I just modeled two coils counter wound and one inside the other as a
complete closed circuit , end fed. Counter winding is quite the norm
with special purpose machinery to prevent inter tangling of coils when
compressed.
With the coils wound opposite to each other
it made quite a nice antenna when placed on a flat plate. Beam was
pencil shaped without side lobes and sensitive to all polarities.Thus
any such dishes could be used for 'point to point' using any type
circular polarization. Smaller in size compared to other designs is
rather obvious. Where Kraus determined such an antenna single wound
form demanded a certain angular pitch such a requirement is not
apparent with this design. Kraus assumed a certain pitch was required
when wave composition clashed, but the opposite happens when particles
vectors add. Another example of particle versus waves disputes.It also
confirms Maxwells equation by removing the effect of lumped loads
which was not included in his equation as was not the stipulation that
a radiator must be straight.

Caution:
Above details not yet "printed" in a book so it must be considered
questionable.
Regards
Art