Art wrote:
"At the end of the radiator you state the energy is transfered to the
field so I would imagine there is zero skin effect at that point and the
chain of skin effect es still present on the outside of the radiator,
this is because the full period has not elapsed."

It will elapse as it does in every period so that the higher resistance
at RF will take its toll as predicted.

Because of skin effect, hollow conducting pipes exhibit almost as much
conducting ability as solid rods of the same material. This creates a
market for aluminum tubes as radiating elements and Copperweld wire in
antennas. High-powered transmitters use silver-plated coiled pipes to
carry distilled water to cool their final amplifiers. The space within
the coiled pipes carries no significant RF. RF energy does not flow out
on the surface of a conductor and return in the conducting material
within the conductor in ordinary circumstances, although phase lag
within a conductor increases as penetration depth increases.

Best regards, Richard Harrison, KB5WZI