If you want to improve the output of solar energy systems, why not also run them at night? That's the question researchers in Qatar and Jordan addressed as they successfully devised a system that promises to more than double energy output of current solar power stations.
So you admit they do not exist?
The technologies on which these reactor designs are based have been demonstrated previously. The specific designs are in progress and well on their way. AGR, EBR-II, and MSRE are examples.