As I recall, gamma rays cannot be generated by thermal processes such as electron orbit decay - so we would need a nuclear radiator which converted waste heat i

As I recall, gamma rays cannot be generated by thermal processes such as electron orbit decay - so we would need a nuclear radiator which converted waste heat into atoms which would rapidly decay into gamma rays. Assuming we’ve done all of that… you would still need to deal with the rocket engine you’ve created. Sending out a tight beam of a suns worth of energy is equivalent to a rocket engine with 1x10^18 newtons, creating challenges of its own - including an appreciable acceleration of the planet earth. A more plausible escape hatch for the energy may be a black hole heat sink. In theory, such a device could perfectly “recycle” waste heat into usable energy.