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Since publication, we have realized that the results from the minimum electromagnetic entropy (MEMEP) method (see section 3.3 in the original paper [1]) used a different voltage definition, causing a slight discrepancy with the results obtained from the other methods in figures 3 and 4. Instead of Veq (t) = −LEave (t), as given by equation (5) in [1], we used −∆V(t) as defined by equation (22) in [2]: ∆V ≈ L· [∂tAav,J + Eave (J)] . Although both definitions result in the same DC voltage, the instantaneous signal differs, as shown in figure 1 in this corrigendum. Indeed, the used ∆V for the MEMEP method in [1] adds an extra contribution, ∂tAav,J, the vector potential due to the superconducting current. As a result, the new curve has much better qualitative and quantitative agreement with the waveforms calculated by the other methods shown in figure 3 of the original article [1]. In the original article [1], we also used the −∆V(t) definition above instead of Veq (t) to calculate the cumulative time-averaged equivalent voltage, defined from equation (6) in [1] as t Vcumul (t) = 1t Veq (t) dt. 0 The new results, using Veq (t) , present only small changes compared to the original calculations, as shown in figure 2 in this corrigendum. This curve also has very good qualitative and quantitative agreement with the waveforms calculated by the other methods, as shown in figure 4 in the original article [1]. The data related to the new calculations for this corrigendum are available at the University of Cambridge data repository (https://doi.org/10.17863/CAM.60437).

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