Magnetic calculations of a superconducting undulator at the ESRF

2D and 3D models of a superconducting undulator suitable for the ESRF storage ring have been developed. The models are based on the performance of superconducting NbTi wire available from the cabling industry. Iron is used in the poles to enhance the peak field. The 2D model shows that it is possible to obtain a peak field of 1.18 T, corresponding to a K-value of 1.65, for a period length of 15 mm, a magnetic gap of 6.5 mm, and a current density of 1050 A/mm2 in the superconducting coils. 1050 A/mm2 corresponds to 80% of the critical current density in the coils. A 3D model of the central parts of the undulator close to the storage ring shows that it is possible to obtain a negligible first and second field integral at the nominal current density of 1050 A/mm2 and moderate field integrals at lower current densities. A full 3D model including the current leads and the path of the current carrying wires shows that an accurate arrangement of the current leads and path of the current carrying wires is essential but difficult to obtain. A precise design of the current leads and the path for the current carrying wire has not yet been found and this requires further empirical knowledge of the winding technique. The heat load to the cold mass of a 100 period superconducting undulator with a vertical accelerator vacuum aperture of 6.0 mm and a period length of 15 mm length has been estimated. The heat load is in the range 3.4-5.8 W, depending on the filling mode of the ESRF storage ring. The dominating heat load is the heating due to the resistive wall effect. Four local cooling machines, each with a cooling capacity of 1.5 W at about 4 K, would give enough cooling capacity for the foreseen filling modes of the ESRF storage ring.