An analytical benchmark for the calculation of current distribution in superconducting cables

Abstract

The validation of numerical codes for the calculation of current distribution and AC loss in superconducting cables versus experimental results is essential, but could be affected by approximations in the electromagnetic model or incertitude in the evaluation of the model parameters. A preliminary validation of the codes by means of a comparison with analytical results can therefore be very useful, in order to distinguish among different error sources. We provide here a benchmark analytical solution for current distribution that applies to the case of a cable described using a distributed parameters electrical circuit model. The analytical solution of current distribution is valid for cables made of a generic number of strands, subjected to well defined symmetry and uniformity conditions in the electrical parameters. The closed form solution for the general case is rather complex to implement, and in this paper we give the analytical solutions for different simplified situations. In particular we examine the influence of different boundary conditions, the effect of a localised resistance in the middle of the cable such as in the case of quench and the effects of localized time dependent magnetic fluxes acting on the cable. AbstractThe validation of numerical codes for the calculation of current distribution and AC loss in superconducting cables versus experimental results is essential, but could be affected by approximations in the electromagnetic model or incertitude in the evaluation of the model parameters. A preliminary validation of the codes by means of a comparison with analytical results can therefore be very useful, in order to distinguish among different error sources. We provide here a benchmark analytical solution for current distribution that applies to the case of a cable described using a distributed parameters electrical circuit model. The analytical solution of current distribution is valid for cables made of a generic number of strands, subjected to well defined symmetry and uniformity conditions in the electrical parameters. The closed form solution for the general case is rather complex to implement, and in this paper we give the analytical solutions for different simplified situations. In particular we examine the influence of different boundary conditions, the effect of a localised resistance in the middle of the cable such as in the case of quench and the effects of localized time dependent magnetic fluxes acting on the cable.

Design of DEMO PF Coils Based on Cable-in-Conduit Conductor

“…The geometry is meshed using iso-parametric bricks. Then the magnetic fields are calculated analytically at the desired point [13], [14]. The plasma is modeled as a small coil at the center.…”

Analysis of Current Redistribution in a CICC Under Transient Heat Pulses

“…As discussed at length in [9], the decay of the current induced by a fast voltage pulse in a multistrand cable follows a time evolution that can be well approximated by a series of exponentials. Assuming that the self field change has the same dynamics as the current redistribution, we have obtained the longest decay time constant fitting an exponential function to the Hall plate signals at times sufficiently long after the end of the pulse (0.5 s).…”

“…We have deduced a range of realistic values of the interstrand conductance per unit length g using the analytical result of [9] for the time constant of free current decay in an Nstrand cable:…”

Analysis of losses in superconducting magnets based on the Nb3Sn Rutherford cable configuration for future gantries

“…The THELMA code developed at the University of Bologna, validated for the study of cable in conduit conductors for the ITER project [17,18], is adapted here to the analysis of ac losses in the Nb 3 Sn Rutherford cable configuration. The model of the Rutherford cable is based on a distributed parameter circuit approach, that was proved suitable for the analysis of long range coupling currents both with numerical [19,20] and analytical studies [21][22][23]. The main development of the model adopted in this work with respect to the models presented in [19][20][21][22][23] consists in the adoption of nonhomogenous interstrand contact conductances along the cable length, which allow a proper description of the short range coupling currents and related losses.…”

“…The model of the Rutherford cable is based on a distributed parameter circuit approach, that was proved suitable for the analysis of long range coupling currents both with numerical [19,20] and analytical studies [21][22][23]. The main development of the model adopted in this work with respect to the models presented in [19][20][21][22][23] consists in the adoption of nonhomogenous interstrand contact conductances along the cable length, which allow a proper description of the short range coupling currents and related losses. The computation of coupling losses is validated in simplified cases versus analytical formulae available in the literature.…”