A little help with blackbody photon gas calculations for thermonukes?

Good day nerds, I'm in the process of designing a thermonuclear explosive, generally called a Hydrogen bomb, but I need a hand with one calculation. For a bit of perspective, thermonukes work as follows: A plutonium/uranium fission bomb (called primary stage) sits inside a radiation case, along with a fusion capsule (secondary) To simplify, the type of fission bomb I'm using consists of a spherical plutonium core, surrounded by conventional plastic explosives. These compress the core, neutrons are injected and the fission reaction starts. This heats the core, causing it to emit black body radiation, which then fills the radiation case, and impinges on the secondary stage to compress it and ignite a fusion reaction. Again, that's incredibly simplified, if anyone's interested in more detail, just ask. I'm clueless about the behaviour of photon gas. The peak temperature of my plutonium core is 50 million kelvin. It has a surface area of 0.014m² and a volume of 152cm^3. It emits x-rays of 21.4 KeV. So, what I'm trying to work out is the parameters (e.i. fluence, radiation density, radiation temperature, radiation pressure, photon energy, etc.) of this gas when allowed into expand into a container (the radiation case) of 23,500cm^3. Thanks in advance.