Quench Simulation Studies: Program documentation of SPQR

Quench experiments are being performed on prototypes of the superconducting magnets and busbars to determine the adequate design and protection. Many tests can only be understood correctly with the help of quench simulations that model the thermo-hydraulic and electrodynamic processes during a quench. In some cases simulations are the only method to scale the experimental results of prototype measurements to match the situation of quenching superconducting elements in the LHC. This note introduces the theoretical quench model and the use of the simulation program SPQR (Simulation Program for Quench Research), which has been developed to compute the quench process in superconducting magnets and busbars. The model approximates the heat balance equation with the finite difference method including the temperature dependence of the material parameters. SPQR allows the simulation of longitudinal quench propagation along a superconducting cable, the transverse propagation between adjacent conductors, heat transfer into a helium bath through an insulation layer, forced quenching by heaters, and the impact of induced eddy currents due to a changing magnetic field. The simulation output includes quench data such as the longitudinal and transverse quench propagation velocity, the impact of cooling conditions on the hot spot temperature, the quench heater delays, and the quench back effect. The numerical approach is adequate for a more precise modelling of the complex quench processes with respect to analytical models. After the theoretical description of the model, the numerical realization is presented. It follows the program description and its documentation. Some examples how to use SPQR are given.