Superconductors, analysis and applications, with special reference to the utilisation of bulk (Re)BCO materials T.A. Coombs * University of Cambridge, Department of Engineering, Trumpington Street, Cambridge CB2 1PZ, UK article info Article history: Available online 16 May 2010 Keywords: Superconducting machines Y-based cuprates AC loss Finite element modelling abstract The Electrical Power and Energy Conversion (EPEC) superconductivity group at Cambridge University has been working on the application of superconductivity to large scale devices. This work is taking place over a range of areas which cover FCLs, motors and generators, SMES, accelerator magnets and MRI. The research is underpinned by advanced modelling techniques using both pure Critical State models and E–J models to analyse the behaviour of the superconductors. As part of the device design we are con- centrating on the analysis of AC losses in complicated geometries such as are found in motor windings and the magnetisation of bulk superconductors to enable their full potential to be realised. We are interested in the full range of high-temperature superconductors and have measured and predicted the performance of YBCO, MgB 2 and BSCCO at a range of temperatures and in wire, tape and bulk forms. This paper concentrates on recent work which includes: modelling of coils using formulations based on H and A. A critical state model for the analysis of coils in SMES; crossed field effects in bulk superconduc- tors; a magnetic model together with experimental results which explain and describe the method of flux pumping whereby a bulk superconductor can be magnetised to a high flux density using a repeatedly applied field of low flux density and finally a new configuration for MRI magnets Ó 2010 Elsevier B.V. All rights reserved. 1. Introduction Since high-temperature superconductors (HTS) were dis- covered in 1986, there have been extensive research efforts to understand the nature of superconductivity in these materials and to fashion them into forms that can be used in practical appli- cations. Bulk HTS materials, being attractive for their magical elec- tromagnetic property of being able to trap magnetic field, is one of the most popular areas in HTS and have received significant amount of interest in recent decades. The current material of choice for most applications requiring HTS bulks are RE–Ba–Cu– O (ReBCO, RE denotes the rare earth elements) where Y–Ba–Cu– O (YBCO) is the most well known. These materials exhibit a high magnetic irreversibility field H irr at liquid nitrogen temperatures and many have the ability to grow large grains. The H irr marks a phase transition between the region where magnetic flux is solidly pinned in the superconductor and the region where flux may move. When compared with some of the members of the Bi, Tl or Hg HTS families, YBCO exhibits a relatively low critical temper- ature of 92 K, but its irreversibility curve is one of the highest at 77 K and lower temperatures. The potential of bulk melt-processed ReBCO single domains to trap significant magnetic field at 77 K makes them particularly attractive for a variety of engineering applications, including superconducting magnets, magnetic bear- ings and motors. Machines made using these HTS materials will be smaller, lighter, and have higher power densities and efficien- cies than existing machines. In most of the applications mentioned above, the full potential requires the HTS bulk to be used as trapped field magnets. The magnetisation of the superconductor is proportional to the product of the critical current density (J c ) and the grain diameter [1]. In the present state of the technology, the upper limit of the grain diameter produced by this process is nearly 15 cm. The ability to produce good-quality YBCO thin films are also limited to approximately this size. The article proposed here reviews the development work in different areas to apply YBCO in both bulk and tape form into areas like magnetic bearings, electrical machines and superconducting magnets. This paper presents work which has been carried out and is cur- rently under way in the Electrical Power and Energy Conversion (EPEC) Superconductivity group at Cambridge. It is arranged over six sections: First, Section 1 provides some general background. Then, there is a section on numerical modelling which introduces some of the models which have been developed through the years to solve for current and field distributions in superconductors. These models are applicable to superconductors in both bulk and tape form and have been developed to enable us to predict amongst other things the magnetisation, losses and current 0921-4534/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2010.05.220 * Tel.: +44 1223 748 315; fax: +44 1223 748 348. E-mail address: tac1000@cam.ac.uk Physica C 470 (2010) 1845–1852 Contents lists available at ScienceDirect Physica C journal homepage: www.elsevier.com/locate/physc