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In the critical state model, the critical current, Ic, of a superconductor defines the upper limit of dissipation-free current flow. However conventional transport Ic measurements of practical superconductors rely on the detection of a voltage drop along the length of the conductor. This requires that the superconductor has entered the dissipative regime, and hence inherently over-estimates the current at which geometric saturation occurs. Nonetheless, the convenience of the 1 µV cm⁻¹ criterion means that it has become the widely adopted definition of transport Ic. Here, we present an alternative definition for the transport critical current of a superconducting tape under self-field conditions, which is based on the concept of geometric current saturation across the full cross-sectional area. This saturation threshold can be experimentally determined through simple Hall sensor measurements of the evolving perpendicular magnetic field at the tape surface. The surface field exhibits a signature transition when the transport current increases beyond the current-saturation threshold. We present an analytical model which describes this effect and defines the critical saturated current as a function of d^2 B⊥/d It^2. This definition is first validated using finite element (FE) modelling, and then experimentally demonstrated through measurements on a variety of commercial REBCO and Bi-2223 tapes of differing widths. It is found that the 1 µV cm⁻¹ criterion consistently leads to an overestimation of the saturated critical current by ~15% in REBCO tapes, and up to 30% in a Bi-2223 tape. FE modelling indicates that this overestimate is most prominent in superconductors exhibiting a low n-value (i.e. n ≲ 20). A key advantage of the measurement approach presented here is that it allows the unambiguous measurement of a transport Ic value to be completed at lower currents, without entering the dissipative region in which sample damage can occur. There are also implications as to the correct choice of Ic value which should be employed within the well-known Norris and Brandt equations for AC loss.

The charging/discharging delays in superconducting coils wound without insulation (NI coils) are a major drawback of the technique. While removing the insulation improves safety margins, the increase in the characteristic time constant τ_c can make a coil unfit for a particular purpose. It is widely accepted for instance that NI coils will not be used in ac applications where τ_c ~ 1/f. To decrease τ_c of the NI coils, the same length of superconductor can be wound/connected in parallel rather than in series — decreasing the inductance L, and hence the time constant τ_c, while maintaining the number of amp-turns I_op*N. Here we investigate the effect of parallel connecting coils in a magnet using a 2D axially symmetric model which captures all the necessary electromagnetic properties of the HTS NI coils. These properties include: critical current anisotropy Jc(B, θ), turn-to-turn conductivity, as well as winding parallelism. Our modeling results show that the parallel connected magnet experiences magnet-wide shielding current effects. Whilst these shielding currents affect field homogeneity — the model enables this effect to be quantified. Furthermore, shielding currents are not an issue when running NI coils in saturated mode. The modeling work presented here provides a simple initial example of how magnet designers may approach designing, optimizing, and operating high current, HTS NI coils.

The high-Tc superconducting (HTS) dynamo is a promising device that can inject large DC supercurrents into a closed superconducting circuit. This is particularly attractive to energise HTS coils in NMR/MRI magnets and superconducting rotating machines without the need for connection to a power supply via current leads. It is only very recently that quantitatively accurate, predictive models have been developed which are capable of analysing HTS dynamos and explain their underlying physical mechanism. In this work, we propose to use the HTS dynamo as a new benchmark problem for the HTS modelling community. The benchmark geometry consists of a permanent magnet rotating past a stationary HTS coated-conductor wire in the open-circuit configuration, assuming for simplicity the 2D (infinitely long) case. Despite this geometric simplicity the solution is complex, comprising time-varying spatially-inhomogeneous currents and fields throughout the superconducting volume. In this work, this benchmark problem has been implemented using several different methods, including H-formulation-based methods, coupled H-A and T-A formulations, the Minimum Electromagnetic Entropy Production method, and integral equation and volume integral equation-based equivalent circuit methods. Each of these approaches show excellent qualitative and quantitative agreement for the open-circuit equivalent instantaneous voltage and the cumulative time-averaged equivalent voltage, as well as the current density and electric field distributions within the HTS wire at key positions during the magnet transit. A critical analysis and comparison of each of the modelling frameworks is presented, based on the following key metrics: number of mesh elements in the HTS wire, total number of mesh elements in the model, number of degrees of freedom (DOFs), tolerance settings and the approximate time taken per cycle for each model., 22 pages, 7 figures, 2 tables

High-Tc 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 overcritical 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.