Art wrote:
"By the same token I am challenging to prove the veracity of the
statement that a sino soidal current is present at every segment point."

An antenna is generally a linear passive device meaning that a
sinusoidal wave entering an antenna produces sinusoidal fields which
induce sinusoidal voltages and currents in the distant receiving
antenna.

Sinusoidal voltages appear at every point on such an antenna and
sinusoidal currents pass over the surface of every point of the antenna.
Insulators of course interrupt conduction currents and allow the rise of
voltage gradients.

Induced currents are produced by the electric field of the wave in the
insulation of free space by the displacement (capacitive action) current
of an antenna. Maxwell speculated that displacement generated a magnetic
field same as conduction did, and that was the secret of radiation. He
was proved correct. A magnetic field generated an electric field and an
electric field generated a magnetic field so that the two fields locked
and traveling together go on ond on forever.

Most antennas have two waves traveling in opposite directions, an
incident wave and a reflected wave. Both pass through every point on the
antenna conductor.

A directional coupler can access the wave traveling in one direction
while ignoring the wave traveling in the opposite direction.

Large variations in voltage appearing on the antenna make the familiar
standing wave pattern but this is not a true picture of the individual
waves making up the combined wave. The effective values of the incident
and reflected waves decline steadily but gradually along the antenna as
they travel in opposite directions.

A sinusoidal current is present at every segment point and only slowly
changes from point to point. Two sine waves of the same frequency always
combine at a point to create another sine wave of the same frequency.

Best regards, Richard Harrison, KB5WZI