Analytical estimation of quench protection limits in insulated, non-insulated, and metal-insulated ReBCO accelerator dipoles and quadrupoles

Future particle accelerators require high-field dipole and quadrupole magnets to guide the particles inside the collider ring. Magnets based on High-Temperature Superconductors (HTS) allow operation with higher magnetic field and higher operation temperature compared with the Low-Temperature Superconductor (LTS) based options. One of the issues presently limiting the HTS technology seems to be their protection in case of an unwanted resistive transition, i.e., a quench. New magnet technologies based on non-insulated or partially insulated (metal-insulated) winding technologies ease the problem compared with traditionally insulated magnets. In these magnets, the current can by-bass the quenched segment and the peak temperature remains lower. However, in high current density and high energy density operation, also the insulation-free options will have limitations, and the quench temperatures should be analyzed. In this contribution we present a method for analytical estimation of the protection limits in insulated, non-insulated and metal-insulated magnets. The equations can be used in early stages of magnet design to assess the feasibility and performance requirements of the eventual protection systems. The work stems from the International Muon Collider Collaboration and the results shown here review the protection limits in the dipoles and quadrupoles considered in its collider ring design. We discuss how parameters such as the coil size, metal insulation thickness and the amount of stabilizer copper in the tape impact the protectability of the magnet. This analysis considers only an adiabatic estimation of the peak temperature. Other potentially critical aspects such as voltages and mechanical stresses must be considered with more detailed models as the magnet designs mature.