No abstract

There is a class of antennas whose pattern as well as impedance is practically independent of frequency for all frequencies above a certain value. The general formula for their shape is r = e F(#) where r;0,f>are the usual spherical coordinates, a and

The spatial spectrum of intensity fluctuations due to a concentrated layer of turbulence is derived from the parabolic wave equation. The spectrum of refractive index fluctuations is taken to be an unmodified power law of arbitrary strength, with exponent a, 2 ( a ( 6. For 2 • a ( 4 it is shown that the intensity spectra for a plane wave can be expressed in terms of a single parameter U, which is the Born approximation to m a, the normalized variance of intensity fluctuation. For U << 1 the Born approximation applies. The high frequency approximation to the intensity spectrum is the angular spectrum that would result from twice the strength of turbulence. It applies above the spatial frequency Kt or 2•r ,•t/U, whichever is. smaller, where ,• is the frequency at the first null of the Born approximation. For U > 30, it represents essentially all of the intensity fluctuations and shows that m saturates at unity for a plane wave as U .--• •o. Simple formulas for m when the source has finite angular extent show that m decreases with increasing turbulence as Ua-a for U >> 1. These results are confirmed by exact calculations for the case a = 3 and by extensive observations of interplanetary scintillations. DUE TO A CONCENTRATED LAYER 113

Several theorems are derived by using the reaction concept. They apply to single frequency sources of finite extent, and to fields which are finite and continuous on a hypothetical closed surface S whose inside or outside is source-free. 1) The field on the source-free side of S is uniquely determined by the normal components E,, and H , on S. 2) For measurements on the source-free side of S, the primary source can be replaced by any of the following secondary sources on S: (a) Normal electric and magnetic dipoles in free space. (b) Normal electric and magnetic quadrupoles backed by a medium which makes E , = O and H , = 0. (c) A certain combination of electric and magnetic normal dipoles and quadrupoles which gives zero field on the source side of S. The prescription for (a) requires the solution for the field of the primary source when it is inside a cavity on whose walls E , = 0 and H , = 0. The surface densities of the various components of secondary sources @) and (c) are given in terms of the free-space primary field. The formulas are comparatively simple when S is plane. Many applications are cited including a combination of multipoles, consisting of vertical electric and magnetic dipoles, which is equivalent to a horizontal electric dipole.

No abstract