A synchronous superconductive rotary machine comprising: - a rotor arranged rotatably relative to a stator, wherein - the rotor comprises at least a back iron configured to be connected to a drive shaft via a rotor structure, the rotor further comprises a plurality of first pole units arranged on the back iron, the first pole units extend in at least a radial direction relative to the back iron, wherein a magnetic air gap is formed in circumferential direction between circumferential side surface of one of said first pole units and a corresponding opposite circumferential side surface of an adjacent first pole unit in which at least one second pole unit is arranged, wherein the at least one second pole unit comprises at least one superconductive rotor coil, the at least one rotor coil is configured to interact with at least one stator coil arranged in the stator via an electromagnetic field when the rotor is rotated relative to the stator, wherein the first pole units and the at least one second pole unit are arranged inside an evacuated chamber defined by a housing, wherein the first pole units and the back iron are configured to be operated at an ambient temperature, and wherein the at least one second pole unit is configured to be operated at a cryogenic temperature, wherein the at least one second pole unit is spaced apart from the back iron by means of at least one thermally insulating support element extended in radial direction of the rotor and arranged at respective components of the rotor and the rotor structure, so a first magnetic air gap is formed between the at least one second pole unit and the back iron and at least a second magnetic air gap is formed between the at least one second pole unit and at least one front wall of the housing of the evacuated chamber, wherein a radially outer end of the at least one thermally insulating support element is mounted to a thermal shield (30,31) of the second pole unit and a radially inner end of the at least one thermally insulating support element is mounted to the rotor structure between the back iron and the drive shaft. - a rotor arranged rotatably relative to a stator, wherein - the rotor comprises at least a back iron configured to be connected to a drive shaft via a rotor structure, the rotor further comprises a plurality of first pole units arranged on the back iron, the first pole units extend in at least a radial direction relative to the back iron, wherein a magnetic air gap is formed in circumferential direction between circumferential side surface of one of said first pole units and a corresponding opposite circumferential side surface of an adjacent first pole unit in which at least one second pole unit is arranged, wherein the at least one second pole unit comprises at least one superconductive rotor coil, the at least one rotor coil is configured to interact with at least one stator coil arranged in the stator via an electromagnetic field when the rotor is rotated relative to the stator, wherein the first pole units and the at least one second pole unit are arranged inside an evacuated chamber defined by a housing, wherein the first pole units and the back iron are configured to be operated at an ambient temperature, and wherein the at least one second pole unit is configured to be operated at a cryogenic temperature, wherein the at least one second pole unit is spaced apart from the back iron by means of at least one thermally insulating support element extended in radial direction of the rotor and arranged at respective components of the rotor and the rotor structure, so a first magnetic air gap is formed between the at least one second pole unit and the back iron and at least a second magnetic air gap is formed between the at least one second pole unit and at least one front wall of the housing of the evacuated chamber, wherein a radially outer end of the at least one thermally insulating support element is mounted to a thermal shield (30,31) of the second pole unit and a radially inner end of the at least one thermally insulating support element is mounted to the rotor structure between the back iron and the drive shaft.