Superconductivity and superfluidity are macroscopic quantum-effects that are used in technology. One of the most important applications of superconductivity is the design of strong magnets, which guide particles at very high energies in circular accelerators. In the Large Hadron Collider (LHC), which is being constructed at the European Laboratory for Particle Physics (CERN) close to Geneva, magnets wound with conventional superconductors are cooled with superfluid helium to access even higher magnetic field strengths. The resistive transition from the superconducting to the normal-conducting state (known as a quench) can be characterised by mechanical, electrodynamic and thermodynamic processes. Due to the high amount of stored magnetic energy, a quench can potentially cause damage in superconducting elements by overheating or excessive voltages. A detailed description of the related mechanisms is needed to understand the quench process better and to design a reliable protection system. This requires analytical and more importantly numerical models, which include the heat generation of the superconductor, cooling by helium, the thermodynamic propagation of the normal-conducting zone, as well as the impact of induced eddy currents. In the framework of this thesis, a new numerical algorithm has been developed. The improvements and advancements made in the quench modelling are explained in this thesis. It also includes detailed analyses and simulation studies of the quench processes in LHC superconducting cables and magnets. The LHC protection system that has been optimised by the outcome of this thesis is presented. The results and consequences of the performed analyses and simulations are summarised.
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