A rotating electric machine, comprising: at least one rotor comprising a set of superconducting axial magnetic flux barrier elements distributed in a plane perpendicular to the axis of rotation in a tangential direction about the axis of rotation, said superconducting axial magnetic flux barrier elements being spaced by axial magnetic flux passage areas distributed in the tangential direction about the axis of rotation, at least one armature, comprising armature windings distributed in the tangential direction about the axis of rotation, at least one superconducting inductor coil surrounding the superconducting axial magnetic flux barrier elements and the at least one armature in the tangential direction about the axis of rotation, the at least one superconducting inductor coil being able to induce an axial magnetic field directed along the axis of rotation, the at least one rotor being rotatably mounted on the axis of rotation with respect to the armature and to the at least one inductor coil, the machine comprising as a rotor (2, 21, 22, 23) at least one first rotor and at least one second rotor (22, 23), the at least one first rotor and the at least one second rotor (22, 23) being spaced from each other along the axis of rotation, the at least one armature being positioned between the at least one first rotor and the at least one second rotor (22, 23), the superconducting axial magnetic flux barrier elements of the at least one first rotor being coaxial at least partly with the superconducting axial magnetic flux barrier elements of the at least one second rotor (22, 23), the axial magnetic flux passage areas of the at least one first rotor being coaxial at least partly with the axial magnetic flux passage areas of the at least one second rotor (22, 23), the rotating electric machine comprising a first cryogenic cooling enclosure, which has an annular shape about the axis of rotation and which is delimited radially by a first external wall, characterized in that the first cryogenic cooling enclosure is delimited radially by a second internal annular wall, the at least one superconducting inductor coil being located in the first cryogenic cooling enclosure between the first external wall and the second internal annular wall, the machine comprising a second cryogenic cooling enclosure, which has a circular cylindrical shape about the axis of rotation and which is delimited radially by a third external wall located inside the second internal annular wall, the rotors (2, 21, 22, 23) and the at least one armature being located in the second cryogenic cooling enclosure. at least one rotor comprising a set of superconducting axial magnetic flux barrier elements distributed in a plane perpendicular to the axis of rotation in a tangential direction about the axis of rotation, said superconducting axial magnetic flux barrier elements being spaced by axial magnetic flux passage areas distributed in the tangential direction about the axis of rotation, at least one armature, comprising armature windings distributed in the tangential direction about the axis of rotation, at least one superconducting inductor coil surrounding the superconducting axial magnetic flux barrier elements and the at least one armature in the tangential direction about the axis of rotation, the at least one superconducting inductor coil being able to induce an axial magnetic field directed along the axis of rotation, the at least one rotor being rotatably mounted on the axis of rotation with respect to the armature and to the at least one inductor coil, the machine comprising as a rotor (2, 21, 22, 23) at least one first rotor and at least one second rotor (22, 23), the at least one first rotor and the at least one second rotor (22, 23) being spaced from each other along the axis of rotation, the at least one armature being positioned between the at least one first rotor and the at least one second rotor (22, 23), the superconducting axial magnetic flux barrier elements of the at least one first rotor being coaxial at least partly with the superconducting axial magnetic flux barrier elements of the at least one second rotor (22, 23), the axial magnetic flux passage areas of the at least one first rotor being coaxial at least partly with the axial magnetic flux passage areas of the at least one second rotor (22, 23), the rotating electric machine comprising a first cryogenic cooling enclosure, which has an annular shape about the axis of rotation and which is delimited radially by a first external wall, characterized in that the first cryogenic cooling enclosure is delimited radially by a second internal annular wall, the at least one superconducting inductor coil being located in the first cryogenic cooling enclosure between the first external wall and the second internal annular wall, the machine comprising a second cryogenic cooling enclosure, which has a circular cylindrical shape about the axis of rotation and which is delimited radially by a third external wall located inside the second internal annular wall, the rotors (2, 21, 22, 23) and the at least one armature being located in the second cryogenic cooling enclosure.