Alexander Petrov

The Spherical Tokamak for Energy Production (STEP) requires high-field magnet designs and has therefore adopted the REBCO-based high-temperature superconductor (HTS) as its current carrier. The HTS enables the toroidal field (TF) coils to be remountable, which unlocks STEP’s vertical maintenance approach; however, remountable joints, approximately 18 GJ of stored energy and limited space down the centre of a spherical tokamak, make the TF coils the most challenging. STEP has pursued a passive approach to TF coil quench protection in order to limit coil terminal voltage. Initial results suggest that a solution may rely on tuning internal coil resistance coupled with actively powered heaters. The pre-conceptual inter-coil structure demonstrates acceptable stresses and deflections under steady-state operating conditions and preliminary fault scenarios, and loads are distributed to limit the tensile force on the TF centre rod. Finally, the HTS must operate reliably in a high radiation environment and endure high neutron fluences, ensuring commercially relevant magnet lifetimes. Initial experiments indicate that instantaneous gamma irradiation of HTS has no negative impact on current carrying capacity. Experimental programmes are underway to cold irradiate HTS to fusion-relevant fluences and to develop a method of assuring tape irradiation tolerance using oxygen ions as an analogue for neutrons. This article is part of the theme issue ‘Delivering Fusion Energy – The Spherical Tokamak for Energy Production (STEP)’.

High-current flux pumps are an enabling technology for high-temperature superconducting (HTS) magnets operating in a quasi-persistent current mode (qPCM). For fusion energy specifically, flux pumps must be capable of delivering more than 10 kA of DC output to a superconducting magnet. Recent HTS flux pumps have yet to achieve more than 1–3 kA of current. In this report, we present progress towards a 10 kA HTS flux pump using the transformer-rectifier circuit topology at the Paihau-Robinson Research Institute. A 10 kA test solenoid has been designed and the fabrication has been commenced. The main requirements of the rectifier switches and transformer have been identified and evaluated, with a circuit simulation demonstrating 10 kA of output expected in under 15 s, with a current ripple of only 0.33%. Finally, a method of low-resistance solder joint fabrication using indium-foil is validated.

High temperature superconducting (HTS) magnets in Tokamak devices are used to build strong magnetic fields for increasing plasma density and power, making the confinement system more compact. However, rapid changes in currents and magnetic fields can also result in ac losses in magnets. For example, the charge and discharge of the central solenoid (CS) induces ac losses within the CS magnet and the surrounding TF magnets. Therefore, using finite element method (FEM) modelling, this paper first analysed the inductance, magnetic field, and ac losses in the CS. Then, by equivalently transforming the magnetomotive force (MMF) of the CS, the impact of CS charge and discharge on the TF limbs in the centre column was investigated. Particularly, over the CS fast discharge, the self-field loss in the CS was 0.24 MJ, mainly attributed to hysteresis loss, and the induced loss in each TF limb inside the centre column was 2.5 kJ/m. Three different algorithms were discussed to model the large-scale CS: the H formulation, H-Φ formulation, and T-A formulation. The H formulation and H-Φ formulation yielded converged electromagnetic characteristics, and H-Φ formulation reduced computation time significantly. However, the T-A formulation, ignoring the axial magnetic field inside conductors, was not applicable for calculating ac losses in vertically stacked tapes (VST) cable magnets. This modelling work from the Spherical Tokamak for Energy Production (STEP) programme provides essential reference for optimizing HTS magnet designs in commercial Tokamak endeavours.

The performance of HTS transformers is integral to predictability of outputs in HTS transformer-rectifier flux pumps. To date, little attention has been given to compact HTS transformers using stacked-tape cables. Current sharing behaviour in HTS transformers with stacked-tape cable secondary windings is studied here experimentally. Secondaries of 1–4 tapes are tested with a 500:1 transformer. Two modes of coupling are identified. Firstly, primary inductive coupling determines secondary current during changes in primary current. Secondly, current is shared inductive between loops when primary current is held constant. This is caused by secondary circuit resistance. The transition between sharing modes causes strong hysteresis in the current output of the transformer. However, this is found to have little impact on the RMS current in the secondary if the resistance is sufficiently low. Outputs greater than 600 A are demonstrated from a compact transformer. These results may lead to more compact transformers in future transformer-rectifier flux pump devices.

