A New Method for the Determination of Far Fields With Applications to the Proble

Cover A New Method for the Determination of Far Fields With Applications to the Proble
A New Method for the Determination of Far Fields With Applications to the Proble
Frank Karal
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II, Determination of Operator In the problems that follow we shall need an operator L that transforms the impedance boundary condition given by -u- m^Au^o » =o Hi -0 » -Of (2-1) (2-2) into the simpler boundary conditions given by V = O ^ O (2-3) |g = ^ a » o- '^I. C-^^fO^A (2. 5) where Cf(^^^) '^^se"**"" ' k=Zj4; 2f? (2-6) and D is the complex operator ^ . Along the real axis D has the value r-, and along the imaginary axis the value vi i i . Hence the appropriate operator for a wedge of angle ...•x- with an impedance boundary condition on the upper surface and a zero normal derivative condition on the lower surface becomes L = -^^ {a^ "fii+c^^ij -^] (2-7) The transformation that simplifies the original boundary conditions (2-1) and (2-2) is V s LUL (2-8) We make the important observation that the same operator and transformation applies to the case of a wedge of twice the exterior angle when the lower face has the same impedance boimdary condition as the upper face.

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