Minimum energy to start a quench and optimum copper-to-NbTi ration

The optimum copper-to-NbTi (Cu/Nb) ratio in a superconducting cable inside a dipole is estimated by computing the minimum point-deposition energy required to quench the cable. The copper in the narrow gaps between the closely packed NbTi filaments may not conduct heat and electricity well and has been taken care of. An attempt is made to use the quench current density instead of the critical current density which is defined arbitrarily. The numerical solutions of the time-dependent equation are approximated by analytic solutions of the time-dependent equation with the introduction of the concept of the minimum propagating zone (MPZ). For the SSC cable, the three-dimensional analysis produces an optimum Cu/Nb ratio of ~1.71, which agrees with the experimental measurements done at Brookhaven