The present invention relates to a synchronous superconductive rotary machine with a superconductive rotor, a wind turbine, an assembly method and a repair method thereof. The rotor comprises a back iron connected to a thermally insulating support structure which is further connected to a base element. A coupling element is arranged on a peripheral surface of the base element for coupling to a matching coupling element located on a peripheral surface of a pole unit. The pole unit comprises a core element on which the coupling element is located and superconductive coils are wound on the core element. The pole unit is slid into position in an axial direction and fixed relative to the back iron by using fastening means. The base element, support structure and pole unit are wrapped in a thermal insulating laminate. This provides a simple and easy assembly and repair process that does require the rotor to be separated from the stator in order to replace a pole unit.