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A new numerical method for solving the critical state, based on the force–displacement curve of the flux lines, is described. The equation can be expressed in terms of the vector potential and can be solved by commercial finite element programs. It gives the critical state directly as a first approximation but a flux flow resistivity can easily be added. It avoids some of the numerical problems that occur if an E–J curve of the form is used with large values of n. It is particularly advantageous for problems involving trapped flux where a power law leads to decay at a rate dependent on the power assumed and the very low electric fields mean that the E–J curve is probably exponential. The flux flow resistivity can be included and since the relevant power law is 1/n rather than n the solutions are more stable. Multiphysics packages, such as FlexPDE, which allow simultaneous equations to be solved, can find the temperature distribution by adding the heat flow equation.

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A study has been made of the decay of the trapped magnetisation in superconductors when exposed to a crossed field. Numerical results have been compared with the theory of Brandt and Mikitik (4) which solves the problem for a thin strip superconductor. FlexPDE with the A formulation and COMSOL with the H formulation were both used. Simulations of a strip with a cross section aspect ratio of 20 showed good agreement with theory both for the case of a transverse field larger than the transverse penetration field and for one smaller. In the latter case the magnetisation saturates as predicted, however the simulations show a slow decay after many cycles. In the case of stacked YBCO tapes the movement of flux lines is very small and the effects of the reversible motion were investigated. This can decrease the decay initially for very thin decoupled tapes, but cause a steady decay after very large numbers of cycles. Simulations on stacked strips showed that the decay constant increased approximately linearly with the number of strips. When combined with the theory for one tape this can explain the very slow decay observed in previous experiments. Experimental results were qualitatively in agreement with theory and simulations but showed some discrepancies. However there are a number of differences between the experimental situation and theory so good agreement is not expected. IntroductionIn most applications of bulk superconductors using trapped fields the bulk will be exposed to external fields which will change in both angle and magnitude. While changes in in magnitude are easily incorporated in the Bean model, changes in angle lead to much more complex situations, in many cases involving flux cutting and force free configurations. However many experimental measurements have shown that in general trapped fields are always reduced by the application of crossed fields and this effect may limit the application of bulk superconductors in electrical machines. Most of the experiments were at relatively high fields compared with the crossed fields and directed at elucidating the physics, rather than practical applications of bulk superconductors in motors and generators. In this paper we consider geometries in which the induced currents are mostly perpendicular to the fields so that the standard Bean model can be applied. One of the first observations was that of Sychev et. al. (1), who applied an oscillating field to a wire carrying a current and observed a DC voltage. Sakamoto et. al. (2) used a thin film carrying a current in an applied field and measured the decay of the trapped magnetisation when a transverse field was applied, as in this paper. They showed that the flux lines pivoted about two points alternately and 'walked' out of the film, a bit like penguins heading for their breeding grounds in the Antarctic. They proposed an approximate theory which assumed a uniform current density in the film. The DC voltage generated by an AC field was termed the 'dynamic resistance' and the clearest explanation of t...

We measured AC losses in RABiTS nonstriated as well as striated coated conductors provided by the US Air Force Research Laboratory. In addition, samples with different kinds of well defined inter-filament bridging have been measured and their losses compared with those of samples with unbridged filaments and with mono-layer samples. This bridging is designed to aid current sharing between filaments, which is advantageous, but it is necessary to determine if the effect on AC losses is detrimental. It was found that AC losses of striated samples with multiple bridges are higher than those of the samples with no bridges due to significant filament coupling but even so the losses are still substantially lower than those of a monolayer sample.

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