Analytical Model of Thermo-electrical Behaviour in Superconducting Resistive Core Cables

High field superconducting Nb$_{3}$Sn accelerators magnets above 14 T, for future High Energy Physics applications, call for improvements in the design of the protection system against resistive transitions. The longitudinal quench propagation velocity (vq) is one of the parameters defining the requirements of the protection. Up to now vq has been always considered as a physical parameter defined by the operating conditions (the bath temperature, cooling conditions, the magnetic field and the over all current density) and the type of superconductor and stabilizer used. It is possible to enhance the quench propagation velocity by segregating a percent of the stabilizer into the core, although keeping the total amount constant and tuning the contact resistance between the superconducting strands and the core. Analytical model and computer simulations are presented to explain the phenomenon. The consequences with respect to minimum quench energy are evidenced and the strategy to optimize the cable designed is discussed.