I have a near future starship that weighs about 10,000 tons. I've determined that the ship needs a 500 megawatt fission reactor, but the problem is that even though nuclear fuel rods are obscenely small for thier power capacity, a whole power plant is generally not small at all. My original thought was to just copy the power systems from a naval ship or terrestrial power plant, but these reactors typically use external sources of water for cooling/steam... but in space, cooling is way less easy, and all water has to be internally stored. I image that this will make the size of the power system significantly bigger and heavier, but I don't know by how much.
To try to make things easier, the ship only needs to be able to operate for up to 20 days between resupply and refueling as opposed to naval nuclear ships that are expected to operate for many months at a time.
What I need to do is figure out how small (size and weight) a whole nuclear power system of this output could be if used in space. The best answer will be one that uses known technologies to minimize the size of the reactor while taking into account the limitations of operating in space.
Based on comments: If it is not doable in the mass allowed, then the next best answer would be one that demonstrates how close to doable one can come.