Advanced Numerical Modelling of Bulk Superconductor Magnetisation

Abstract

Superconductivity is the observation of the vanishing electrical resistance of a material, and the expulsion of magnetic fields from within its volume, below a certain (critical) temperature. Superconductors can be subdivided into two classifications; type-I, or type-II, with the latter exhibiting a ‘mixed-state’ of superconductivity across their volume. Through appropriate magnetisation, magnetic flux may become ‘pinned’ within type-II superconductors fabricated into bulk (i.e. large sized) forms, therefore creating quasi-permanent trapped field magnets of extraordinary strength and engineering importance [1–3]. Type-II superconductors acting as trapped field magnets have to date been shown to trap in excess of 17 T [4], and have the potential to trap significantly greater magnetic fields [5]. Meanwhile, the best conventional permanent magnets have a saturation magnetisation of approximately 1.4 T [6]. One such group of type-II superconductors are (RE)-BaCuO materials (where RE = rare-earth element or Y/Gd, Barium-Copper-Oxide), which exhibit superconductivity at approximately 90 K or higher. Magnesium diboride (MgB2) is another promising type-II superconductor, which exhibits superconductivity below 39 K. Despite the extensive research into fabricating and using bulk superconductors as trapped field magnets, magnetising them to high fields with a compact, efficient, and practical method is still challenging. The focus of this PhD is therefore to use a modelling-first approach to investigate practical methods of trapping magnetic fields within bulk superconductors, with the goal of providing deeper insight into the techniques which may enhance their magnetisation. One particular focus of this study is on the phenomenon of flux jumps, which have traditionally been seen as a blight in the stable operation of superconductors. Flux jumps are the spontaneous and ‘avalanche’ like motion of magnetic flux through a superconducting medium [7–11]. Such instabilities for example have historically posed a challenge in early (c. 1969) multi-filamentary superconducting wires. Carefully spacing filaments, or ‘twisting’ them around the wire core, have proven effective methods for eliminating flux jumps in wires and coils [12]. Flux jumps generally result in the rapid, and often mechanically destructive, demagnetisation of a bulk superconductor during field-cooled (FC), or zero-field cooled (ZFC) magnetisation (which are quasi-static, energy intensive magnetisation techniques). Using numerical techniques in 3, flux jumps in bulk superconductors under FC & ZFC magnetisation are modelled, and validated against analytical solutions as well as experimental data. Using these models, the controlling variables and properties of thermomagnetic instabilities are explored (such as the influence of bulk geometry and size, the critical current density distribution (see section 1.1.1), and the thermal properties). Methods for avoiding them, controlling them, or better monitoring them are suggested and discussed throughout section 3.3.2.4. Another method of magnetising bulk superconductors, which is more efficient and practical, is pulsed-field magnetisation (PFM). Using this technique, significant thermal stresses are often generated within the bulk, which can reduce the trapped field potential or damage the sample. However, it has been practically demonstrated that thermomagnetic instabilities during PFM can permit the ‘jumping-in’ (and successful trapping) of magnetic flux within bulks. This type of ‘assistive’ flux jump could be a viable method of efficiently and practically magnetising HTS bulk superconductors, and lead to higher trapped fields. Later in 3, numerical techniques are used to model experimentally observed flux jumps during PFM, then the controlling variables that generate the circumstances for instability to flux jumps are explored (such as the critical current distribution, the bulk geometry, the effectiveness of cooling, and the n-value distribution, see section 3.4). Based on these results, techniques for researchers to trap even greater fields using PFM are suggested and discussed. Continuing with the goal of enhancing magnetisation in 4, a series of models are presented which numerically describe the experimentally obtained magnetisation of a new record-breaking composite MgB2 bulk under PFM, with excellent agreement to the experiments. Using these models, a number of powerful extension studies are presented, which explore the controlling variables of the experiment and the composite bulk (such as the influence of multi-pulsing, the use of an iron yoke, the number of included copper layers, and the effect of cooling the composite bulk, see section 4.2.2). A number of suggestions for researchers to further increase the trapped field within these bulks are finally given. An analysis comparing the intrinsic instability of (RE)-BaCuO and MgB2 materials to flux jumps is also given, demonstrating why it is generally best to avoid them in MgB2 bulks. 1 and 2 are supplementary to this study, introducing the main aims and background to the PhD study, as well as the numerical methods used. 5 finally concludes the study, and outlines the next steps, and suggested continued research.