There is a myriad of variables that must be considered when designing a superconducting magnet. Two of these are: the local magnetic field, dictating the response of the superconductor, and the mutual inductance matrix, dictating the generated voltage. These issues may be resolved with the help of finite element analysis tools, but this is not practical at the very beginning of coil design or when many concepts must be analysed quickly. Then comes the problem of robustly constructing the coil's winding pack such that it will operate as required. Analytical Python Electromagnetic Coil Simulator (APECS) offers one solution to the above. It uses accepted analytical and semi-numerical methods to calculate, at any point in space, the magnetic field generated by circular loop coils, such as a tokamak's poloidal field magnets, as well as straight-edge loop coils, such as a rectangular toroidal field magnet in a spherical tokamak. Combined with knowledge about the performance of the superconducting material and a user-specified cable design, APECS can construct a “minimum viable” winding pack for each poloidal field magnet to aid further analysis and design iteration. Despite that it cannot presently optimize the cable design or the thermo-hydraulics, superconductor/copper content, or the stress and failure, it is an invaluable tool used extensively in the design and analysis of the poloidal field (PF) magnet system on U.K.’s Spherical Tokamak for Energy Production (STEP).

High temperature superconducting (HTS) fusion magnets must avoid quenching when subjected to a rapidly changing field, in normal operation and due to transient events. To this end, correct understanding of the AC losses is key. Their calculation in structures made with HTS tapes such as conductor on round core (CORC), twisted stacked tape conductor (TSTC), etc., still faces challenges due to the unique structure and geometry of the HTS tapes-normally made of Rare-Earth Barium Copper Oxide (REBCO)-in addition to twisting and/or transposition. To estimate the losses in the CORC cable of a poloidal field magnet carrying being subjected to a sinusoidal waveform field and/or current, two methods are used in this paper. First, the well-established H-formulation via the finite element method. Second, an analytical formula, available in literature, for calculating the hysteresis loss in a straight tape. It is then shown that the typically 3D finite element model (FEM) problem of AC loss in twisted and transposed tapes in CORCs can be simulated in 2D when the peak background field is high. Simultaneously, the analytical formula is corrected for a twisted and transposed tape, allowing to analytically model twisted and transposed tape assemblies such as CORC. A comparison is made between the results of the two AC loss calculation methods, demonstrating the limitations of the analytical calculation, but also that a close match in the loss is possible under certain conditions.

Iron-core electromagnets are widely used as applied-field switches in high-temperature superconducting (HTS) flux pumps. It was recently reported that the critical current ( I c ) of the HTS wire is suppressed by up to 45% in the air gap of the iron core. Here, it is reported that the self-field I c of a single tape (unifilar) is suppressed from 357 A to 195 A while in the air gap of an iron core, agreeing closely with the previous study. This is extended by showing that the I c response to a perpendicular magnetic field is asymmetric, with a peak I c of 249 A found to be at 0.16 T of applied magnetic field. This effect can be eliminated using an anti-parallel current configuration (bifilar), which is shown experimentally to recover close to the no-core self-field I c of 357 A with no observed asymmetry. The results of both types of switch configurations are closely replicated in finite-element modelling using COMSOL Multiphysics^®. This is caused by the asymmetric interaction between the self-induced magnetic field of the HTS switch element and the magnetic circuit of the iron-core electromagnet.

In this article, the problem of a high temperature superconducting cable (HTSC) response to and recovery from a transient short circuit fault is discussed and a finite element solution to the problem is presented. The full model consists of three subroutines, connecting together: 1) electromagnetic phenomena in HTSCs and associated Joule heat release; 2) heat transfer from the HTSC to the cooling circuit; 3) convective heat transport in liquid nitrogen. These subroutines are connected via geometric and variable couplings. The background of the real cable to be modeled is laid out together with its key properties. The most important parameter and variable calculations are explained in detail. In order to facilitate a computational speedup through manipulation of the active physics during selected intervals of time, the simulation is split in three distinct stages-steady state, transient fault, and recovery. Moreover, it was shown how the entire simulation may be performed over a moderately reasonable amount of time using low computational resources when certain approximations are exploited-namely, using the electromagnetic model only on a limited number of cross sections along the cable. This article shows that fairly accurate results can be achieved on an office PC using a commercial FEM software even without access to computing clusters, and that the same model can be used to examine both normal and transient operation.

A simple model is proposed which can estimate the total AC transport power loss of a multi-layered Bi-2223 cable, with the effect of the twisted geometry approximated in 2D, thus greatly decreasing the required computational resources. The model operates by applying a modified current value on the cable's cross-section. This can be achieved mathematically by taking into account the layer's twist angle. Several multi-layer cable models with varying layer pitch lengths and magnitudes of transport current were simulated, and the power loss estimated using 3D models; the same was done for their corresponding 2D models and then the results were compared. Furthermore, the 2D model was used to simulate a real 4-layer Bi-2223 cable, where the difference between the simulated power loss and loss presented in literature was under 10%. It was shown that due to the favourable results, the methodology has sufficient basis for further investigation and implementation.