In this paper a new superconducting inductor topology intended for synchronous machine is presented. The studied machine has a standard 3-phase armature and a new kind of 2-poles inductor (claw-pole structure) excited by two coaxial superconducting coils. The air-gap spatial variation of the radial flux density is obtained by inserting a superconducting bulk which deviates the magnetic field due to the coils. The complex geometry of this inductor usually needs 3D finite elements (FEM) for its analysis. However, to avoid a long computational time inherent to 3D FEM, we propose in this work an alternative modeling which uses a 3D meshed reluctance network. The results obtained with the developed model are compared to 3D FEM computations as well as to measurements carried out on a laboratory prototype. Finally, a 3D FEM study of the shielding properties of the superconducting screen demonstrates the suitability of using a diamagnetic-like model of the superconducting screen.