On the Electromagnetic Field Equations in the Ionosphere

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On the Electromagnetic Field Equations in the Ionosphere
Herbert Bishop Keller
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Explicitly we introduce the new variables U(z) as in equations (2. 8) with U (2. 13) U(z) = ^, (z) ^2(0 . -"2(2); . P(z)= "JZJu) rr-1 . P'MO= Jl^v. Hz) \ 1 Uj 1 u 1 1 \ u \ 1 -y rr-l, The quantity u(z), as yet unspecified, is determined by the condition that P AP Bhall have zero off-diagonal blocks (i. E.. That the coefficient matrix in the equation -12- for U(z) "be avich. That the Tmcoupling of the system is optimal under the given condit- ions), IVom tthe matrix (2. 10) and (2, 13) we find t...hat this condition reqiiires (2. 14) u2 + [M^ + 1 = Tliis equation has two solutions u and -• » where « = (^) - 7(^)^-1 (2. 15) The equation satisfied "by Tl(z) is given "by equation (2. 9) where, with the above choice of u(z).
0-100 T ■-^"(z) [2. 16) P"-^ AP = ' ^ xliz)!*" ^^ u 1-u 10 • du ♦ Here we have introduced the notation u = t~ and dz \?(z) = a+- = P-Va 1 — u — \^(z) = a + Yu = P - Jf = 1 - -A 10 10 ;-l J Tf T "-H ^Tbyt/f^F^cby; *^ This system of equations is coupled in a sli^tly more conrplicated manner than the previous system "but still has only one coupling coefficient.


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