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High temperature superconducting (HTS) machines have been demonstrated to benefit applications requiring high power density and torque. However, power density of existing superconducting machinery is limited by achievable flux density in the air gap and could be significantly increased with larger rotor currents. We propose a rotor based on MgB2 conductor running in persistent current mode. A novel MgB2 HTS flux pump transformer enables currents of several thousand amps in the rotor in a persistent mode. Large cryogenic heat loads associated with current leads are diminished by using a flux pump transformer for rotor excitation. All coils in the rotor and flux pump transformer are based on the double-helix winding configuration, which offers unmatched rotor robustness and reliability. This winding configuration also facilitates large bending radii, leading to an outstanding stress management and thus improved current carrying capacity of stress sensitive HTS conductors. The research presented in this paper analyses the performance of such a system through the design of a synchronous rotor for motors, generators and synchronous condensers.