Influence of 3-D Effects on Field Quality in the Straight Part of Accelerator Magnets for the High-Luminosity Large Hadron Collider

A dedicated D1 beam separation dipole is currently being developed at KEK for the large hadron collider luminosity upgrade (HL-LHC). Four 150-mm aperture, 5.6-T magnetic field, and 6.7-m-long Nb–Ti magnets will replace resistive D1 dipoles. The development includes fabrication and testing of 2.2-m model magnets. The dipole has a single-layer coil and thin spacers between coil and iron, giving a nonnegligible impact of saturation on field quality at nominal field. The magnetic design of the straight section coil cross section is based on two-dimensional (2-D) optimization and a separate optimization concerns the coil ends. However, magnetic measurements of the short model showed a large difference (tens of units) between the sextupole harmonic in the straight part and the 2-D calculation. This difference is correctly modeled only by a 3-D analysis: 3-D calculations show that the magnetic field quality in the straight part is influenced by the coil ends, even for the 6.7-m-long magnets. The effect is even more remarkable in the short model. We investigate similar 3-D effects for other magnets, namely the 11-T dipole for HL-LHC. We also consider the case of the 4.5-T recombination magnets for HL-LHC (D2), where the larger space between coil and iron makes this effect less important, but still visible. We conclude the paper by outlining the different classes of accelerator magnets, where this coupling between 3-D effects and iron saturation can be relevant.