This invention relates generally to a generator having a rotor with a rotor structure, a set of flux pumps secured to the rotor structure and a cooling system secured to the rotor structure for cooling each one of the flux pumps. The flux pump includes separate superconducting loops in separate layers with each superconducting loop including a plurality of sections in revolutions in its respective layer. Each cooling system includes a compressor, heat exchanger, expansion valve, and cryocooler inline with one another. The rotor is rotatably mounted to a stator component through a bearing. A power supply circuit includes components integrated within the rotor for providing power to the flux pump and the compressor.