The superconducting rotor (10) includes at least one field coil (12) made of a superconductor material having a given superconducting transition temperature. A cryocooler system is mounted for rotation with the rotor (fig. 2). The cryocooler includes a cold head portion (24) mounted in heat transfer relation with the field coil (12) to cool the field coil to a temperature below its transition temperature and includes a piston/regenerator (42), (figs. 3, 4 and 5) adapted to allow passage of a working fluid at a mass flow rate which is substantially uniform over the cross section of the piston/regenerator during the operation of the system. Heat is conducted away from the field coils (12) by heat pipes (80) or by conduction through high thermally conductive material. Mounting the cryocooler cold head (24) for rotation with the rotor eliminates the use of a cryogenic liquid pool for rotor cooling.