Well, I should have known that LPPF would have known about such a material – after all it has been around for over a decade. Don’t I feel stupid…
Apparently, Lerner is considering CNT as a coating for the electrodes.
http://lawrencevilleplasmaphysics.com/carbon-nanotubes-may-protect-electrodes/
I assume its absorption of X-rays has been deemed too great to use CNT as a monolithic cathode, but it seems the properties of CNT would allow for a smaller cathode…