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Kraus’s definition of the boundary between the near and far field makes good physical sense. I have the first edition of Kraus (1950), which, unfortunately, does not have the information contained in the figure in Kraus 3.
A person I sometimes refer to in this Forum is Prof. Valentin Trainotti, who, I think, is the leading authority on short medium-wave AM antennas still extant. In “Short Low-and Medium-Frequency Antenna Performance” in the October, 2005 issue of IEEE Antennas and Propagation Magazine, Trainotti defines a “Radiating Hemisphere” a half wavelength in radius. He says that, “The antenna consists not only of the conductive wires, but a hemispherical free space wave generator a half wavelength in radius. The area of the Earth under this hemisphere is…very important, because all of the conductive currents flowing through it are part of the antenna’s circuit…” Trainotti considers the circle under the hemisphere, which is a half wavelength in radius, to be the boundary of the near field. The energy exiting the radiating hemisphere is almost entirely radiated. Inside the hemispere, some of the energy does not propagate, but returns to the short antenna to form a standing wave.
I calculated the vertical electric field for a distance of lambda/2 from a differential current element and found that the real part of the field exceeds the imaginary part by a factor of only 2.824. So, even at a distance of a half wavelength, some of the near field still exists. Trainotti makes the important point, however, that the area a half wavelength from the short antenna forms part of the transmitter and antenna circuit, and the earth in this area should be highly conductive for good efficiency.
The Poynting vector does not apply to the near field, because very little of the energy of the fields near the antenna flows away from the antenna. Instead, the displacement current generated by the electric field mostly returns to the antenna. A very short antenna is basically a capacitor.