I was thinking more that if the anode had a 10 to 20nm thick skin of something like carbon in some highly conductive configuration (eg graphene) then this would mitigate the surface vaporization and lessen the joule heating due to the large current flowing in the skin compared to beryllium.
The surface layer would still have to be thin relative to the absorption depth of the X-rays. So it would be a trade off between the lower Joule heating and the increase X-Ray absorption drive heating.
Then if the anode skin temp can rise to say 1200K and so the coolant exit temperature can rise to 900K then the Brayton cycle becomes viable
