Modeling of Stator Versus Magnet Width Effects in High-$T_c$ Superconducting Dynamos

High-T_c superconducting (HTS) dynamos are simple devices for injecting and sustaining dc currents in superconducting coils/magnets. The simple geometry of these devices consists of a superconducting stator(s) and one or more rotor magnets arranged in identical fashion to a classical alternator. However, unlike the classical alternator, the HTS dynamo gives a self-rectified dc output. This somewhat anomalous result is caused by the non-linear resistivity of HTS materials and the large over-critical eddy currents that flow in the stator. As these over-critical currents must recirculate in the HTS stator, the stator's width becomes a key parameter in the physics of the device. In this work we explore the effect of increasing the stator width through using recent advances in modeling these systems. We find that given enough space in the stator, the total sum of circulating and transport currents do not drive the full width of the stator into the flux-flow regime. Operation of the device in this regime results in a non-linear $I$-$V$ curve, a marked decrease in the internal resistance at open circuit $R_{oc}$, a saturation of the open circuit voltage $V_{oc}$, and a short-circuit current $I_{sc}$ that approaches the in-field critical current of the stator itself $I_{c,min}$. These behaviors lead to the conclusion that optimal HTS dynamo design should ensure that the stator width be sufficient to avoid current saturation of the superconductor at the target operating current.