Numerical calculation of transient field effects in quenching superconducting magnets

The maximum obtainable magnetic induction of accelerator magnets, relying on normal conducting cables and iron poles, is limited to around 2 T because of ohmic losses and iron saturation. Using superconducting cables, and employing permeable materials merely to reduce the fringe field, this limit can be exceeded and fields of more than 10 T can be obtained. A quench denotes the sudden transition from the superconducting to the normal conducting state. The drastic increase in electrical resistivity causes ohmic heating. The dissipated heat yields a temperature rise in the coil and causes the quench to propagate. The resulting high voltages and excessive temperatures can result in an irreversible damage of the magnet - to the extend of a cable melt-down. The quench behavior of a magnet depends on numerous factors, e.g. the magnet design, the applied magnet protection measures, the external electrical network, electrical and thermal material properties, and induced eddy current losses. The analysis and optimization of the quench behavior is an integral part of the construction of any superconducting magnet. The dissertation is divided in three complementary parts, i.e. the thesis, the detailed treatment and the appendix. In the thesis the quench process in superconducting accelerator magnets is studied. At first, we give an overview over features of accelerator magnets and physical phenomena occurring during a quench. For all relevant effects numerical models are introduced and adapted. The different models are weakly coupled in the quench algorithm and solved by means of an adaptive time-stepping method. This allows to resolve the variation of material properties as well as time constants. The quench model is validated by means of measurement data from magnets of the Large Hadron Collider. In a second step, we show results of protection studies for future accelerator magnets. The thesis ends with a summary of the results and a critical outlook on aspects which could be subjected to further studies. Common definitions and concepts in the design of superconducting magnets, derivations of electromagnetic models, and explanations of typical effects are collected in the detailed treatment. We introduce, e.g., the temperature margin to quench and the MIITs, and define the magnetic energy and inductance in case of materials exhibiting hysteresis and diffusive behavior. The momentarily dissipated hysteresis losses are derived for the critical state model of hard superconductors. Furthermore, we review magnet protection methods and the voltages occurring during a quench. The appendix contains all information required for the reproduction of the presented results. It comprises material properties such as the electrical resistivity or the heat capacity for a temperature range spanning from cryogenic temperatures to some hundred kelvins. The model an d simulation parameters for the magnets used for this work are collected at the end.