[stboz]

What’s the fission cross section for U-233? IOW, will it burn up in the core along with the thorium?

[CurlyDave]

Thorium itself is non-fissionable. The way it is converted to energy in the reactor is through neutron capture, after which it rapidly decays to U-233. The U-233 is fissionable and it is this fission which produces most of the energy. So the answer is, Yes, it will "burn" in the reactor. Nothing ever completely burns, and some U-233 always comes out.

If the fuel is removed before the optimum time for Thorium consumption, there is more U-233 present. It is possible to operate the reactor to optimize U-233 production, which produces a lot more U-233 than otherwise.

Whether you "burn" U-235, U-233 from Thorium-232, or Plutonium-239 from U-238, there are always fission fragments -- highly radioactive light elements produced by the fission process. These are always nasty. I don't know all the details of the Thorium cycle, but anyone who tells you that there is no radioactive waste is lying, just like they are lying about no bombs.