Current diffusion modelled by THEA

THEA is primarily designed to siumulate problems involving the interaction among current distribution, heat diffusion and cooling of a superconducting cable. The interplay of these phenomena can lead to very complex situations, especially because the time scales span over a large interval, often several orders of magnitude. Few experiments exist to validate coimputer codes in this regime. One such experiment has been performed by L. Krempaski and C. Schmidt, and is described in Cryogenics , 39 , pp. 23-33, (1999).

The experiment was performed on a two-strand cable prepared with a 0.3 mm diameter, NbTi/Cu strand. The cable was twisted with a pitch of 10 mm and soldered with Sn(50%)In. In the middle of the cable, and over a length of approximately half a twist pitch (5 mm), a loop with a cross section of approximately 70 mm2 was formed between the strands. The cable was wound into a test coil, with the loop placed in the coil center, normal to the coil axis. The coil was then placed in a background magnet providing an AC vertical field. The AC field caused a variation of the flux linked with the loop in the centre of the sample. This induced currents in opposite directions in the two superconducting strands, closing through the solder along the whole cable length (supercurrents). The supercurrent circulating in the centre of the sample was measured by means of a Hall plate placed in the loop. In this experiment the cable behaved as a bi-filar line with an inductance per unit length of 0.5 mH/m. The loop in the centre of the cable length had an estimated inductance of 0.02 mH. The transverse conductivity per unit length was 58 MS/m. The figure below shows schematically the cable with its central loop. Further details on the experiment, results and interpretation can be found in the reference quoted above.

Results

We show in this figure a first comparison of experimentally measured current and simulation results. The measurements reported were made with a sample length of 4.7 m and under the field sweep reported in the inset. A step-like field variation of 0.26 T, was applied to the sample in a time of approximately 7.5 s. The sample was superconducting throughout the transient, and the supercurrent induced could circulate freely in the sample. The time constant of the supercurrent is such that it is not fully developed during the transient, as can be seen by the clear lack of saturation. The agreement of measurements and simulations is excellent.

In this second figure we report the comparison in a case where the sample length was of 1.66 m and under the field sweep reported in the inset. The field change in this case was continuous, following a triangular waveform with peak amplitude of 0.26 T and ramp time of approximately 125 s. Also in this case the sample was superconducting throughout the transient, and the field sweep was slow enough to reach steady state conditions (see again inset). The agreement of measurements and simulations remains excellent, especially noting that no "geometrical" or "electrical" parameters were adapted from the previous case to fit data.

In the last case presented the supercurrent was induced by a 0.65 T field sweep in 4 s. Right after the end of the sweep a 4 cm long heater covering the center of the sample was switched on for 1.6 s. This caused a quench of the central part of the cable, followed by a recovery as soon as the heater was switched off. The increased longitudinal resistance pushed the supercurrent out of the quenched region. The supercurrent still flowed in the unquenched length of the sample, and, as soon as the central part recovered, diffused back into the center. In this case the agreement between experimental and simulation results is still satisfactory, although for this case the simulation overestimates the peak current by 20 %. Examining in detail the figure we note that the maximum error is found at the end of the field sweep, i.e. before the heater is fired, and that the simulation is in good agreement with the measurement during the first second. The difference between simulation and experiment can be explained if we postulate that during the strong field sweep, and above a certain field, the strands develop a finite longitudinal resistance caused either by onset of saturation in the filaments or by AC loss (i.e. a dynamic resistance). These effects are not included explicitly in the model.