So my question is: Since the voltage and current are always in phase
in a traveling-wave antenna, is the near field of a traveling-wave
antenna ever reactive?
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Cec, you're leading yourself astray again. What's reactance to do with
anything other feedpoint impedance?

Stand at a distance from a very long Beverage antenna. Focus your attention
on a particular half-wave length of it.

The voltage at one end of the half-wave will whizz up and down at a
frequency of x megahertz.

At the the other end of the half-wave length the voltage will whizz down and
up at x megahertz, ie., in time-antiphase with it.

Therefore, from where you are standing, the half-wavelength of wire will
behave and radiate exactly like a half-wave dipole. You have no means of
knowing whether there are standing waves along the wire or not. And clearly
it doesn't matter. To segregate antennas between standing-wave and
non-standing-wave types can be misleading.

To continue with the Beverage. Adjacent 1/2-wavelengths of wire form a
co-linear array are in antiphase with each other. Therefore there is no
broadside radiation from a long Beverage which contains an even number
number of halfwavelengths. There is a sharp null at an angle of 90 degrees
from the wire and as overall length increases so does the number of lobes in
the general direction of the wire.

This is just the opposite of a co-linear array, a standing-wave antenna,
along which the successive half-wave dipoles are all in time-phase with each
other.

But both types of antenna incorporate radiating 1/2-wave dipoles. And if
the near-field of one type has a reactive near-field (whatever THAT means)
then so must the other.

If there are no standing waves it does NOT mean the voltage along the whole
length of line or antenna is whizzing up and down in simultaneous time-phase
in which case there would indeed be a non-reactive near field. But neither
could there be any length or time delay involved.

Don't confuse instantaneous RF volts over a cycle with the envelope which
may remain constant or vary with time or distance.
----
Reg, G4FGQ.