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Many large-scale applications require electromagnetic modelling withextensive numerical computations, such as magnets or 3-dimensional (3D) objectslike transposed conductors or motors and generators. Therefore, it is necessaryto develop computationally time-efficient but still accurate numerical methods.This article develops a general variational formalism for any ${\bf E}({\bfJ})$ relation and applies it to model coated-conductor coils containing up tothousands of turns, taking magnetization currents fully into account. Thevariational principle, valid for any 3D situation, restricts the computationsto the sample volume, reducing the computation time. However, no additionalmagnetic materials interacting with the superconductor are taken directly intoaccount. Regarding the coil modelling, we use a power law $E(J)$ relation withmagnetic field-dependent critical current density, $J_c$, and power lawexponent, $n$. We test the numerical model by comparing the results toanalytical formulas for thin strips and experiments for stacks of pancakecoils, finding a very good agreement. Afterwards, we model a magnet-size coilof 4000 turns (stack of 20 pancake coils of 200 turns each). We found that theAC loss is mainly due to magnetization currents. We also found that for an $n$exponent of 20, the magnetization currents are greatly suppressed after 1 hourrelaxation. In addition, in coated conductor coils magnetization currents havean important impact on the generated magnetic field; which should be taken intoaccount for magnet design. In conclusion, the presented numerical methodfulfills the requirements for electromagnetic design of coated conductorwindings.

superconductor science and technology/superconductor science and technology

Electromagnetic modelling of superconductors with a smooth  current-voltage relation: variational principle and coils from a few turns to  large magnets