Different kinds of analysis methods on a rectangular combined function bending magnet

Abstract

Magnetic field features of a rectangular combined function bending magnet are different from the sector magnet. A strong edge focusing factor (i.e., thin lens effect) intrinsically exists at the two magnet edges for the rectangular bending magnet. Therefore, in this study, we develop two kinds of Hall probe mapping trajectory with four analysis methods to measure and analyze the bending magnet's field behavior. A sufficient correlation among the four methods is an important feature. Those methods are individually used to derive the pole face tilt and bent, the effective magnetic length and to check the specification establish by the beam dynamics group. As for the two mapping methods, one is called “Radial Mapping” whose mapping trajectories in the longitudinal direction ( s-axis) follow the different arc lengths of radius ϱ± r and the transverse trajectories follow the radial displacement ± r perpendicular to the arc trajectory. The other one is called “Lamination Mapping” whose mapping trajectories in the longitudinal direction follow the constant arc length of circle radius ϱ and the transverse trajectories follow the transverse axis displacement ± x parallel to the lamination direction. This study also discusses the differences between those two mapping methods. Results obtained from the harmonic field distribution along the longitudinal direction (including the fringing field) and the main components of the integral strength are compared. The subsequent error of the four analysis methods is 0.01% for the dipole strength and 0.3% for the quadrupole strength individually. According to the specifications, those analysis errors are acceptable. Meanwhile, the accuracies of different methods for the higher multipole strengths are all within tolerances. The peculiar sextupole field behavior at the two magnet edges from the different mapping methods is owing to the effective magnet pole face that will be discussed.