Auchmann, Bernard Russenschuck, Stephan 2003 2003 An integrated design approach is used at CERN for the design and optimization of superconducting accelerator magnets, with the ROXIE program package as the key tool. The layout of the coil ends has proven in most cases to be the limiting factor for the magnets' quench performance. The objectives for coil end design are therefore to minimize the mechanical stress on the cables, to optimize the integrated multipole content and to limit the peak field enhancement. This paper introduces a new approach based on differential geometry methods that allows for the geometrical and mechanical optimization of cos nq coil ends. Aleksa, Martin Auchmann, Bernard Russenschuck, Stephan Völlinger, C IEEE Trans. Magn. 10.1109/TMAG.2004.825464 864-7 40 2 pt.2 CERN accelerator magnets critical current density critical state model field dependence field errors hadron collider project magnetic field magnetic induction nested orbit corrector magnet numerical field computation persistent currents semianalytical two dimensional model superconducting filament magnetization superconducting magnets superconductivity vector hysteresis model 2004 2004 Magnetic field changes in the coils of superconducting magnets are shielded from the filaments' core by so-called persistent currents which can be modeled by means of the critical state model. This paper presents a semi-analytical 2-dimensional model of the filament magnetization due to persistent currents for changes of the magnitude of the magnetic induction and its direction while taking the field dependence of the critical current density into account. The model is combined with numerical field computation for the calculation of field errors in superconducting magnets. The filament magnetization and the field errors in a nested orbit corrector magnet for the LHC project at CERN have been calculated as an example.