As I’ve seen on your drawing, you suggest to “snug fit” the cooling pipes into the anode. Don’t snug any pipes into the anode, the anode is the pipe itself. Same thing, drilled holes from bottom to top with the cap on (the coolant shouldn’t spill into the vacuum chamber).
Actually not drilled at all, because you can’t drill a hole that turns in the end. Much better for that is laser sintering. The Wikipedia article doesn’t mention Beryllium as commonly used material, so that needs to be developed. Maybe it needs to be sintered in a protective atmosphere (N, He, or whatever).
So some info about materials they’re using currently: http://www.eos.info/en/products/materials/materials-for-metal-systems.html
And a turbine as a result: http://www.eos.info/en/applications/aerospace.html
Oh, and I just read Beryllium melts at 1287°C, so that’s below the boiling point of Lithium of 1342°C.