I think hydrogen it a pretty poor coolant anyway. They could presumably use a mixed fuel or use an inert gas like argon for cooling.
If they wanted to be "fuel rich" they could just release some excess oxygen as process waste.
So that's not why this is a dumb idea
The reason this is a dumb idea is because eloctrolysis is the hardest and least efficient way to get hydrogen.
And also because hydrogen is a really hard gas to store and handle, which is why every hydrogen effort going back to the Bush administration has failed.
> The reason this is a dumb idea is because eloctrolysis is the hardest and least efficient way to get hydrogen.
That's irrelevant in this case - power comes from the solar panels, electrolysis breaks enough water for the next engine firing, and the result is they get higher thrust than they would with an electric engine for the same total mass. Water is just a dense way of packing hydrogen and oxygen to run the chemical rocket, without requiring cryogenic storage, and it also works as shielding and heat transfer for on-board electronics.
To expand on this: Turbogenerators use hydrogen because it causes little drag, its cooling properties are good for a gas and it's much cheaper than helium.
Liquid cooling would be better but cooling pipes are not very amenable to spinning around at 3000 RPM and you have to keep the rotor inside the generator as compact as possible so centrifugal force won't rip things apart.
The non-rotating part of the generator is typically water cooled in bigger generators by piping the water straight through the hollow copper windings themselves (in slower rotating generator types, water cooling is also used for the spinning rotor).
If they wanted to be "fuel rich" they could just release some excess oxygen as process waste.
So that's not why this is a dumb idea
The reason this is a dumb idea is because eloctrolysis is the hardest and least efficient way to get hydrogen.
And also because hydrogen is a really hard gas to store and handle, which is why every hydrogen effort going back to the Bush administration has failed.