T) = Yl V (z)iA (7)e ° ^ (25) n=l ^ ^ k _ i[-U)t+kx+/\ Odt] E(x, 7, t) = Y. V^(z)D„(z)e n=l " ^ into Maxwell's equations, v;here A, D and h satisfy the algebraic ^ n' n n relations (26) (^) -Vny = -"^\x ^'^ -Wv = k ^^'^r?. __ (c) kA^y = -"i. D^^ (f) kD^ = ^ (PA^), which are equivalent to Maxwell's equations for a plane wave i [-u)t+k^+h^z] E = A e n n ^^^^ if-cut+k +h z] _ — *- X n -^ H = D n n *H. Bremmer, Loc. Cit.
- 17 - traveling in a homogeneous medium whose properties are the same as thos
...e of the actual medi\m at the point z. This suhstitution yields, for n = l, 2, 3.^t the differential equations satisfied by ^ (z) dV (28) !^ dz = -e -•" " r a (z)V^(z)e ° "^ ■'o n m=l where (29a) (29h) A mn mn A ^l, ' ^2x* %• ^.
A = ^17' ^ay- *3. - ^y hhr V2y "3*3^ Vi. Y h' »2- ^3- \ and A is equal to A with the n column removed and replaced "by the column dA mx dA my dB d7 • dz • dz^ m my''* dz with (29c) B = h A - kA "n n m Thus, for example (29d) a "23 " A nz h' ^3x dz • d- A 33C' ^37- fc(V3y^' V3i dB- dz B«, t ^/^x V/.


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