Ed Cregger wrote:

I have quite a few engineering books on antennas (that I use G), so I
can appreciate the value of good, solid engineering text/sources.

However, the point that the OP was trying to make was that it is likely
that superconductive radiating elements could establish the need for a
serious rethinking of antenna theory. After all, superconductive
radiating elements did not exist before and the math has not been done.
Perhaps, their inclusion, will demand something more than a simple
extrapolation of existing antenna theory. I believe this to be the point
of the OP.
. . .

And I disagree. The assumption of zero loss is implicit or explicit in
nearly all the analyses in your antenna texts and mine. So no new math
or "rethinking of antenna theory" is required to deal with lossless
conductors. It is, in fact, the simplest case and so underlies virtually
all the current theory. What it would do is cause a change in tradeoffs
which would be made by engineers in the design of real antennas.

However, superconductors (at least all known conventional and
high-temperature superconductors) are lossless only at DC.
Superconductor loss increases with frequency and, except at DC, with
temperature. The resistivity of copper decreases quite dramatically with
temperature, so it's not uncommon to find situations at very high
frequencies and very cold temperatures where copper does better than a
superconductor. Even high temperature superconductors have to be cooled
to cryogenic temperatures to do reasonably well at very high
frequencies. But again no new math or "rethinking of antenna theory" is
necessary to deal with them -- the same electromagnetic principles apply
and they can be treated like any other conductors with finite resistivity.

Roy Lewallen, W7EL