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A significant challenge in the design of fully superconducting (SC) machines is managing ac losses in the SC armature. Recent developments in MgB2 superconducting conductors promise low ac loss conductors suitable for fully SC machines. This paper presents an optimized design targeting low losses and low weight for a 10-MW fully SC generator suitable for offshore wind turbine applications. An outer rotor air-core machine topology is investigated to optimize the design with low weight and low losses. An active shielding concept is used to minimize the pole count without adding excessive weight. This enables a reduction in the electrical frequency for a practical design by a factor of 4 to 5 over current designs, driving ac losses and active components weight lower by an order of magnitude. In this study, armature current is varied to control electrical and magnetic loading in order to minimize losses. A pole count study is conducted to identify the design space suitable for MW scale machines. A comparison is made between active shield, passive shield and a hybrid topology to address the benefits of an active shield for weight reduction. Results suggest that low-pole-count designs with MgB2 conductors will enable machines with less than 1 kW of ac losses.