Remanent Magnetic Flux Distribution in Superconducting-Ferromagnetic Layered Heterostructures
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Stacks of superconducting tape, made of second-generation coated conductors, present an interesting alternative to bulk superconductors. The layered geometry allows incorporation of other functional, namely ferromagnetic, materials. The ferromagnetic material changes the field configuration within the superconductor and can be used to shape or divert the flux density from its interior. This can be used to optimise the remanent flux density after magnetisation. FEM simulations are employed to test the performance of a variety of superconductor/ferromagnet structures and explain the role of the ferromagnetic material in the composite structure. Cases where trapped field is much higher and lower than remanent magnetisation of the ferromagnetic material are considered, showing that performance can be enhanced or maintained by using ferromagnetic material while reducing the usage of costly superconducting tape.
KeywordsTrapped field magnet HTS tape Stack of tapes HTS modeling
A number of works have demonstrated that the use of ferromagnetic materials can improve the properties of trapped field magnets (TFMs). Most of the work so far has been focused on trapped field magnets made of bulk superconductors (SCs), where ferromagnetic materials (FMs) have shown the ability to tailor the magnetic field profile , reduce crossed-field demagnetisation  or just increase the trapped field above a bulk superconductor . Other work on second-generation high-temperature superconducting (2G HTS) tapes using numerical modelling showed that magnetic shielding of filaments by ferromagnetic material reduces AC losses in self-field conditions due to decoupling of the filaments and, at the same time, it increases the critical current of the composite . Previous work in the group has shown that a composite TFM made of layers of HTS tape layered with ferromagnetic layers increased the trapped field above the stack as compared to a stack made of only HTS tape . However, the magnetisation was performed using pulsed field magnetisation (PFM) where thermal effects have a significant role; hence, it is not clear if it was the thermal or magnetic properties of the ferromagnetic layers that have led to the improvement in trapped flux. This work aims to use finite element method (FEM) modelling to gauge the possible improvements to trapped field using ferromagnetic materials by simulating “fully saturated” TFM, similar to a condition after field cooling magnetisation (FCM). Several cases are modelled considering bulk FM material outside the stack or FM layered together with SC material with or without considering the anisotropy of the critical current Jc(B, θ).
2 Methods and Techniques
2.1 Modelling Framework and Material Properties
A homogenised model was used, i.e. individual HTS layers were not modelled, instead the superconducting domains carried an engineering critical current density, Je = Ic/A, where A is the total cross-section area of the tape that corresponds to the SuperOx tape measured in .
Two ferromagnetic materials were considered in this work, namely Ni-W alloy, which is used for substrate in HTS tape made by RABiTS process (e.g. in American Superconductor tape) and a CoFe alloy, trademark Vacoflux 50, which has a very high saturation magnetisation close to 2.3 T. Typical applications for Vacoflux 50 include rotating machinery. Magnetic properties for Ni-W can be found in , and data for Vacoflux was found in Comsol materials’ library. The magnetisation curves are shown in Fig. 1c.
2.2 Modelled Cases
In addition, the effect of ferromagnetic material was determined for several conditions: range of temperatures (30–80 K); anisotropic critical current Jc(B, T, θ) vs Jc(B, T, θ = 0°); and different width of tape, standard 12 mm and 46 mm wide (currently widest commercially available). Magnetic flux density and total flux 1 mm above the stack as shown in Fig. 2b were taken as a merit index for comparison between different cases considered.
3 Modelling Results
3.1 Stack with No Modifications
3.2 Stack with External Ferromagnetic Material
The improvements of using external FM material with optimised dimensions are detailed in Fig. 5. The results show that stacks made of wide tape benefit much more from the ferromagnetic material, and the improvement is close to 15% at 30 K. While Fig. 4b shows the magnetic field distribution in and around the stack with and without FeCo present. It is worth noting that changing the n-value in the model with fixed h1, w1 = 92 mm in the range n = 10–30 modified the absolute trapped field (higher n value leading to larger field), but the improvement with respect to case with no FM component at 30 K was maintained at 15–18%.
3.3 Ferromagnetic Substrate and Layered Stack
The results have shown that a substantial enhancement of field above a trapped field magnet is possible by the use of external ferromagnetic material even at flux densities well above the saturation magnetisation of the ferromagnetic material in question. However, internally added ferromagnetic material by layering or otherwise was detrimental to flux density outside the TFM, and the reduction of flux density was worse with ferromagnetic materials with higher saturation magnetisation.
Lastly, it was determined that it is important to consider the anisotropy of critical current density as it changes the flux density profile and the total amount of magnetic flux above the TFM, although it did not change the maximum flux density above the centre of the stack.
Further work is needed to determine the effect of n-value dependence on temperature and magnetic field and time-dependant simulations should shed light on how flux creep is affected by presence of FM. Additional optimisation, especially moving beyond the simple geometry of the FM and tailored for specific Jc(B, T, θ) of the superconductor, could lead to higher trapped fields.
Algirdas Baskys, Anup Patel and Bartek Glowacki acknowledge the support of an EPSRC grant EP/P000738/1, while Vicente Climente-Alarcon is funded by Horizon 2020 grant 723199.
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