High temperature superconductor (HTS) magnets have the potential to drive a range of world-changing technologies including Fusion reactors and high field (>23.5T) MRI/NMR magnets. Flux pumps are an enabling technology for the creation of the high current magnet power supplies necessary for this next generation of HTS magnets. HTS flux pumps utilize inherent superconducting properties to drive the charging mechanism that can use the high current capacity of modern coated conductors (>kA) and allows these currents to be generated using low electrical and cooling power.The Paihau-Robinson Research Institute has an extensive history exploring a variety of flux pumps – starting with travelling wave flux pumps [1–3] up to our recent work in transformer-rectifier flux pumps (TRFPs) [4,5]. We believe that TRFPs are ideally suited for high current (> 1 kA), relatively high inductance (>1mH) applications. In this talk, I will outline how we are improving the Technology Readiness Level (TRL) for application in systems and discuss our continuing work in TRFPs demonstrating:Development of a TRFP Simulink modelAs TRFPs transition from lab-based research to real world applications, the creation of a modelling infrastructure is essential. Accurate modelling can drive understanding and rapid design optimisation essential for prototyping real-world flux pumps. However, existing modelling techniques [6–8] do not integrate the magnetic or superconducting properties in a robust fashion. As will be shown, our Simulink technique allows all elements to be realistically embedded within the model enabling the production of qualitatively accurate data. Furthermore, the Simulink framework can model any TRFP topology and allows the addition of other superconducting properties (such as ac loss) or experimental variables (such as operating temperature).Conduction Cooled J_C (B) TRFPRecently, Paihau developed a new style of TRFP based directly on the J_C (B) characteristics of the HTS wire [4]. This work was conducted in liquid nitrogen; however, we anticipate that many real-world TRFPs will need to operate within conduction cooled systems. To this end, we have created the first J_C (B) TRFP in a conduction cooled system. I will present data outlining how the finite cooling power and operating temperature influence the pumping behaviour and will discuss design optimisation for conduction-cooled TRFPs.Scaling Conduction Cooled TRFPs to high currentsThe long-term goal is the creation of a conduction-cooled TRFP capable of achieving load currents greater than 10kA. This challenge will require precise thermal management and a thorough comprehension of the factors driving the rectification. To ensure complete understanding, we have explored the  J_C (B) switching mechanism using finite element modelling and highly focussed experiments. This work has highlighted that the interplay between the superconducting and passive circuit elements can lead to significant asymmetrical behaviour. However, this asymmetry, if correctly harnessed, may prove beneficial for high current TRFPs.[1] Hoffmann C, Pooke D and Caplin A D 2011 Flux pump for HTS magnets IEEE Trans. Appl. Supercond. 21 1628–31[2] Hamilton K, Pantoja A E, Storey J G, Jiang Z, Badcock R A and Bumby C W 2018 Design and Performance of a “squirrel-Cage” Dynamo-Type HTS Flux Pump IEEE Trans. Appl. Supercond. 28[3] Mataira R C, Ainslie M D, Badcock R A and Bumby C W 2019 Origin of the DC output voltage from a high- Tc superconducting dynamo Appl. Phys. Lett. 114[4] Leuw B, Geng J, Rice J H P, Moseley D A and Badcock R A 2022 A half-wave superconducting transformer-rectifier flux pump using J c (B) switches Supercond. Sci. Technol. 35 035009[5] Rice J H P, Geng J, Bumby C W, Weijers H W, Wray S, Zhang H, Schoofs F and Badcock R A 2022 Design of a 60 kA Flux Pump for Fusion Toroidal Field Coils IEEE Trans. Appl. Supercond. 32 1–5[6] Li C, Yang J, Shen B, Ma J, Gawith J, Ozturk Y, Geng J and Coombs T A 2020 A HTS Flux Pump Simulation Methodology Based on the Electrical Circuit IEEE Trans. Appl. Supercond. 30 1–5[7] Gawith J D D, Geng J, Li C, Shen B, Zhang X, Ma J and Coombs T A 2018 A half-bridge HTS transformer–rectifier flux pump with two AC field-controlled switches Supercond. Sci. Technol. 31 085002[8] Li C, Wang S, Jia H, He J, Li B and Coombs T A 2021 Impacts of the Saturated Transformer on the HTS Flux Pump IEEE Trans. Appl. Supercond. 31 1–4

Keywords: High temperature superconductors, Flux pumps, Superconducting magnets, Fusion energy