Given the pulsed nature of the device, I’m thinking any stratified surface layers would be problematic unless they had very closely matched thermal expansion coefficients.

In the central well of the anode where the electron beam hits you could consider a special coating in this area (such as 20um of tungsten), but for the main shaft of the anode, and cathodes where the current is flowing then you want as low a stress due to thermal & pinch forces as possible. The overall cooling aspect I think is manageable if you pump enough helium through. It is the fatigue and cracking due to many cycles that I’m beginning to get more concerned about.

If you carefully graduated the electrical conductivity near the surface, in the opposite sense to the skin current’s normal preference so you got a more even current distribution deeper through the top 1mm of material it may help.