Use a soft alloy for the ring, not the cut off from a high alloy tube.
Right.
Actually, "soft" isn't quite the same as "pure", although it is a good
rough guide. You want something reasonably pure, to minimize the
contribution of _impurity scattering_ to the resistance.
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If you want to make something with REALLY high conductivity, use
high-purity aluminum and soak it in liquid nitrogen before use (to minimize
the contribution of _thermal scattering_ to the resistance). You can get
high-purity stuff from http://espi-metals.com/ http://espi-metals.com/aluminum.pdf
which appears to be an analysis of the jumping-ring demo, complete with
MATLAB script for modelling the system. It looks like a competent
job; for instance they account for skin-depth effects.